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ОС","\u002Fcsharp\u002Fsystem-programming-windows\u002Fwindows-hooks-services","01.csharp\u002F07.system-programming-windows\u002F20.windows-hooks-services",{"title":376,"path":377,"stem":378},"Системне Програмування C# (Windows) — 07.system-programming-windows","\u002Fcsharp\u002Fsystem-programming-windows\u002Fimplementation_plan","01.csharp\u002F07.system-programming-windows\u002Fimplementation_plan",{"title":380,"icon":132,"path":381,"stem":382,"children":383,"page":59},"Io","\u002Fcsharp\u002Fio","01.csharp\u002F08.io",[384,388,392,396,400],{"title":385,"path":386,"stem":387},"8.1.1. Основи роботи з файловою системою","\u002Fcsharp\u002Fio\u002Ffile-system-basics","01.csharp\u002F08.io\u002F01.file-system-basics",{"title":389,"path":390,"stem":391},"8.1.2. Потоки (Streams) та Серіалізація Даних","\u002Fcsharp\u002Fio\u002Fstreams-serialization","01.csharp\u002F08.io\u002F02.streams-serialization",{"title":393,"path":394,"stem":395},"8.2.1. JSON Serialization з System.Text.Json","\u002Fcsharp\u002Fio\u002Fjson-serialization","01.csharp\u002F08.io\u002F03.json-serialization",{"title":397,"path":398,"stem":399},"8.2.2. XML Serialization та LINQ to XML","\u002Fcsharp\u002Fio\u002Fxml-serialization","01.csharp\u002F08.io\u002F04.xml-serialization",{"title":401,"path":402,"stem":403},"8.2.3. Binary Serialization: MessagePack та Protocol Buffers","\u002Fcsharp\u002Fio\u002Fbinary-serialization","01.csharp\u002F08.io\u002F05.binary-serialization",{"title":405,"icon":132,"path":406,"stem":407,"children":408,"page":59},"Ado Net","\u002Fcsharp\u002Fado-net","01.csharp\u002F09.ado-net",[409,413,417,421,425,429,433,437,441,445,449,453],{"title":410,"path":411,"stem":412},"9.1. Введення в ADO.NET","\u002Fcsharp\u002Fado-net\u002Fintroduction-to-adonet","01.csharp\u002F09.ado-net\u002F01.introduction-to-adonet",{"title":414,"path":415,"stem":416},"9.2. Клас DbConnection — з'єднання з базою даних","\u002Fcsharp\u002Fado-net\u002Fconnection","01.csharp\u002F09.ado-net\u002F02.connection",{"title":418,"path":419,"stem":420},"9.3. Клас DbCommand — виконання SQL-запитів","\u002Fcsharp\u002Fado-net\u002Fcommand-and-queries","01.csharp\u002F09.ado-net\u002F03.command-and-queries",{"title":422,"path":423,"stem":424},"9.4. Клас DbDataReader — ефективне читання даних","\u002Fcsharp\u002Fado-net\u002Fdatareader","01.csharp\u002F09.ado-net\u002F04.datareader",{"title":426,"path":427,"stem":428},"9.5. Параметризовані запити та захист від SQL Injection","\u002Fcsharp\u002Fado-net\u002Fparameters-and-sql-injection","01.csharp\u002F09.ado-net\u002F05.parameters-and-sql-injection",{"title":430,"path":431,"stem":432},"9.6. Транзакції в ADO.NET","\u002Fcsharp\u002Fado-net\u002Ftransactions","01.csharp\u002F09.ado-net\u002F06.transactions",{"title":434,"path":435,"stem":436},"9.7. DbProviderFactory — провайдер-незалежний код","\u002Fcsharp\u002Fado-net\u002Fprovider-factory","01.csharp\u002F09.ado-net\u002F07.provider-factory",{"title":438,"path":439,"stem":440},"9.8. Асинхронний доступ до даних","\u002Fcsharp\u002Fado-net\u002Fasync-data-access","01.csharp\u002F09.ado-net\u002F08.async-data-access",{"title":442,"path":443,"stem":444},"9.9. Від'єднаний режим: DataSet, DataTable, DataRow","\u002Fcsharp\u002Fado-net\u002Fdisconnected-mode-dataset","01.csharp\u002F09.ado-net\u002F09.disconnected-mode-dataset",{"title":446,"path":447,"stem":448},"9.10. DataAdapter — міст між DataSet та базою даних","\u002Fcsharp\u002Fado-net\u002Fdata-adapter","01.csharp\u002F09.ado-net\u002F10.data-adapter",{"title":450,"path":451,"stem":452},"9.11. Data Mapper та Repository: Архітектура доступу до даних","\u002Fcsharp\u002Fado-net\u002Fdata-mapper-repository","01.csharp\u002F09.ado-net\u002F11.data-mapper-repository",{"title":454,"path":455,"stem":456},"9.12. Identity Map, Unit of Work та Specification Pattern","\u002Fcsharp\u002Fado-net\u002Fadvanced-patterns","01.csharp\u002F09.ado-net\u002F12.advanced-patterns",{"title":458,"icon":255,"path":459,"stem":460,"children":461,"page":59},"Ef Core","\u002Fcsharp\u002Fef-core","01.csharp\u002F10.ef-core",[462,466,470,474,478,482,486,490,494,498,502,506,510,514,518,522,526,532,538,542,546,550,554,558,562,566,570,574,578,582,586,590,594,598,602,606,610,614,618,622,626,630,634,638,642,646],{"title":463,"path":464,"stem":465},"Що таке ORM? Від SQL до об'єктів","\u002Fcsharp\u002Fef-core\u002Fwhat-is-orm","01.csharp\u002F10.ef-core\u002F01.what-is-orm",{"title":467,"path":468,"stem":469},"Перший проєкт — від нуля до CRUD","\u002Fcsharp\u002Fef-core\u002Ffirst-project","01.csharp\u002F10.ef-core\u002F02.first-project",{"title":471,"path":472,"stem":473},"DbContext — Серце EF Core","\u002Fcsharp\u002Fef-core\u002Fdbcontext-deep-dive","01.csharp\u002F10.ef-core\u002F03.dbcontext-deep-dive",{"title":475,"path":476,"stem":477},"Провайдери баз даних — Архітектура та Вибір СУБД","\u002Fcsharp\u002Fef-core\u002Fdatabase-providers","01.csharp\u002F10.ef-core\u002F04.database-providers",{"title":479,"path":480,"stem":481},"Конвенції EF Core — Магія без конфігурації","\u002Fcsharp\u002Fef-core\u002Fconventions","01.csharp\u002F10.ef-core\u002F05.conventions",{"title":483,"path":484,"stem":485},"Fluent API та Data Annotations — Явна конфігурація моделі","\u002Fcsharp\u002Fef-core\u002Ffluent-api-vs-annotations","01.csharp\u002F10.ef-core\u002F06.fluent-api-vs-annotations",{"title":487,"path":488,"stem":489},"Зв'язки — One-to-One та One-to-Many","\u002Fcsharp\u002Fef-core\u002Frelationships-basics","01.csharp\u002F10.ef-core\u002F07.relationships-basics",{"title":491,"path":492,"stem":493},"Зв'язки Advanced — Many-to-Many та Складні Сценарії","\u002Fcsharp\u002Fef-core\u002Frelationships-advanced","01.csharp\u002F10.ef-core\u002F08.relationships-advanced",{"title":495,"path":496,"stem":497},"Властивості — Типи, Конвертери, Компаратори (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fproperty-configuration-part1","01.csharp\u002F10.ef-core\u002F09.property-configuration-part1",{"title":499,"path":500,"stem":501},"Властивості — Value Comparers, Generators, Shadow Properties (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fproperty-configuration-part2","01.csharp\u002F10.ef-core\u002F09.property-configuration-part2",{"title":503,"path":504,"stem":505},"Складні типи — Owned Types та Complex Types (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fcomplex-types-owned-part1","01.csharp\u002F10.ef-core\u002F10.complex-types-owned-part1",{"title":507,"path":508,"stem":509},"Складні типи — Complex Types, Keyless Entities, Порівняння (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fcomplex-types-owned-part2","01.csharp\u002F10.ef-core\u002F10.complex-types-owned-part2",{"title":511,"path":512,"stem":513},"JSON Columns — Складні дані у JSON (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fjson-columns-part1","01.csharp\u002F10.ef-core\u002F11.json-columns-part1",{"title":515,"path":516,"stem":517},"JSON Columns — Value Comparers, Індекси, Провайдери (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fjson-columns-part2","01.csharp\u002F10.ef-core\u002F11.json-columns-part2",{"title":519,"path":520,"stem":521},"Успадкування — Абстрактні класи та TPH (Частина 1)","\u002Fcsharp\u002Fef-core\u002Finheritance-part1","01.csharp\u002F10.ef-core\u002F12.inheritance-part1",{"title":523,"path":524,"stem":525},"Успадкування — TPT, TPC та Порівняння Стратегій (Частина 2)","\u002Fcsharp\u002Fef-core\u002Finheritance-part2","01.csharp\u002F10.ef-core\u002F12.inheritance-part2",{"title":527,"path":528,"stem":529,"children":530},"Індекси, Обмеження та Схема (Частина 1)","\u002Fcsharp\u002Fef-core\u002Findexes-constraints-part1","01.csharp\u002F10.ef-core\u002F13.indexes-constraints-part1",[531],{"title":527,"path":528,"stem":529},{"title":533,"path":534,"stem":535,"children":536},"Індекси, Обмеження та Схема (Частина 2)","\u002Fcsharp\u002Fef-core\u002Findexes-constraints-part2","01.csharp\u002F10.ef-core\u002F13.indexes-constraints-part2",[537],{"title":533,"path":534,"stem":535},{"title":539,"path":540,"stem":541},"Seed Data — Початкові Дані (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fseeding-part1","01.csharp\u002F10.ef-core\u002F14.seeding-part1",{"title":543,"path":544,"stem":545},"Seed Data — SQL-скрипти, Bogus та Стратегії (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fseeding-part2","01.csharp\u002F10.ef-core\u002F14.seeding-part2",{"title":547,"path":548,"stem":549},"Global Query Filters — Глобальні Фільтри (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fglobal-query-filters-part1","01.csharp\u002F10.ef-core\u002F15.global-query-filters-part1",{"title":551,"path":552,"stem":553},"Global Query Filters — Підводні камені та Інтеграція (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fglobal-query-filters-part2","01.csharp\u002F10.ef-core\u002F15.global-query-filters-part2",{"title":555,"path":556,"stem":557},"LINQ-запити в EF Core (Частина 1)","\u002Fcsharp\u002Fef-core\u002Flinq-queries-part1","01.csharp\u002F10.ef-core\u002F16.linq-queries-part1",{"title":559,"path":560,"stem":561},"LINQ-запити в EF Core (Частина 2)","\u002Fcsharp\u002Fef-core\u002Flinq-queries-part2","01.csharp\u002F10.ef-core\u002F16.linq-queries-part2",{"title":563,"path":564,"stem":565},"Завантаження Пов'язаних Даних (Частина 1)","\u002Fcsharp\u002Fef-core\u002Floading-related-data-part1","01.csharp\u002F10.ef-core\u002F17.loading-related-data-part1",{"title":567,"path":568,"stem":569},"Завантаження Пов'язаних Даних (Частина 2)","\u002Fcsharp\u002Fef-core\u002Floading-related-data-part2","01.csharp\u002F10.ef-core\u002F17.loading-related-data-part2",{"title":571,"path":572,"stem":573},"Raw SQL, Views та Stored Procedures (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fraw-sql-part1","01.csharp\u002F10.ef-core\u002F18.raw-sql-part1",{"title":575,"path":576,"stem":577},"Raw SQL — Stored Procedures, DbFunction та Bulk Operations (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fraw-sql-part2","01.csharp\u002F10.ef-core\u002F18.raw-sql-part2",{"title":579,"path":580,"stem":581},"Продвинуті Запити — Compiled Queries, Bulk та Оптимізація (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fadvanced-queries-part1","01.csharp\u002F10.ef-core\u002F19.advanced-queries-part1",{"title":583,"path":584,"stem":585},"Продвинуті Запити — Query Tags, Bulk та Interceptors (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fadvanced-queries-part2","01.csharp\u002F10.ef-core\u002F19.advanced-queries-part2",{"title":587,"path":588,"stem":589},"Change Tracker — Відстеження Змін (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fchange-tracking-part1","01.csharp\u002F10.ef-core\u002F20.change-tracking-part1",{"title":591,"path":592,"stem":593},"Change Tracker — Графи Об'єктів та Disconnected (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fchange-tracking-part2","01.csharp\u002F10.ef-core\u002F20.change-tracking-part2",{"title":595,"path":596,"stem":597},"Збереження Даних та Транзакції (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fsaving-data-part1","01.csharp\u002F10.ef-core\u002F21.saving-data-part1",{"title":599,"path":600,"stem":601},"Збереження Даних — Concurrency та Outbox (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fsaving-data-part2","01.csharp\u002F10.ef-core\u002F21.saving-data-part2",{"title":603,"path":604,"stem":605},"Конкурентність та Блокування (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fconcurrency-part1","01.csharp\u002F10.ef-core\u002F22.concurrency-part1",{"title":607,"path":608,"stem":609},"Конкурентність — Дедлоки та Queue Processing (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fconcurrency-part2","01.csharp\u002F10.ef-core\u002F22.concurrency-part2",{"title":611,"path":612,"stem":613},"Міграції в EF Core — Основи (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fmigrations-basics-part1","01.csharp\u002F10.ef-core\u002F23.migrations-basics-part1",{"title":615,"path":616,"stem":617},"Міграції в EF Core — Основи (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fmigrations-basics-part2","01.csharp\u002F10.ef-core\u002F23.migrations-basics-part2",{"title":619,"path":620,"stem":621},"Міграції — Просунуті Сценарії (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fmigrations-advanced-part1","01.csharp\u002F10.ef-core\u002F24.migrations-advanced-part1",{"title":623,"path":624,"stem":625},"Міграції — Просунуті Сценарії (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fmigrations-advanced-part2","01.csharp\u002F10.ef-core\u002F24.migrations-advanced-part2",{"title":627,"path":628,"stem":629},"Управління Схемою та Database-First (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fschema-management-part1","01.csharp\u002F10.ef-core\u002F25.schema-management-part1",{"title":631,"path":632,"stem":633},"Управління Схемою та Database-First (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fschema-management-part2","01.csharp\u002F10.ef-core\u002F25.schema-management-part2",{"title":635,"path":636,"stem":637},"Продуктивність EF Core — Основи (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fperformance-fundamentals-part1","01.csharp\u002F10.ef-core\u002F26.performance-fundamentals-part1",{"title":639,"path":640,"stem":641},"Interceptors в EF Core (Частина 1)","\u002Fcsharp\u002Fef-core\u002Finterceptors-part1","01.csharp\u002F10.ef-core\u002F29.interceptors-part1",{"title":643,"path":644,"stem":645},"Interceptors в EF Core — Connection, Transaction та Materialization (Частина 2)","\u002Fcsharp\u002Fef-core\u002Finterceptors-part2","01.csharp\u002F10.ef-core\u002F29.interceptors-part2",{"title":647,"path":648,"stem":649},"План вивчення Entity Framework Core — Повний курс","\u002Fcsharp\u002Fef-core\u002Fimplementation_plan","01.csharp\u002F10.ef-core\u002Fimplementation_plan",{"title":651,"icon":652,"path":653,"stem":654,"children":655,"page":59},"ASP.NET","i-devicon-dotnetcore","\u002Fcsharp\u002Faspnet","01.csharp\u002F11.aspnet",[656,730,791,869,927,941,967,1057,1111,1182,1212,1289,1346],{"title":657,"icon":658,"path":659,"stem":660,"children":661,"page":59},"Minimal API","i-lucide-network","\u002Fcsharp\u002Faspnet\u002Fminimal-api","01.csharp\u002F11.aspnet\u002F01.minimal-api",[662,666,670,674,678,682,686,690,694,698,702,706,710,714,718,722,726],{"title":663,"path":664,"stem":665},"Вступ до ASP.NET та еволюція фреймворку","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fintroduction","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F01.introduction",{"title":667,"path":668,"stem":669},"Перший додаток на ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Ffirst-application","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F02.first-application",{"title":671,"path":672,"stem":673},"WebApplication, Builder та Dependency Injection","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fwebapplication-builder","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F03.webapplication-builder",{"title":675,"path":676,"stem":677},"Конвеєр запитів та Middleware","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Frequest-pipeline-middleware","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F04.request-pipeline-middleware",{"title":679,"path":680,"stem":681},"Маршрутизація в ASP.NET Core: Основи","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Frouting-basics","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F05.routing-basics",{"title":683,"path":684,"stem":685},"Маршрутизація в ASP.NET Core: Розширені можливості","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Frouting-advanced","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F06.routing-advanced",{"title":687,"path":688,"stem":689},"Статичні файли в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fstatic-files","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F07.static-files",{"title":691,"path":692,"stem":693},"Статичні Активи: MapStaticAssets (ASP.NET Core 9.0)","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fstatic-assets","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F08.static-assets",{"title":695,"path":696,"stem":697},"Конфігурація в ASP.NET Core: Основи","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fconfiguration-fundamentals","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F09.configuration-fundamentals",{"title":699,"path":700,"stem":701},"Конфігурація: Паттерн Options","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fconfiguration-options","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F10.configuration-options",{"title":703,"path":704,"stem":705},"Логування в ASP.NET Core: Основи","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Flogging-basics","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F11.logging-basics",{"title":707,"path":708,"stem":709},"Логування: Serilog та Middleware","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Flogging-advanced","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F12.logging-advanced",{"title":711,"path":712,"stem":713},"Управління станом: HttpContext.Items та Cookies","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fstate-management","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F13.state-management",{"title":715,"path":716,"stem":717},"Стан сесії: Sessions","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fsession-state","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F14.session-state",{"title":719,"path":720,"stem":721},"Структура проєкту: від хаосу до архітектури","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fproject-structure","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F15.project-structure",{"title":723,"path":724,"stem":725},"Scalar у Minimal API: повний проєкт і Fluent OpenAPI","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fscalar-openapi-fluent","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F16.scalar-openapi-fluent",{"title":727,"path":728,"stem":729},"Swagger \u002F Swashbuckle у Minimal API: окремий класичний шлях","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fswagger-swashbuckle","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F17.swagger-swashbuckle",{"title":731,"icon":658,"path":732,"stem":733,"children":734,"page":59},"API","\u002Fcsharp\u002Faspnet\u002Fapi","01.csharp\u002F11.aspnet\u002F02.api",[735,739,743,747,751,755,759,763,767,771,775,779,783,787],{"title":736,"path":737,"stem":738},"Що таке API. Клієнт-серверна архітектура","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fwhat-is-api","01.csharp\u002F11.aspnet\u002F02.api\u002F01.what-is-api",{"title":740,"path":741,"stem":742},"Формати даних: JSON, XML, TOML та бінарні формати","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fdata-formats","01.csharp\u002F11.aspnet\u002F02.api\u002F02.data-formats",{"title":744,"path":745,"stem":746},"Парадигми API та концепція REST","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fapi-paradigms-rest","01.csharp\u002F11.aspnet\u002F02.api\u002F03.api-paradigms-rest",{"title":748,"path":749,"stem":750},"HTTP-методи, статус-коди та заголовки","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fhttp-methods-status-codes","01.csharp\u002F11.aspnet\u002F02.api\u002F04.http-methods-status-codes",{"title":752,"path":753,"stem":754},"Організація HTTP API за принципами REST","\u002Fcsharp\u002Faspnet\u002Fapi\u002Frest-organizing","01.csharp\u002F11.aspnet\u002F02.api\u002F05.rest-organizing",{"title":756,"path":757,"stem":758},"Номенклатура URL та CRUD-операції","\u002Fcsharp\u002Faspnet\u002Fapi\u002Furl-nomenclature-crud","01.csharp\u002F11.aspnet\u002F02.api\u002F06.url-nomenclature-crud",{"title":760,"path":761,"stem":762},"Правила дизайну: іменування та стандарти","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fapi-design-naming","01.csharp\u002F11.aspnet\u002F02.api\u002F07.api-design-naming",{"title":764,"path":765,"stem":766},"Валідація, ліміти та обробка помилок","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fapi-design-validation","01.csharp\u002F11.aspnet\u002F02.api\u002F08.api-design-validation",{"title":768,"path":769,"stem":770},"Обробка помилок у Minimal API","\u002Fcsharp\u002Faspnet\u002Fapi\u002Ferror-handling-http","01.csharp\u002F11.aspnet\u002F02.api\u002F09.error-handling-http",{"title":772,"path":773,"stem":774},"Ідемпотентність та синхронізація стану","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fidempotency-sync","01.csharp\u002F11.aspnet\u002F02.api\u002F10.idempotency-sync",{"title":776,"path":777,"stem":778},"Пагінація та організація списків","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fpagination-lists","01.csharp\u002F11.aspnet\u002F02.api\u002F11.pagination-lists",{"title":780,"path":781,"stem":782},"Безпека API, кешування та інтернаціоналізація","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fsecurity-auth","01.csharp\u002F11.aspnet\u002F02.api\u002F12.security-auth",{"title":784,"path":785,"stem":786},"Процес проєктування API та документування","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fapi-design-process","01.csharp\u002F11.aspnet\u002F02.api\u002F13.api-design-process",{"title":788,"path":789,"stem":790},"OpenAPI: контракт, специфікація та документація API","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fopenapi","01.csharp\u002F11.aspnet\u002F02.api\u002F14.openapi",{"title":792,"icon":793,"path":794,"stem":795,"children":796,"page":59},"Auth","i-lucide-shield-check","\u002Fcsharp\u002Faspnet\u002Fauth","01.csharp\u002F11.aspnet\u002F03.auth",[797,801,805,809,813,817,821,825,829,833,837,841,845,849,853,857,861,865],{"title":798,"path":799,"stem":800},"Основи аутентифікації та авторизації","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fauth-fundamentals","01.csharp\u002F11.aspnet\u002F03.auth\u002F01.auth-fundamentals",{"title":802,"path":803,"stem":804},"JWT-аутентифікація","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fjwt-authentication","01.csharp\u002F11.aspnet\u002F03.auth\u002F02.jwt-authentication",{"title":806,"path":807,"stem":808},"Авторизація: ролі, політики та resource-based доступ","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fauthorization-policies","01.csharp\u002F11.aspnet\u002F03.auth\u002F03.authorization-policies",{"title":810,"path":811,"stem":812},"Cookie-аутентифікація та ASP.NET Core Identity","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fcookie-auth-identity","01.csharp\u002F11.aspnet\u002F03.auth\u002F04.cookie-auth-identity",{"title":814,"path":815,"stem":816},"JWT + Refresh Tokens (HttpOnly Cookie)","\u002Fcsharp\u002Faspnet\u002Fauth\u002F04b.identity-auth-jwt","01.csharp\u002F11.aspnet\u002F03.auth\u002F04b.identity-auth-jwt",{"title":818,"path":819,"stem":820},"Identity: Підтвердження Email та Скидання Пароля","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fidentity-email-confirmation","01.csharp\u002F11.aspnet\u002F03.auth\u002F05.identity-email-confirmation",{"title":822,"path":823,"stem":824},"Identity: Двофакторна Аутентифікація (2FA)","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fidentity-two-factor","01.csharp\u002F11.aspnet\u002F03.auth\u002F06.identity-two-factor",{"title":826,"path":827,"stem":828},"Identity: Внутрішня Архітектура та Кастомізація","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fidentity-internals","01.csharp\u002F11.aspnet\u002F03.auth\u002F07.identity-internals",{"title":830,"path":831,"stem":832},"OAuth 2.0 та зовнішні провайдери","\u002Fcsharp\u002Faspnet\u002Fauth\u002Foauth-external-providers","01.csharp\u002F11.aspnet\u002F03.auth\u002F08.oauth-external-providers",{"title":834,"path":835,"stem":836},"Безпека на практиці: CORS, HTTPS та захист від атак","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fsecurity-hardening","01.csharp\u002F11.aspnet\u002F03.auth\u002F09.security-hardening",{"title":838,"path":839,"stem":840},"Теорія OAuth 2.0: Поняття, Аналогії та Флоу","\u002Fcsharp\u002Faspnet\u002Fauth\u002Foauth-theory","01.csharp\u002F11.aspnet\u002F03.auth\u002F10.oauth-theory",{"title":842,"path":843,"stem":844},"OIDC, OAuth 2.0 та Keycloak в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Foidc-keycloak","01.csharp\u002F11.aspnet\u002F03.auth\u002F10.oidc-keycloak",{"title":846,"path":847,"stem":848},"API Keys аутентифікація в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fapi-keys","01.csharp\u002F11.aspnet\u002F03.auth\u002F11.api-keys",{"title":850,"path":851,"stem":852},"Rate Limiting та Throttling в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Frate-limiting","01.csharp\u002F11.aspnet\u002F03.auth\u002F12.rate-limiting",{"title":854,"path":855,"stem":856},"Refresh Token Rotation в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Frefresh-token-rotation","01.csharp\u002F11.aspnet\u002F03.auth\u002F13.refresh-token-rotation",{"title":858,"path":859,"stem":860},"Certificate Authentication та mTLS в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fcertificate-auth","01.csharp\u002F11.aspnet\u002F03.auth\u002F14.certificate-auth",{"title":862,"path":863,"stem":864},"RBAC, ABAC та ReBAC в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Frbac-abac-rebac","01.csharp\u002F11.aspnet\u002F03.auth\u002F15.rbac-abac-rebac",{"title":866,"path":867,"stem":868},"Multi-tenancy та ізоляція даних в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fmulti-tenancy","01.csharp\u002F11.aspnet\u002F03.auth\u002F16.multi-tenancy",{"title":870,"icon":871,"path":872,"stem":873,"children":874,"page":59},"Нотифікації","i-lucide-bell","\u002Fcsharp\u002Faspnet\u002Fnotifications","01.csharp\u002F11.aspnet\u002F04.notifications",[875,879,883,887,891,895,899,903,907,911,915,919,923],{"title":876,"path":877,"stem":878},"In-App нотифікації через базу даних","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fin-app-database-notifications","01.csharp\u002F11.aspnet\u002F04.notifications\u002F01.in-app-database-notifications",{"title":880,"path":881,"stem":882},"Polling: Регулярний запит оновлень","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fpolling","01.csharp\u002F11.aspnet\u002F04.notifications\u002F02.polling",{"title":884,"path":885,"stem":886},"Server-Sent Events: Однострімовий push від сервера","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fserver-sent-events","01.csharp\u002F11.aspnet\u002F04.notifications\u002F03.server-sent-events",{"title":888,"path":889,"stem":890},"WebSockets: Двостороннє з'єднання в реальному часі","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fwebsockets","01.csharp\u002F11.aspnet\u002F04.notifications\u002F04.websockets",{"title":892,"path":893,"stem":894},"SignalR: Абстракція над транспортами реального часу","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fsignalr","01.csharp\u002F11.aspnet\u002F04.notifications\u002F05.signalr",{"title":896,"path":897,"stem":898},"Background Services: Фонові задачі в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fbackground-services","01.csharp\u002F11.aspnet\u002F04.notifications\u002F06.background-services",{"title":900,"path":901,"stem":902},"Web Push нотифікації","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fweb-push","01.csharp\u002F11.aspnet\u002F04.notifications\u002F07.web-push",{"title":904,"path":905,"stem":906},"Email нотифікації","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Femail-notifications","01.csharp\u002F11.aspnet\u002F04.notifications\u002F08.email-notifications",{"title":908,"path":909,"stem":910},"Порівняння підходів: Як вибрати правильну технологію нотифікацій","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fchoosing-the-right-approach","01.csharp\u002F11.aspnet\u002F04.notifications\u002F09.choosing-the-right-approach",{"title":912,"path":913,"stem":914},"Hangfire: Надійне планування фонових задач","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fhangfire","01.csharp\u002F11.aspnet\u002F04.notifications\u002F10.hangfire",{"title":916,"path":917,"stem":918},"Практика: Конвертація зображень у WebP через Hangfire","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fhangfire-image-webp","01.csharp\u002F11.aspnet\u002F04.notifications\u002F11.hangfire-image-webp",{"title":920,"path":921,"stem":922},"Практика: Підготовка відео до HLS-стрімінгу через Hangfire","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fhangfire-video-hls","01.csharp\u002F11.aspnet\u002F04.notifications\u002F12.hangfire-video-hls",{"title":924,"path":925,"stem":926},"Telegram-нотифікації: від одного повідомлення до масових розсилок і мульти-канального підходу","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Ftelegram-notifications","01.csharp\u002F11.aspnet\u002F04.notifications\u002F13.telegram-notifications",{"title":928,"icon":929,"path":930,"stem":931,"children":932,"page":59},"Інтернаціоналізація","i-lucide-languages","\u002Fcsharp\u002Faspnet\u002Fi18n","01.csharp\u002F11.aspnet\u002F05.i18n",[933,937],{"title":934,"path":935,"stem":936},"Інтернаціоналізація (i18n) у Minimal API: від A до Я","\u002Fcsharp\u002Faspnet\u002Fi18n\u002Finternationalization","01.csharp\u002F11.aspnet\u002F05.i18n\u002F01.internationalization",{"title":938,"path":939,"stem":940},"Humanizer: людиномовні рядки у .NET","\u002Fcsharp\u002Faspnet\u002Fi18n\u002Fhumanizer","01.csharp\u002F11.aspnet\u002F05.i18n\u002F02.humanizer",{"title":942,"icon":943,"path":944,"stem":945,"children":946,"page":59},"Кешування","i-lucide-layers","\u002Fcsharp\u002Faspnet\u002Fcaching","01.csharp\u002F11.aspnet\u002F06.caching",[947,951,955,959,963],{"title":948,"path":949,"stem":950},"Огляд кешування: чотири рівні і коли що обирати","\u002Fcsharp\u002Faspnet\u002Fcaching\u002Fcaching","01.csharp\u002F11.aspnet\u002F06.caching\u002F01.caching",{"title":952,"path":953,"stem":954},"IMemoryCache: кеш в оперативній пам'яті","\u002Fcsharp\u002Faspnet\u002Fcaching\u002Fmemory-cache","01.csharp\u002F11.aspnet\u002F06.caching\u002F02.memory-cache",{"title":956,"path":957,"stem":958},"IDistributedCache і Redis: розподілений кеш","\u002Fcsharp\u002Faspnet\u002Fcaching\u002Fdistributed-cache","01.csharp\u002F11.aspnet\u002F06.caching\u002F03.distributed-cache",{"title":960,"path":961,"stem":962},"Response Cache: HTTP-кешування через Cache-Control","\u002Fcsharp\u002Faspnet\u002Fcaching\u002Fresponse-cache","01.csharp\u002F11.aspnet\u002F06.caching\u002F04.response-cache",{"title":964,"path":965,"stem":966},"Output Cache: серверний кеш HTTP-відповідей (.NET 7+)","\u002Fcsharp\u002Faspnet\u002Fcaching\u002Foutput-cache","01.csharp\u002F11.aspnet\u002F06.caching\u002F05.output-cache",{"title":968,"icon":969,"path":970,"stem":971,"children":972,"page":59},"Тестування","i-lucide-test-tube","\u002Fcsharp\u002Faspnet\u002Ftesting","01.csharp\u002F11.aspnet\u002F07.testing",[973,977,981,985,989,993,997,1001,1005,1009,1013,1017,1021,1025,1029,1033,1037,1041,1045,1049,1053],{"title":974,"path":975,"stem":976},"Що таке тестування? Від інтуїції до науки","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fwhat-is-testing","01.csharp\u002F11.aspnet\u002F07.testing\u002F01.what-is-testing",{"title":978,"path":979,"stem":980},"Піраміда тестування — Стратегія, а не Догма","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Ftesting-pyramid","01.csharp\u002F11.aspnet\u002F07.testing\u002F02.testing-pyramid",{"title":982,"path":983,"stem":984},"Дві Школи Тестування — Лондон проти Детройту","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Ftesting-schools","01.csharp\u002F11.aspnet\u002F07.testing\u002F03.testing-schools",{"title":986,"path":987,"stem":988},"TDD та BDD — Тести як Дизайн-інструмент","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Ftdd-and-bdd","01.csharp\u002F11.aspnet\u002F07.testing\u002F04.tdd-and-bdd",{"title":990,"path":991,"stem":992},"Що саме тестувати — Техніки аналізу та Циклomatична складність","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fwhat-to-test","01.csharp\u002F11.aspnet\u002F07.testing\u002F05.what-to-test",{"title":994,"path":995,"stem":996},"Тестові Фреймворки — Навіщо вони і що всередині","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Ftest-frameworks","01.csharp\u002F11.aspnet\u002F07.testing\u002F06.test-frameworks",{"title":998,"path":999,"stem":1000},"xUnit — Факти, Теорії та Lifecycle тестів","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fxunit-basics","01.csharp\u002F11.aspnet\u002F07.testing\u002F07.xunit-basics",{"title":1002,"path":1003,"stem":1004},"xUnit Advanced — Fixtures, Кастомізація та Розширення","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fxunit-advanced","01.csharp\u002F11.aspnet\u002F07.testing\u002F08.xunit-advanced",{"title":1006,"path":1007,"stem":1008},"Moq — Глибоке занурення в мокування","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fmocking-with-moq","01.csharp\u002F11.aspnet\u002F07.testing\u002F09.mocking-with-moq",{"title":1010,"path":1011,"stem":1012},"Тестування Баз Даних — EF Core, SQLite та Testcontainers","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fdatabase-testing","01.csharp\u002F11.aspnet\u002F07.testing\u002F10.database-testing",{"title":1014,"path":1015,"stem":1016},"Integration Testing — Частина 1 [Теорія та WebApplicationFactory]","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fintegration-testing","01.csharp\u002F11.aspnet\u002F07.testing\u002F11.integration-testing",{"title":1018,"path":1019,"stem":1020},"Інтеграційне тестування — Практика","\u002Fcsharp\u002Faspnet\u002Ftesting\u002F11a.integration-testing-practice","01.csharp\u002F11.aspnet\u002F07.testing\u002F11a.integration-testing-practice",{"title":1022,"path":1023,"stem":1024},"Integration Testing — Частина 2 [Просунуті Сценарії та Testcontainers]","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fintegration-testing-advanced","01.csharp\u002F11.aspnet\u002F07.testing\u002F12.integration-testing-advanced",{"title":1026,"path":1027,"stem":1028},"Професійний Postman: Колекції, Змінні та GitHub Інтеграція","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fpostman-professional","01.csharp\u002F11.aspnet\u002F07.testing\u002F13.postman-professional",{"title":1030,"path":1031,"stem":1032},"HttpClient у Тестах Частина 1: Архітектура та MockHttpMessageHandler","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fhttpclient-testing","01.csharp\u002F11.aspnet\u002F07.testing\u002F14.httpclient-testing",{"title":1034,"path":1035,"stem":1036},"HttpClient у Тестах Частина 2: WireMock.Net та Resilience","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fwiremock-net","01.csharp\u002F11.aspnet\u002F07.testing\u002F15.wiremock-net",{"title":1038,"path":1039,"stem":1040},"Патерни та Анти-патерни Тестування: Test Smells","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Ftesting-patterns","01.csharp\u002F11.aspnet\u002F07.testing\u002F16.testing-patterns",{"title":1042,"path":1043,"stem":1044},"Просунуті інструменти: Time, Snapshots та Властивості","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fadvanced-testing-tools","01.csharp\u002F11.aspnet\u002F07.testing\u002F17.advanced-testing-tools",{"title":1046,"path":1047,"stem":1048},"Тестування Архітектури з NetArchTest","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Farchitecture-testing","01.csharp\u002F11.aspnet\u002F07.testing\u002F18.architecture-testing",{"title":1050,"path":1051,"stem":1052},"Тестування Продуктивності: BenchmarkDotNet, NBomber та k6","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fperformance-testing","01.csharp\u002F11.aspnet\u002F07.testing\u002F19.performance-testing",{"title":1054,"path":1055,"stem":1056},"Залишок плану для курсу \"Тестування ASP.NET Minimal API\"","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fremaining_plan","01.csharp\u002F11.aspnet\u002F07.testing\u002Fremaining_plan",{"title":1058,"icon":1059,"path":1060,"stem":1061,"children":1062,"page":59},"Платежі","i-lucide-credit-card","\u002Fcsharp\u002Faspnet\u002Fpayments","01.csharp\u002F11.aspnet\u002F08.payments",[1063,1067,1071,1075,1079,1083,1087,1091,1095,1099,1103,1107],{"title":1064,"path":1065,"stem":1066},"Основи платіжної інфраструктури","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fpayment-fundamentals","01.csharp\u002F11.aspnet\u002F08.payments\u002F01.payment-fundamentals",{"title":1068,"path":1069,"stem":1070},"Методи оплати в Україні","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fpayment-methods-ukraine","01.csharp\u002F11.aspnet\u002F08.payments\u002F02.payment-methods-ukraine",{"title":1072,"path":1073,"stem":1074},"PCI DSS та безпека платежів","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fpci-dss-security","01.csharp\u002F11.aspnet\u002F08.payments\u002F03.pci-dss-security",{"title":1076,"path":1077,"stem":1078},"Архітектура платіжної підсистеми","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fpayment-architecture","01.csharp\u002F11.aspnet\u002F08.payments\u002F04.payment-architecture",{"title":1080,"path":1081,"stem":1082},"Інтеграція LiqPay (ПриватБанк)","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fliqpay-integration","01.csharp\u002F11.aspnet\u002F08.payments\u002F05.liqpay-integration",{"title":1084,"path":1085,"stem":1086},"Інтеграція Monobank Acquiring API","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fmonobank-acquiring","01.csharp\u002F11.aspnet\u002F08.payments\u002F06.monobank-acquiring",{"title":1088,"path":1089,"stem":1090},"Інтеграція Stripe","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fstripe-integration","01.csharp\u002F11.aspnet\u002F08.payments\u002F07.stripe-integration",{"title":1092,"path":1093,"stem":1094},"Webhooks — глибоке занурення","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fwebhooks-deep-dive","01.csharp\u002F11.aspnet\u002F08.payments\u002F08.webhooks-deep-dive",{"title":1096,"path":1097,"stem":1098},"Підписки та рекурентні платежі","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fsubscriptions-recurring","01.csharp\u002F11.aspnet\u002F08.payments\u002F09.subscriptions-recurring",{"title":1100,"path":1101,"stem":1102},"Повернення коштів та диспути","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Frefunds-disputes","01.csharp\u002F11.aspnet\u002F08.payments\u002F10.refunds-disputes",{"title":1104,"path":1105,"stem":1106},"Тестування платіжних інтеграцій","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Ftesting-payments","01.csharp\u002F11.aspnet\u002F08.payments\u002F11.testing-payments",{"title":1108,"path":1109,"stem":1110},"Чекліст виходу в Production","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fproduction-checklist","01.csharp\u002F11.aspnet\u002F08.payments\u002F12.production-checklist",{"title":1112,"icon":1113,"items":1114,"path":1127,"stem":1128,"children":1129,"page":59},"Популярні бібліотеки","lucide:box",[1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126],"01.fluent-validation","02.mapster","03.erroror-result-pattern","04.serilog","05.mediatr","06.polly","07.health-checks","08.feature-management","09.fluent-email","10.quest-pdf","11.bogus","12.humanizer-guard","\u002Fcsharp\u002Faspnet\u002Flibraries","01.csharp\u002F11.aspnet\u002F09.libraries",[1130,1134,1138,1142,1146,1150,1154,1158,1162,1166,1170,1174,1178],{"title":1131,"path":1132,"stem":1133},"Валідація з FluentValidation в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Ffluent-validation","01.csharp\u002F11.aspnet\u002F09.libraries\u002F01.fluent-validation",{"title":1135,"path":1136,"stem":1137},"Маппінг об","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fmapster","01.csharp\u002F11.aspnet\u002F09.libraries\u002F02.mapster",{"title":1139,"path":1140,"stem":1141},"Обробка помилок з ErrorOr та Result Pattern в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Ferroror-result-pattern","01.csharp\u002F11.aspnet\u002F09.libraries\u002F03.erroror-result-pattern",{"title":1143,"path":1144,"stem":1145},"Структуроване логування з Serilog в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fserilog","01.csharp\u002F11.aspnet\u002F09.libraries\u002F04.serilog",{"title":1147,"path":1148,"stem":1149},"CQRS та Mediator з MediatR в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fmediatr","01.csharp\u002F11.aspnet\u002F09.libraries\u002F05.mediatr",{"title":1151,"path":1152,"stem":1153},"Відмовостійкість з Polly в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fpolly","01.csharp\u002F11.aspnet\u002F09.libraries\u002F06.polly",{"title":1155,"path":1156,"stem":1157},"Health Checks в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fhealth-checks","01.csharp\u002F11.aspnet\u002F09.libraries\u002F07.health-checks",{"title":1159,"path":1160,"stem":1161},"Feature Management та Feature Flags в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Ffeature-management","01.csharp\u002F11.aspnet\u002F09.libraries\u002F08.feature-management",{"title":1163,"path":1164,"stem":1165},"Відправка Email з FluentEmail в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Ffluent-email","01.csharp\u002F11.aspnet\u002F09.libraries\u002F09.fluent-email",{"title":1167,"path":1168,"stem":1169},"Генерація PDF з QuestPDF в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fquest-pdf","01.csharp\u002F11.aspnet\u002F09.libraries\u002F10.quest-pdf",{"title":1171,"path":1172,"stem":1173},"Генерація тестових даних з Bogus в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fbogus","01.csharp\u002F11.aspnet\u002F09.libraries\u002F11.bogus",{"title":1175,"path":1176,"stem":1177},"Humanizer та Guard Clauses в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fhumanizer-guard","01.csharp\u002F11.aspnet\u002F09.libraries\u002F12.humanizer-guard",{"title":1179,"path":1180,"stem":1181},"План модуля 10.libraries — Популярні бібліотеки ASP.NET","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fplan","01.csharp\u002F11.aspnet\u002F09.libraries\u002Fplan",{"title":1183,"icon":1184,"path":1185,"stem":1186,"children":1187,"page":59},"Razor Pages","i-lucide-layout-template","\u002Fcsharp\u002Faspnet\u002Frazor-pages","01.csharp\u002F11.aspnet\u002F10.razor-pages",[1188,1192,1196,1200,1204,1208],{"title":1189,"path":1190,"stem":1191},"Від Minimal API до Razor Pages: концептуальний перехід","\u002Fcsharp\u002Faspnet\u002Frazor-pages\u002Ffrom-minimal-api","01.csharp\u002F11.aspnet\u002F10.razor-pages\u002F01.from-minimal-api",{"title":1193,"path":1194,"stem":1195},"PageModel: логіка сторінки Razor Pages","\u002Fcsharp\u002Faspnet\u002Frazor-pages\u002Fpage-model","01.csharp\u002F11.aspnet\u002F10.razor-pages\u002F02.page-model",{"title":1197,"path":1198,"stem":1199},"Razor синтаксис: шаблонізатор у .cshtml","\u002Fcsharp\u002Faspnet\u002Frazor-pages\u002Frazor-syntax","01.csharp\u002F11.aspnet\u002F10.razor-pages\u002F03.razor-syntax",{"title":1201,"path":1202,"stem":1203},"Tag Helpers: типізований HTML","\u002Fcsharp\u002Faspnet\u002Frazor-pages\u002Ftag-helpers","01.csharp\u002F11.aspnet\u002F10.razor-pages\u002F04.tag-helpers",{"title":1205,"path":1206,"stem":1207},"Форми і валідація: повний цикл обробки даних","\u002Fcsharp\u002Faspnet\u002Frazor-pages\u002Fforms-validation","01.csharp\u002F11.aspnet\u002F10.razor-pages\u002F05.forms-validation",{"title":1209,"path":1210,"stem":1211},"Практичний проєкт: TaskManager на Razor Pages","\u002Fcsharp\u002Faspnet\u002Frazor-pages\u002Fproject-task-manager","01.csharp\u002F11.aspnet\u002F10.razor-pages\u002F06.project-task-manager",{"title":1213,"path":1214,"stem":1215,"children":1216,"page":59},"ASP.NET Core MVC","\u002Fcsharp\u002Faspnet\u002Fmvc","01.csharp\u002F11.aspnet\u002F11.mvc",[1217,1221,1225,1229,1233,1237,1241,1245,1249,1253,1257,1261,1265,1269,1273,1277,1281,1285],{"title":1218,"path":1219,"stem":1220},"Патерн MVC: архітектура, що змінила веб","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fmvc-pattern","01.csharp\u002F11.aspnet\u002F11.mvc\u002F01.mvc-pattern",{"title":1222,"path":1223,"stem":1224},"Від Razor Pages до MVC: концептуальний перехід","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Ffrom-razor-pages","01.csharp\u002F11.aspnet\u002F11.mvc\u002F02.from-razor-pages",{"title":1226,"path":1227,"stem":1228},"Controllers та Actions: серце MVC","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fcontrollers-actions","01.csharp\u002F11.aspnet\u002F11.mvc\u002F03.controllers-actions",{"title":1230,"path":1231,"stem":1232},"Маршрутизація в MVC: Convention vs Attribute Routing","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Frouting-mvc","01.csharp\u002F11.aspnet\u002F11.mvc\u002F04.routing-mvc",{"title":1234,"path":1235,"stem":1236},"Model Binding: від HTTP до C#","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fmodel-binding","01.csharp\u002F11.aspnet\u002F11.mvc\u002F05.model-binding",{"title":1238,"path":1239,"stem":1240},"Views, ViewData, ViewBag, TempData і ViewModel","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fviews-viewdata-tempdata","01.csharp\u002F11.aspnet\u002F11.mvc\u002F06.views-viewdata-tempdata",{"title":1242,"path":1243,"stem":1244},"Filters: аспектно-орієнтоване програмування в MVC","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Ffilters","01.csharp\u002F11.aspnet\u002F11.mvc\u002F07.filters",{"title":1246,"path":1247,"stem":1248},"Areas: структурування великих застосунків","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fareas","01.csharp\u002F11.aspnet\u002F11.mvc\u002F08.areas",{"title":1250,"path":1251,"stem":1252},"View Components: повторювані незалежні блоки UI","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fview-components","01.csharp\u002F11.aspnet\u002F11.mvc\u002F09.view-components",{"title":1254,"path":1255,"stem":1256},"Display та Editor Templates","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fdisplay-editor-templates","01.csharp\u002F11.aspnet\u002F11.mvc\u002F10.display-editor-templates",{"title":1258,"path":1259,"stem":1260},"Валідація: IValidatableObject та FluentValidation","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fvalidation-advanced","01.csharp\u002F11.aspnet\u002F11.mvc\u002F11.validation-advanced",{"title":1262,"path":1263,"stem":1264},"HTMX: інтерактивність через HTML-атрибути","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fhtmx","01.csharp\u002F11.aspnet\u002F11.mvc\u002F12.htmx",{"title":1266,"path":1267,"stem":1268},"HTMX у ASP.NET Core MVC: серверна інтеграція","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fajax-htmx-mvc","01.csharp\u002F11.aspnet\u002F11.mvc\u002F13.ajax-htmx-mvc",{"title":1270,"path":1271,"stem":1272},"Практичний проєкт: Каталог товарів з HTMX","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fhtmx-project","01.csharp\u002F11.aspnet\u002F11.mvc\u002F14.htmx-project",{"title":1274,"path":1275,"stem":1276},"Завантаження та обробка файлів","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Ffile-upload","01.csharp\u002F11.aspnet\u002F11.mvc\u002F15.file-upload",{"title":1278,"path":1279,"stem":1280},"Глобалізація та Локалізація MVC","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fglobalization-localization","01.csharp\u002F11.aspnet\u002F11.mvc\u002F16.globalization-localization",{"title":1282,"path":1283,"stem":1284},"Підсумковий проєкт: Блог-платформа","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fmvc-project","01.csharp\u002F11.aspnet\u002F11.mvc\u002F17.mvc-project",{"title":1286,"path":1287,"stem":1288},"План курсу: ASP.NET Core MVC","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fplan","01.csharp\u002F11.aspnet\u002F11.mvc\u002Fplan",{"title":1290,"path":1291,"stem":1292,"children":1293,"page":59},"Web Api","\u002Fcsharp\u002Faspnet\u002Fweb-api","01.csharp\u002F11.aspnet\u002F12.web-api",[1294,1298,1302,1306,1310,1314,1318,1322,1326,1330,1334,1338,1342],{"title":1295,"path":1296,"stem":1297},"Від Minimal API до Controller-based API","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Ffrom-minimal-api-to-controllers","01.csharp\u002F11.aspnet\u002F12.web-api\u002F01.from-minimal-api-to-controllers",{"title":1299,"path":1300,"stem":1301},"ControllerBase, ActionResult\u003CT> та Response Types","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fcontroller-base-actionresult","01.csharp\u002F11.aspnet\u002F12.web-api\u002F02.controller-base-actionresult",{"title":1303,"path":1304,"stem":1305},"Content Negotiation - JSON, XML та власні форматери","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fcontent-negotiation","01.csharp\u002F11.aspnet\u002F12.web-api\u002F03.content-negotiation",{"title":1307,"path":1308,"stem":1309},"Версіонування API","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fapi-versioning","01.csharp\u002F11.aspnet\u002F12.web-api\u002F04.api-versioning",{"title":1311,"path":1312,"stem":1313},"ProblemDetails та структурована обробка помилок","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fproblemdetails-error-handling","01.csharp\u002F11.aspnet\u002F12.web-api\u002F05.problemdetails-error-handling",{"title":1315,"path":1316,"stem":1317},"Фільтри у Web API контексті","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Ffilters-for-api","01.csharp\u002F11.aspnet\u002F12.web-api\u002F06.filters-for-api",{"title":1319,"path":1320,"stem":1321},"Пагінація, фільтрація та сортування","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fpagination-filtering-sorting","01.csharp\u002F11.aspnet\u002F12.web-api\u002F07.pagination-filtering-sorting",{"title":1323,"path":1324,"stem":1325},"HATEOAS та Resource Expansion","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fhateoas-resource-expansion","01.csharp\u002F11.aspnet\u002F12.web-api\u002F08.hateoas-resource-expansion",{"title":1327,"path":1328,"stem":1329},"Гібридна архітектура - Minimal API + Controllers","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fminimal-api-vs-controllers-hybrid","01.csharp\u002F11.aspnet\u002F12.web-api\u002F09.minimal-api-vs-controllers-hybrid",{"title":1331,"path":1332,"stem":1333},"Документація API - Swashbuckle, NSwag та генерація клієнтів","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fapi-documentation-generation","01.csharp\u002F11.aspnet\u002F12.web-api\u002F10.api-documentation-generation",{"title":1335,"path":1336,"stem":1337},"Health Checks та моніторинг API","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fhealth-checks-monitoring","01.csharp\u002F11.aspnet\u002F12.web-api\u002F11.health-checks-monitoring",{"title":1339,"path":1340,"stem":1341},"Підсумковий проєкт - Production-Ready REST API","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fweb-api-project","01.csharp\u002F11.aspnet\u002F12.web-api\u002F12.web-api-project",{"title":1343,"path":1344,"stem":1345},"План курсу: ASP.NET Core Web API (Controllers)","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fplan","01.csharp\u002F11.aspnet\u002F12.web-api\u002Fplan",{"title":1347,"icon":1348,"path":1349,"stem":1350,"children":1351,"page":59},"Моніторинг","i-lucide-activity","\u002Fcsharp\u002Faspnet\u002Fmonitoring","01.csharp\u002F11.aspnet\u002F13.monitoring",[1352,1356,1360],{"title":1353,"path":1354,"stem":1355},"Спостережуваність: від console.log до production-систем","\u002Fcsharp\u002Faspnet\u002Fmonitoring\u002Fobservability-intro","01.csharp\u002F11.aspnet\u002F13.monitoring\u002F01.observability-intro",{"title":1357,"path":1358,"stem":1359},"Health Checks: перший рівень observability","\u002Fcsharp\u002Faspnet\u002Fmonitoring\u002Fhealth-checks","01.csharp\u002F11.aspnet\u002F13.monitoring\u002F02.health-checks",{"title":1361,"path":1362,"stem":1363},"Вбудовані метрики .NET 10 та System.Diagnostics.Metrics","\u002Fcsharp\u002Faspnet\u002Fmonitoring\u002Fdotnet-metrics","01.csharp\u002F11.aspnet\u002F13.monitoring\u002F03.dotnet-metrics",{"title":1365,"icon":1366,"path":1367,"stem":1368,"children":1369,"page":59},"Desktop UI","i-lucide-app-window","\u002Fcsharp\u002Fdesktop-ui","01.csharp\u002F12.desktop-ui",[1370,1374,1378,1382,1386,1390,1394,1398,1402,1406,1410,1414,1418,1422,1426,1430,1434,1438,1442,1446,1450,1454,1458,1462,1466,1470,1474,1478,1482,1486,1490,1494,1498,1502,1506,1510,1514,1518,1522,1526,1530,1534,1538,1542,1546,1550,1554,1558,1562,1566,1570,1574,1578,1582,1586,1590,1594,1598,1602,1606,1610,1614,1618,1622,1626,1630,1634,1638,1642,1646,1650],{"title":1371,"path":1372,"stem":1373},"Що таке десктопна розробка?","\u002Fcsharp\u002Fdesktop-ui\u002Fwhat-is-desktop-dev","01.csharp\u002F12.desktop-ui\u002F01.what-is-desktop-dev",{"title":1375,"path":1376,"stem":1377},"Архітектура WPF — як влаштований графічний інтерфейс","\u002Fcsharp\u002Fdesktop-ui\u002Fwpf-architecture","01.csharp\u002F12.desktop-ui\u002F02.wpf-architecture",{"title":1379,"path":1380,"stem":1381},"Перший WPF-проєкт — від нуля до вікна","\u002Fcsharp\u002Fdesktop-ui\u002Ffirst-wpf-app","01.csharp\u002F12.desktop-ui\u002F03.first-wpf-app",{"title":1383,"path":1384,"stem":1385},"Перший Avalonia-проєкт: WPF для всіх платформ","\u002Fcsharp\u002Fdesktop-ui\u002F03a.first-avalonia-app","01.csharp\u002F12.desktop-ui\u002F03a.first-avalonia-app",{"title":1387,"path":1388,"stem":1389},"XAML: декларативний інтерфейс","\u002Fcsharp\u002Fdesktop-ui\u002Fxaml-basics","01.csharp\u002F12.desktop-ui\u002F04.xaml-basics",{"title":1391,"path":1392,"stem":1393},"Fluent UI у WPF — сучасний дизайн Windows 11","\u002Fcsharp\u002Fdesktop-ui\u002F04a.wpf-fluent-ui","01.csharp\u002F12.desktop-ui\u002F04a.wpf-fluent-ui",{"title":1395,"path":1396,"stem":1397},"WPF UI — сучасна бібліотека Fluent контролів","\u002Fcsharp\u002Fdesktop-ui\u002F04b.wpf-ui-library","01.csharp\u002F12.desktop-ui\u002F04b.wpf-ui-library",{"title":1399,"path":1400,"stem":1401},"HandyControl — велика бібліотека UI контролів для WPF","\u002Fcsharp\u002Fdesktop-ui\u002F04c.handycontrol-library","01.csharp\u002F12.desktop-ui\u002F04c.handycontrol-library",{"title":1403,"path":1404,"stem":1405},"Простори імен та ресурси XAML","\u002Fcsharp\u002Fdesktop-ui\u002Fxaml-namespaces-resources","01.csharp\u002F12.desktop-ui\u002F05.xaml-namespaces-resources",{"title":1407,"path":1408,"stem":1409},"XAML в Avalonia: ключові відмінності від WPF","\u002Fcsharp\u002Fdesktop-ui\u002F05a.avalonia-xaml-differences","01.csharp\u002F12.desktop-ui\u002F05a.avalonia-xaml-differences",{"title":1411,"path":1412,"stem":1413},"Розширення розмітки XAML (Markup Extensions)","\u002Fcsharp\u002Fdesktop-ui\u002Fxaml-markup-extensions","01.csharp\u002F12.desktop-ui\u002F06.xaml-markup-extensions",{"title":1415,"path":1416,"stem":1417},"Панелі Layout: StackPanel, WrapPanel, DockPanel","\u002Fcsharp\u002Fdesktop-ui\u002Flayout-panels-part1","01.csharp\u002F12.desktop-ui\u002F07.layout-panels-part1",{"title":1419,"path":1420,"stem":1421},"Grid, Canvas, UniformGrid","\u002Fcsharp\u002Fdesktop-ui\u002Flayout-panels-part2","01.csharp\u002F12.desktop-ui\u002F07.layout-panels-part2",{"title":1423,"path":1424,"stem":1425},"Просунуті техніки Layout","\u002Fcsharp\u002Fdesktop-ui\u002Flayout-advanced","01.csharp\u002F12.desktop-ui\u002F08.layout-advanced",{"title":1427,"path":1428,"stem":1429},"Адаптивний Layout та найкращі практики","\u002Fcsharp\u002Fdesktop-ui\u002Flayout-responsive","01.csharp\u002F12.desktop-ui\u002F09.layout-responsive",{"title":1431,"path":1432,"stem":1433},"Layout в Avalonia: відмінності та нові можливості","\u002Fcsharp\u002Fdesktop-ui\u002F09a.layout-avalonia","01.csharp\u002F12.desktop-ui\u002F09a.layout-avalonia",{"title":1435,"path":1436,"stem":1437},"Button, Image, ProgressBar та інші базові контроли","\u002Fcsharp\u002Fdesktop-ui\u002Fbasic-controls","01.csharp\u002F12.desktop-ui\u002F10.basic-controls",{"title":1439,"path":1440,"stem":1441},"Контроли в Avalonia: відмінності від WPF","\u002Fcsharp\u002Fdesktop-ui\u002F10a.controls-avalonia","01.csharp\u002F12.desktop-ui\u002F10a.controls-avalonia",{"title":1443,"path":1444,"stem":1445},"Текстові контроли — TextBlock, TextBox, RichTextBox","\u002Fcsharp\u002Fdesktop-ui\u002Ftext-controls","01.csharp\u002F12.desktop-ui\u002F11.text-controls",{"title":1447,"path":1448,"stem":1449},"Контроли вибору — CheckBox, RadioButton, ComboBox, ListBox, DatePicker","\u002Fcsharp\u002Fdesktop-ui\u002Fselection-controls","01.csharp\u002F12.desktop-ui\u002F12.selection-controls",{"title":1451,"path":1452,"stem":1453},"Content Model — GroupBox, Expander, TabControl, StatusBar","\u002Fcsharp\u002Fdesktop-ui\u002Fcontent-controls","01.csharp\u002F12.desktop-ui\u002F13.content-controls",{"title":1455,"path":1456,"stem":1457},"UI\u002FUX принципи десктопних застосунків","\u002Fcsharp\u002Fdesktop-ui\u002F13a.ui-ux-principles","01.csharp\u002F12.desktop-ui\u002F13a.ui-ux-principles",{"title":1459,"path":1460,"stem":1461},"Dependency Properties — Концепція та Value Resolution","\u002Fcsharp\u002Fdesktop-ui\u002Fdependency-properties-part1","01.csharp\u002F12.desktop-ui\u002F14.dependency-properties-part1",{"title":1463,"path":1464,"stem":1465},"Avalonia Property System — StyledProperty та DirectProperty","\u002Fcsharp\u002Fdesktop-ui\u002F14a.avalonia-property-system","01.csharp\u002F12.desktop-ui\u002F14a.avalonia-property-system",{"title":1467,"path":1468,"stem":1469},"Attached Properties — Властивості без меж","\u002Fcsharp\u002Fdesktop-ui\u002Fattached-properties","01.csharp\u002F12.desktop-ui\u002F15.attached-properties",{"title":1471,"path":1472,"stem":1473},"Routed Events — Маршрутизація подій у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Frouted-events","01.csharp\u002F12.desktop-ui\u002F16.routed-events",{"title":1475,"path":1476,"stem":1477},"Data Binding — Від Code-Behind до Декларативності","\u002Fcsharp\u002Fdesktop-ui\u002Fdata-binding-basics-part1","01.csharp\u002F12.desktop-ui\u002F17.data-binding-basics-part1",{"title":1479,"path":1480,"stem":1481},"INotifyPropertyChanged — Живе оновлення UI","\u002Fcsharp\u002Fdesktop-ui\u002Fdata-binding-basics-part2","01.csharp\u002F12.desktop-ui\u002F17.data-binding-basics-part2",{"title":1483,"path":1484,"stem":1485},"Compiled Bindings в Avalonia — Безпека на етапі компіляції","\u002Fcsharp\u002Fdesktop-ui\u002F17a.avalonia-compiled-bindings","01.csharp\u002F12.desktop-ui\u002F17a.avalonia-compiled-bindings",{"title":1487,"path":1488,"stem":1489},"Просунутий Data Binding — ElementName, RelativeSource, MultiBinding","\u002Fcsharp\u002Fdesktop-ui\u002Fdata-binding-advanced","01.csharp\u002F12.desktop-ui\u002F18.data-binding-advanced",{"title":1491,"path":1492,"stem":1493},"Value Converters — Перетворення типів даних у Data Binding","\u002Fcsharp\u002Fdesktop-ui\u002Fvalue-converters","01.csharp\u002F12.desktop-ui\u002F19.value-converters",{"title":1495,"path":1496,"stem":1497},"Data Templates — Візуалізація об'єктів у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Fdata-templates","01.csharp\u002F12.desktop-ui\u002F20.data-templates",{"title":1499,"path":1500,"stem":1501},"Collections Binding Part 1 — ObservableCollection та ItemsControl","\u002Fcsharp\u002Fdesktop-ui\u002Fcollections-binding-part1","01.csharp\u002F12.desktop-ui\u002F21.collections-binding-part1",{"title":1503,"path":1504,"stem":1505},"Collections Binding Part 2 — ICollectionView, Filtering, Sorting та Virtualization","\u002Fcsharp\u002Fdesktop-ui\u002Fcollections-binding-part2","01.csharp\u002F12.desktop-ui\u002F21.collections-binding-part2",{"title":1507,"path":1508,"stem":1509},"MVVM Pattern — Від Spaghetti Code до архітектури","\u002Fcsharp\u002Fdesktop-ui\u002Fmvvm-pattern","01.csharp\u002F12.desktop-ui\u002F22.mvvm-pattern",{"title":1511,"path":1512,"stem":1513},"ViewModel Implementation — Від BaseViewModel до валідації","\u002Fcsharp\u002Fdesktop-ui\u002Fviewmodel-implementation","01.csharp\u002F12.desktop-ui\u002F23.viewmodel-implementation",{"title":1515,"path":1516,"stem":1517},"Commands — Від event handlers до декларативних команд","\u002Fcsharp\u002Fdesktop-ui\u002Fcommands","01.csharp\u002F12.desktop-ui\u002F24.commands",{"title":1519,"path":1520,"stem":1521},"MVVM Toolkit — MVVM без boilerplate через Source Generators","\u002Fcsharp\u002Fdesktop-ui\u002Fmvvm-toolkit","01.csharp\u002F12.desktop-ui\u002F25.mvvm-toolkit",{"title":1523,"path":1524,"stem":1525},"Messenger Pattern — Комунікація між ViewModel без прямих посилань","\u002Fcsharp\u002Fdesktop-ui\u002Fmessenger-pattern","01.csharp\u002F12.desktop-ui\u002F26.messenger-pattern",{"title":1527,"path":1528,"stem":1529},"Стилі WPF — CSS для десктопу","\u002Fcsharp\u002Fdesktop-ui\u002Fstyles-basics","01.csharp\u002F12.desktop-ui\u002F27.styles-basics",{"title":1531,"path":1532,"stem":1533},"CSS-like стилі Avalonia","\u002Fcsharp\u002Fdesktop-ui\u002F27a.avalonia-css-styling","01.csharp\u002F12.desktop-ui\u002F27a.avalonia-css-styling",{"title":1535,"path":1536,"stem":1537},"Control Templates — Частина 1. Концепція та TemplateBinding","\u002Fcsharp\u002Fdesktop-ui\u002Fcontrol-templates-part1","01.csharp\u002F12.desktop-ui\u002F28.control-templates-part1",{"title":1539,"path":1540,"stem":1541},"Control Templates — Частина 2. Named Parts та ContentPresenter","\u002Fcsharp\u002Fdesktop-ui\u002Fcontrol-templates-part2","01.csharp\u002F12.desktop-ui\u002F28.control-templates-part2",{"title":1543,"path":1544,"stem":1545},"Control Themes в Avalonia — нова ера стилізації","\u002Fcsharp\u002Fdesktop-ui\u002F28a.avalonia-control-themes","01.csharp\u002F12.desktop-ui\u002F28a.avalonia-control-themes",{"title":1547,"path":1548,"stem":1549},"Triggers та Visual State Manager у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Ftriggers-visual-states","01.csharp\u002F12.desktop-ui\u002F29.triggers-visual-states",{"title":1551,"path":1552,"stem":1553},"Pseudo-classes в Avalonia — замість WPF Triggers","\u002Fcsharp\u002Fdesktop-ui\u002F29a.avalonia-pseudo-classes","01.csharp\u002F12.desktop-ui\u002F29a.avalonia-pseudo-classes",{"title":1555,"path":1556,"stem":1557},"Теми та ресурсні словники у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Fresources-themes","01.csharp\u002F12.desktop-ui\u002F30.resources-themes",{"title":1559,"path":1560,"stem":1561},"Avalonia Themes — Fluent Design та система тематизації","\u002Fcsharp\u002Fdesktop-ui\u002F30a.avalonia-themes-fluent","01.csharp\u002F12.desktop-ui\u002F30a.avalonia-themes-fluent",{"title":1563,"path":1564,"stem":1565},"Контроли колекцій — глибоке занурення","\u002Fcsharp\u002Fdesktop-ui\u002Fcollection-controls","01.csharp\u002F12.desktop-ui\u002F31.collection-controls",{"title":1567,"path":1568,"stem":1569},"DataGrid — колонки та базове відображення","\u002Fcsharp\u002Fdesktop-ui\u002Fdatagrid-part1","01.csharp\u002F12.desktop-ui\u002F32.datagrid-part1",{"title":1571,"path":1572,"stem":1573},"DataGrid — сортування, фільтрація, редагування","\u002Fcsharp\u002Fdesktop-ui\u002Fdatagrid-part2","01.csharp\u002F12.desktop-ui\u002F32.datagrid-part2",{"title":1575,"path":1576,"stem":1577},"TreeView та GridView","\u002Fcsharp\u002Fdesktop-ui\u002Ftreeview-listview","01.csharp\u002F12.desktop-ui\u002F33.treeview-listview",{"title":1579,"path":1580,"stem":1581},"Меню, Toolbar, ContextMenu, StatusBar","\u002Fcsharp\u002Fdesktop-ui\u002Fmenus-toolbars","01.csharp\u002F12.desktop-ui\u002F34.menus-toolbars",{"title":1583,"path":1584,"stem":1585},"Навігація та керування вікнами. Частина 1: вікна та сторінки","\u002Fcsharp\u002Fdesktop-ui\u002Fnavigation-windows-part1","01.csharp\u002F12.desktop-ui\u002F35.navigation-windows-part1",{"title":1587,"path":1588,"stem":1589},"Навігація та керування вікнами. Частина 2: MVVM-навігація","\u002Fcsharp\u002Fdesktop-ui\u002Fnavigation-windows-part2","01.csharp\u002F12.desktop-ui\u002F35.navigation-windows-part2",{"title":1591,"path":1592,"stem":1593},"Avalonia — Навігація та діалоги","\u002Fcsharp\u002Fdesktop-ui\u002F35a.avalonia-navigation-dialogs","01.csharp\u002F12.desktop-ui\u002F35a.avalonia-navigation-dialogs",{"title":1595,"path":1596,"stem":1597},"Діалоги та File Pickers у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Fdialogs-file-pickers","01.csharp\u002F12.desktop-ui\u002F36.dialogs-file-pickers",{"title":1599,"path":1600,"stem":1601},"UserControl: компонентний підхід у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Fuser-controls","01.csharp\u002F12.desktop-ui\u002F37.user-controls",{"title":1603,"path":1604,"stem":1605},"Custom Controls: Lookless Controls у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Fcustom-controls","01.csharp\u002F12.desktop-ui\u002F38.custom-controls",{"title":1607,"path":1608,"stem":1609},"Avalonia TemplatedControl — Lookless Controls","\u002Fcsharp\u002Fdesktop-ui\u002F38a.avalonia-templated-controls","01.csharp\u002F12.desktop-ui\u002F38a.avalonia-templated-controls",{"title":1611,"path":1612,"stem":1613},"Анімації у WPF: Storyboard та Easing Functions","\u002Fcsharp\u002Fdesktop-ui\u002Fanimations-transitions","01.csharp\u002F12.desktop-ui\u002F39.animations-transitions",{"title":1615,"path":1616,"stem":1617},"Анімації в Avalonia","\u002Fcsharp\u002Fdesktop-ui\u002F39a.avalonia-animations","01.csharp\u002F12.desktop-ui\u002F39a.avalonia-animations",{"title":1619,"path":1620,"stem":1621},"2D Графіка та Мультимедіа у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Fmedia-graphics","01.csharp\u002F12.desktop-ui\u002F40.media-graphics",{"title":1623,"path":1624,"stem":1625},"Dependency Injection у WPF та Avalonia","\u002Fcsharp\u002Fdesktop-ui\u002Fdi-integration","01.csharp\u002F12.desktop-ui\u002F41.di-integration",{"title":1627,"path":1628,"stem":1629},"SQLite та EF Core у десктопних додатках","\u002Fcsharp\u002Fdesktop-ui\u002Fdata-persistence-part1","01.csharp\u002F12.desktop-ui\u002F42.data-persistence-part1",{"title":1631,"path":1632,"stem":1633},"Repository Pattern та Unit of Work","\u002Fcsharp\u002Fdesktop-ui\u002Fdata-persistence-part2","01.csharp\u002F12.desktop-ui\u002F43.data-persistence-part2",{"title":1635,"path":1636,"stem":1637},"Тестування ViewModels","\u002Fcsharp\u002Fdesktop-ui\u002Fviewmodel-testing","01.csharp\u002F12.desktop-ui\u002F44.viewmodel-testing",{"title":1639,"path":1640,"stem":1641},"Avalonia Headless Testing — тестування UI без вікон","\u002Fcsharp\u002Fdesktop-ui\u002F44a.avalonia-headless-testing","01.csharp\u002F12.desktop-ui\u002F44a.avalonia-headless-testing",{"title":1643,"path":1644,"stem":1645},"Кросплатформна розробка з Avalonia","\u002Fcsharp\u002Fdesktop-ui\u002Favalonia-cross-platform","01.csharp\u002F12.desktop-ui\u002F45.avalonia-cross-platform",{"title":1647,"path":1648,"stem":1649},"Пакування та розгортання Avalonia додатків","\u002Fcsharp\u002Fdesktop-ui\u002Favalonia-packaging-deployment","01.csharp\u002F12.desktop-ui\u002F46.avalonia-packaging-deployment",{"title":1651,"path":1652,"stem":1653},"Розгортання WPF застосунків","\u002Fcsharp\u002Fdesktop-ui\u002Fwpf-packaging-deployment","01.csharp\u002F12.desktop-ui\u002F47.wpf-packaging-deployment",{"title":1655,"icon":658,"path":1656,"stem":1657,"children":1658,"page":59},"Network Programming","\u002Fcsharp\u002Fnetwork-programming","01.csharp\u002F13.network-programming",[1659,1663,1667,1671,1675,1679,1683,1687,1691,1695,1699],{"title":1660,"path":1661,"stem":1662},"Основи комп'ютерних мереж","\u002Fcsharp\u002Fnetwork-programming\u002Ffoundations","01.csharp\u002F13.network-programming\u002F01.foundations",{"title":1664,"path":1665,"stem":1666},"Модель OSI та стек TCP\u002FIP","\u002Fcsharp\u002Fnetwork-programming\u002Fosi-model","01.csharp\u002F13.network-programming\u002F02.osi-model",{"title":1668,"path":1669,"stem":1670},"IP-протокол та адресація","\u002Fcsharp\u002Fnetwork-programming\u002Fip-addressing","01.csharp\u002F13.network-programming\u002F03.ip-addressing",{"title":1672,"path":1673,"stem":1674},"UDP — протокол без з'єднання","\u002Fcsharp\u002Fnetwork-programming\u002Fudp","01.csharp\u002F13.network-programming\u002F05.udp",{"title":1676,"path":1677,"stem":1678},"UDP Broadcast та Multicast","\u002Fcsharp\u002Fnetwork-programming\u002Fudp-broadcast-multicast","01.csharp\u002F13.network-programming\u002F06.udp-broadcast-multicast",{"title":1680,"path":1681,"stem":1682},"HTTP — протокол вебу","\u002Fcsharp\u002Fnetwork-programming\u002Fhttp-fundamentals","01.csharp\u002F13.network-programming\u002F07.http-fundamentals",{"title":1684,"path":1685,"stem":1686},"HttpListener — вбудований HTTP-сервер .NET","\u002Fcsharp\u002Fnetwork-programming\u002F07a.http-listener","01.csharp\u002F13.network-programming\u002F07a.http-listener",{"title":1688,"path":1689,"stem":1690},"HTTP Advanced — cookies, аутентифікація та HTTPS","\u002Fcsharp\u002Fnetwork-programming\u002Fhttp-advanced","01.csharp\u002F13.network-programming\u002F08.http-advanced",{"title":1692,"path":1693,"stem":1694},"SMTP та протоколи електронної пошти","\u002Fcsharp\u002Fnetwork-programming\u002Fsmtp","01.csharp\u002F13.network-programming\u002F09.smtp",{"title":1696,"path":1697,"stem":1698},"WebSocket — повнодуплексний протокол реального часу","\u002Fcsharp\u002Fnetwork-programming\u002Fwebsockets","01.csharp\u002F13.network-programming\u002F10.websockets",{"title":1700,"path":1701,"stem":1702},"TLS\u002FSSL — криптографічний захист мережевих з'єднань","\u002Fcsharp\u002Fnetwork-programming\u002Ftls-ssl","01.csharp\u002F13.network-programming\u002F11.tls-ssl",{"title":1704,"path":1705,"stem":1706},"C# & .NET: The Ultimate Roadmap","\u002Fcsharp\u002Froadmap","01.csharp\u002Froadmap",{"title":1708,"icon":1709,"path":1710,"stem":1711,"children":1712,"page":59},"C++","i-devicon-cplusplus","\u002Fcpp","02.cpp",[1713,1717,1721,1725,1729,1733,1737,1741,1745,1748,1752,1756,1760,1764,1768,1772,1776,1780,1784,1788,1792,1796,1800,1804,1808,1812,1816,1820,1824,1828,1832,1836,1840,1844,1848,1852,1856,1860,1864,1868,1872,1876,1880,1884,1888,1892,1896,1900,1904,1908,1912,1916,1920,1924,1928,1932,1936,1940,1944,1948,1952,1956,1960,1964,1968,1972,1976,1980,1984,1988,1992,1996,2000,2004,2008,2012,2016,2020,2024,2028,2032,2036,2040,2044,2048,2052,2056,2060,2064,2068,2072,2076,2080,2084,2088,2092,2096],{"title":1714,"path":1715,"stem":1716},"Вступ у програмування та алгоритми","\u002Fcpp\u002Fintro-algorithms","02.cpp\u002F01.intro-algorithms",{"title":1718,"path":1719,"stem":1720},"Code Style: угоди про оформлення коду","\u002Fcpp\u002Fcode-style","02.cpp\u002F02.code-style",{"title":1722,"path":1723,"stem":1724},"Середовище розробки та перший проєкт","\u002Fcpp\u002Fide-setup","02.cpp\u002F03.ide-setup",{"title":1726,"path":1727,"stem":1728},"Вивід даних на екран","\u002Fcpp\u002Fdata-output","02.cpp\u002F04.data-output",{"title":1730,"path":1731,"stem":1732},"Типи даних, змінні та константи","\u002Fcpp\u002Fdata-types-variables","02.cpp\u002F05.data-types-variables",{"title":1734,"path":1735,"stem":1736},"Ввід даних з клавіатури","\u002Fcpp\u002Fdata-input","02.cpp\u002F06.data-input",{"title":1738,"path":1739,"stem":1740},"Оператори, перетворення типів та логічні операції","\u002Fcpp\u002Foperators-type-conversion","02.cpp\u002F07.operators-type-conversion",{"title":1742,"path":1743,"stem":1744},"Цикли","\u002Fcpp\u002Floops","02.cpp\u002F08.loops",{"title":32,"path":1746,"stem":1747},"\u002Fcpp\u002Farrays","02.cpp\u002F09.arrays",{"title":1749,"path":1750,"stem":1751},"Алгоритми сортування та аналіз складності","\u002Fcpp\u002Fsorting","02.cpp\u002F10.sorting",{"title":1753,"path":1754,"stem":1755},"Алгоритми пошуку","\u002Fcpp\u002Fsearching","02.cpp\u002F11.searching",{"title":1757,"path":1758,"stem":1759},"Функції: основи","\u002Fcpp\u002Ffunctions-basics","02.cpp\u002F12.functions-basics",{"title":1761,"path":1762,"stem":1763},"Функції: прототипи, область видимості та додаткові можливості","\u002Fcpp\u002Ffunctions-scope","02.cpp\u002F13.functions-scope",{"title":1765,"path":1766,"stem":1767},"Функції: перевантаження та шаблони","\u002Fcpp\u002Ffunctions-overloading-templates","02.cpp\u002F14.functions-overloading-templates",{"title":1769,"path":1770,"stem":1771},"Вказівники: основи","\u002Fcpp\u002Fpointers-basics","02.cpp\u002F15.pointers-basics",{"title":1773,"path":1774,"stem":1775},"Посилання (References)","\u002Fcpp\u002Freferences","02.cpp\u002F16.references",{"title":1777,"path":1778,"stem":1779},"Вказівники, const і масиви","\u002Fcpp\u002Fpointers-const-arrays","02.cpp\u002F17.pointers-const-arrays",{"title":1781,"path":1782,"stem":1783},"Адресна арифметика","\u002Fcpp\u002Fpointer-arithmetic","02.cpp\u002F18.pointer-arithmetic",{"title":1785,"path":1786,"stem":1787},"Динамічна пам'ять","\u002Fcpp\u002Fdynamic-memory","02.cpp\u002F19.dynamic-memory",{"title":1789,"path":1790,"stem":1791},"Вказівники типу void","\u002Fcpp\u002Fvoid-pointers","02.cpp\u002F20.void-pointers",{"title":1793,"path":1794,"stem":1795},"Вказівники на вказівники","\u002Fcpp\u002Fpointers-to-pointers","02.cpp\u002F21.pointers-to-pointers",{"title":1797,"path":1798,"stem":1799},"Оператор доступу до членів через вказівник (->)","\u002Fcpp\u002Fmember-access-operator","02.cpp\u002F22.member-access-operator",{"title":1801,"path":1802,"stem":1803},"Цикл for-each (Range-based for)","\u002Fcpp\u002Fforeach-loop","02.cpp\u002F23.foreach-loop",{"title":1805,"path":1806,"stem":1807},"Вказівники на функції","\u002Fcpp\u002Ffunction-pointers","02.cpp\u002F24.function-pointers",{"title":1809,"path":1810,"stem":1811},"Лямбда-вирази","\u002Fcpp\u002Flambdas","02.cpp\u002F25.lambdas",{"title":1813,"path":1814,"stem":1815},"Лямбда-захоплення","\u002Fcpp\u002Flambda-captures","02.cpp\u002F26.lambda-captures",{"title":1817,"path":1818,"stem":1819},"Еліпсис","\u002Fcpp\u002Fellipsis","02.cpp\u002F27.ellipsis",{"title":1821,"path":1822,"stem":1823},"Безпечні альтернативи еліпсису","\u002Fcpp\u002F27a.ellipsis","02.cpp\u002F27a.ellipsis",{"title":1825,"path":1826,"stem":1827},"Аргументи командного рядка","\u002Fcpp\u002Fcommand-line-arguments","02.cpp\u002F28.command-line-arguments",{"title":1829,"path":1830,"stem":1831},"Перерахування (enum)","\u002Fcpp\u002Fenum","02.cpp\u002F29.enum",{"title":1833,"path":1834,"stem":1835},"Класи-перерахування (enum class)","\u002Fcpp\u002Fenum-class","02.cpp\u002F30.enum-class",{"title":1837,"path":1838,"stem":1839},"Псевдоніми типів (typedef і using)","\u002Fcpp\u002Ftype-aliases","02.cpp\u002F31.type-aliases",{"title":1841,"path":1842,"stem":1843},"Системи числення та двійкова арифметика","\u002Fcpp\u002Fnumber-systems","02.cpp\u002F32.number-systems",{"title":1845,"path":1846,"stem":1847},"Структури (struct): агрегування даних","\u002Fcpp\u002Fstruct","02.cpp\u002F33.struct",{"title":1849,"path":1850,"stem":1851},"Структури у функціях","\u002Fcpp\u002Fstruct-functions","02.cpp\u002F34.struct-functions",{"title":1853,"path":1854,"stem":1855},"Масиви структур і вкладені структури","\u002Fcpp\u002Fstruct-arrays","02.cpp\u002F35.struct-arrays",{"title":1857,"path":1858,"stem":1859},"Патерни struct та межі застосування","\u002Fcpp\u002Fstruct-patterns","02.cpp\u002F36.struct-patterns",{"title":1861,"path":1862,"stem":1863},"Символи та таблиця ASCII","\u002Fcpp\u002Fascii-characters","02.cpp\u002F37.ascii-characters",{"title":1865,"path":1866,"stem":1867},"Unicode та кодування UTF","\u002Fcpp\u002Funicode-utf","02.cpp\u002F38.unicode-utf",{"title":1869,"path":1870,"stem":1871},"C-style рядки","\u002Fcpp\u002Fc-strings","02.cpp\u002F39.c-strings",{"title":1873,"path":1874,"stem":1875},"Вступ до std::string","\u002Fcpp\u002Fstd-string-intro","02.cpp\u002F40.std-string-intro",{"title":1877,"path":1878,"stem":1879},"Довжина, ємність та доступ до символів std::string","\u002Fcpp\u002Fstd-string-capacity-access","02.cpp\u002F41.std-string-capacity-access",{"title":1881,"path":1882,"stem":1883},"Модифікація std::string: присвоювання, додавання, вставка, видалення та заміна","\u002Fcpp\u002Fstd-string-modification","02.cpp\u002F42.std-string-modification",{"title":1885,"path":1886,"stem":1887},"Пошук у std::string: find, npos та практичні патерни","\u002Fcpp\u002Fstd-string-search","02.cpp\u002F43.std-string-search",{"title":1889,"path":1890,"stem":1891},"std::string_view: невласницький погляд на рядок без копіювання","\u002Fcpp\u002Fstd-string-view","02.cpp\u002F44.std-string-view",{"title":1893,"path":1894,"stem":1895},"Об'єднання (union): один блок пам'яті, кілька інтерпретацій","\u002Fcpp\u002Funion","02.cpp\u002F45.union",{"title":1897,"path":1898,"stem":1899},"Організація коду: файли, препроцесор, простори імен","\u002Fcpp\u002Fmultifile-programs","02.cpp\u002F46.multifile-programs",{"title":1901,"path":1902,"stem":1903},"Робота з файлами: C-стиль (stdio.h)","\u002Fcpp\u002Fc-style-files","02.cpp\u002F47.c-style-files",{"title":1905,"path":1906,"stem":1907},"Робота з файлами: C++-стиль (fstream)","\u002Fcpp\u002Fcpp-style-files","02.cpp\u002F48.cpp-style-files",{"title":1909,"path":1910,"stem":1911},"Введення в ООП: від процедур до об'єктів","\u002Fcpp\u002Foop-intro","02.cpp\u002F49.oop-intro",{"title":1913,"path":1914,"stem":1915},"Класи, об'єкти та методи","\u002Fcpp\u002Fclasses-objects-methods","02.cpp\u002F50.classes-objects-methods",{"title":1917,"path":1918,"stem":1919},"Специфікатори доступу та інкапсуляція","\u002Fcpp\u002Faccess-specifiers-encapsulation","02.cpp\u002F51.access-specifiers-encapsulation",{"title":1921,"path":1922,"stem":1923},"Конструктори: гарантована ініціалізація об'єктів","\u002Fcpp\u002Fconstructors","02.cpp\u002F52.constructors",{"title":1925,"path":1926,"stem":1927},"Списки ініціалізації та делегуючі конструктори","\u002Fcpp\u002Finit-lists-delegating","02.cpp\u002F53.init-lists-delegating",{"title":1929,"path":1930,"stem":1931},"Деструктори та ідіома RAII","\u002Fcpp\u002Fdestructors-raii","02.cpp\u002F54.destructors-raii",{"title":1933,"path":1934,"stem":1935},"Прихований покажчик this","\u002Fcpp\u002Fthis-pointer","02.cpp\u002F55.this-pointer",{"title":1937,"path":1938,"stem":1939},"Розподіл класу на заголовковий файл та файл реалізації","\u002Fcpp\u002Fclass-header-source","02.cpp\u002F56.class-header-source",{"title":1941,"path":1942,"stem":1943},"Класи та const","\u002Fcpp\u002Fconst-classes","02.cpp\u002F57.const-classes",{"title":1945,"path":1946,"stem":1947},"Статичні члени класу","\u002Fcpp\u002Fstatic-members","02.cpp\u002F58.static-members",{"title":1949,"path":1950,"stem":1951},"Конструктор копіювання та запобігання копіюванню","\u002Fcpp\u002Fcopy-constructor","02.cpp\u002F59.copy-constructor",{"title":1953,"path":1954,"stem":1955},"Дружні функції та класи","\u002Fcpp\u002Ffriend-functions-classes","02.cpp\u002F60.friend-functions-classes",{"title":1957,"path":1958,"stem":1959},"Анонімні об'єкти та вкладені типи","\u002Fcpp\u002Fanonymous-objects-nested-types","02.cpp\u002F61.anonymous-objects-nested-types",{"title":1961,"path":1962,"stem":1963},"Вимірювання часу виконання: RAII-таймер","\u002Fcpp\u002Ftiming-raii-timer","02.cpp\u002F62.timing-raii-timer",{"title":1965,"path":1966,"stem":1967},"Перевантаження операторів: основи та арифметика","\u002Fcpp\u002Foperator-overloading-basics","02.cpp\u002F63.operator-overloading-basics",{"title":1969,"path":1970,"stem":1971},"Перевантаження операторів: методи класу та спеціальні оператори","\u002Fcpp\u002Foperator-overloading-methods","02.cpp\u002F64.operator-overloading-methods",{"title":1973,"path":1974,"stem":1975},"Приведення типів, explicit та delete","\u002Fcpp\u002Ftypecast-explicit-delete","02.cpp\u002F65.typecast-explicit-delete",{"title":1977,"path":1978,"stem":1979},"Глибоке копіювання та оператор присвоювання","\u002Fcpp\u002Fdeep-copy-assignment","02.cpp\u002F66.deep-copy-assignment",{"title":1981,"path":1982,"stem":1983},"Зв'язки між об'єктами: композиція та агрегація","\u002Fcpp\u002Fcomposition-aggregation","02.cpp\u002F67.composition-aggregation",{"title":1985,"path":1986,"stem":1987},"Асоціація та залежність між об","\u002Fcpp\u002Fassociation-dependency","02.cpp\u002F68.association-dependency",{"title":1989,"path":1990,"stem":1991},"Контейнерні класи та `std::initializer_list`","\u002Fcpp\u002Fcontainer-classes-initializer-list","02.cpp\u002F69.container-classes-initializer-list",{"title":1993,"path":1994,"stem":1995},"Вступ до наслідування: базові поняття та відношення «is-a»","\u002Fcpp\u002Finheritance-intro","02.cpp\u002F70.inheritance-intro",{"title":1997,"path":1998,"stem":1999},"Конструктори, деструктори та порядок ініціалізації в ієрархіях","\u002Fcpp\u002Finheritance-constructors-destructors","02.cpp\u002F71.inheritance-constructors-destructors",{"title":2001,"path":2002,"stem":2003},"Специфікатор `protected` та види наслідування","\u002Fcpp\u002Finheritance-access-specifiers","02.cpp\u002F72.inheritance-access-specifiers",{"title":2005,"path":2006,"stem":2007},"Перевизначення методів та приховування імен","\u002Fcpp\u002Fmethod-overriding-hiding","02.cpp\u002F73.method-overriding-hiding",{"title":2009,"path":2010,"stem":2011},"Множинне наслідування та проблема ромба","\u002Fcpp\u002Fmultiple-inheritance-diamond","02.cpp\u002F74.multiple-inheritance-diamond",{"title":2013,"path":2014,"stem":2015},"Вказівники на базовий клас та віртуальні функції","\u002Fcpp\u002Fvirtual-functions-polymorphism","02.cpp\u002F75.virtual-functions-polymorphism",{"title":2017,"path":2018,"stem":2019},"Специфікатори override, final та віртуальні деструктори","\u002Fcpp\u002Foverride-final-virtual-destructors","02.cpp\u002F76.override-final-virtual-destructors",{"title":2021,"path":2022,"stem":2023},"Внутрішні механізми поліморфізму: vtable, vptr та зв'язування","\u002Fcpp\u002Fvirtual-table-binding","02.cpp\u002F77.virtual-table-binding",{"title":2025,"path":2026,"stem":2027},"Абстрактні класи та чисті віртуальні функції","\u002Fcpp\u002Fabstract-classes-interfaces","02.cpp\u002F78.abstract-classes-interfaces",{"title":2029,"path":2030,"stem":2031},"Зрізка об'єктів, віртуальне наслідування та поліморфний вивід","\u002Fcpp\u002Fslicing-virtual-base-io","02.cpp\u002F79.slicing-virtual-base-io",{"title":2033,"path":2034,"stem":2035},"Динамічне приведення типів (`dynamic_cast`) та RTTI","\u002Fcpp\u002Fdynamic-cast-rtti","02.cpp\u002F80.dynamic-cast-rtti",{"title":2037,"path":2038,"stem":2039},"Шаблони функцій: узагальнене програмування","\u002Fcpp\u002Ffunction-templates","02.cpp\u002F81.function-templates",{"title":2041,"path":2042,"stem":2043},"Шаблони класів та NTTP-параметри","\u002Fcpp\u002Fclass-templates-nttp","02.cpp\u002F82.class-templates-nttp",{"title":2045,"path":2046,"stem":2047},"Повна (явна) спеціалізація шаблонів","\u002Fcpp\u002Ffull-template-specialization","02.cpp\u002F83.full-template-specialization",{"title":2049,"path":2050,"stem":2051},"Часткова спеціалізація шаблонів класів","\u002Fcpp\u002Fpartial-template-specialization","02.cpp\u002F84.partial-template-specialization",{"title":2053,"path":2054,"stem":2055},"Механізм винятків: try, catch, throw та розкручування стеку","\u002Fcpp\u002Fexceptions-basics","02.cpp\u002F85.exceptions-basics",{"title":2057,"path":2058,"stem":2059},"Ієрархія std::exception та власні класи винятків","\u002Fcpp\u002Fexception-hierarchy-custom","02.cpp\u002F86.exception-hierarchy-custom",{"title":2061,"path":2062,"stem":2063},"Повторне генерування винятків та функціональний try-блок","\u002Fcpp\u002Frethrow-function-try","02.cpp\u002F87.rethrow-function-try",{"title":2065,"path":2066,"stem":2067},"Безпека винятків, noexcept та деструктори","\u002Fcpp\u002Fsafety-noexcept","02.cpp\u002F88.safety-noexcept",{"title":2069,"path":2070,"stem":2071},"Власні структури даних: стек та черга","\u002Fcpp\u002Fcustom-stack-queue","02.cpp\u002F89.custom-stack-queue",{"title":2073,"path":2074,"stem":2075},"Власні структури даних: однозв'язаний список","\u002Fcpp\u002Flinked-list","02.cpp\u002F90.linked-list",{"title":2077,"path":2078,"stem":2079},"Власні структури даних: бінарне дерево пошуку","\u002Fcpp\u002Fbinary-search-tree","02.cpp\u002F91.binary-search-tree",{"title":2081,"path":2082,"stem":2083},"Власні структури даних: хеш-таблиця","\u002Fcpp\u002Fhash-table","02.cpp\u002F92.hash-table",{"title":2085,"path":2086,"stem":2087},"Готові структури даних C++: послідовні контейнери STL","\u002Fcpp\u002Fstl-sequential-containers","02.cpp\u002F93.stl-sequential-containers",{"title":2089,"path":2090,"stem":2091},"Готові структури даних C++: асоціативні контейнери та адаптери","\u002Fcpp\u002Fstl-associative-adapters","02.cpp\u002F94.stl-associative-adapters",{"title":2093,"path":2094,"stem":2095},"Готові структури даних C++: ітератори та алгоритми STL","\u002Fcpp\u002Fstl-iterators-algorithms","02.cpp\u002F95.stl-iterators-algorithms",{"title":2097,"path":2098,"stem":2099},"R-value посилання та move-семантика","\u002Fcpp\u002Frvalue-references-move-semantics","02.cpp\u002F96.rvalue-references-move-semantics",{"title":2101,"icon":2102,"path":2103,"stem":2104,"children":2105,"page":59},"JavaScript","i-devicon-javascript","\u002Fjavascript","03.javascript",[2106,2132,2186,2208,2512,2550,2568],{"title":2107,"icon":2108,"path":2109,"stem":2110,"children":2111,"page":59},"Events","i-lucide-mouse-pointer-click","\u002Fjavascript\u002Fevents","03.javascript\u002F01.events",[2112,2116,2120,2124,2128],{"title":2113,"path":2114,"stem":2115},"Вступ до подій браузера","\u002Fjavascript\u002Fevents\u002Fintro","03.javascript\u002F01.events\u002F01.intro",{"title":2117,"path":2118,"stem":2119},"Бульбашковий механізм (Bubbling) та занурення (Capturing)","\u002Fjavascript\u002Fevents\u002Fbubbling-capturing","03.javascript\u002F01.events\u002F02.bubbling-capturing",{"title":2121,"path":2122,"stem":2123},"Делегування подій (Event Delegation)","\u002Fjavascript\u002Fevents\u002Fdelegate-events","03.javascript\u002F01.events\u002F03.delegate-events",{"title":2125,"path":2126,"stem":2127},"Типові дії браузера та preventDefault()","\u002Fjavascript\u002Fevents\u002Fprevent-default","03.javascript\u002F01.events\u002F04.prevent-default",{"title":2129,"path":2130,"stem":2131},"Запуск користувацьких подій (Custom Events)","\u002Fjavascript\u002Fevents\u002Fcustom-events","03.javascript\u002F01.events\u002F05.custom-events",{"title":2133,"icon":2134,"path":2135,"stem":2136,"children":2137,"page":59},"Network","i-lucide-globe","\u002Fjavascript\u002Fnetwork","03.javascript\u002F02.network",[2138,2142,2146,2150,2154,2158,2162,2166,2170,2174,2178,2182],{"title":2139,"path":2140,"stem":2141},"Fetch API - Сучасний підхід до HTTP-запитів","\u002Fjavascript\u002Fnetwork\u002F01-fetch-api","03.javascript\u002F02.network\u002F01-fetch-api",{"title":2143,"path":2144,"stem":2145},"FormData - Робота з формами та файлами","\u002Fjavascript\u002Fnetwork\u002F02-formdata","03.javascript\u002F02.network\u002F02-formdata",{"title":2147,"path":2148,"stem":2149},"Відстеження прогресу завантаження","\u002Fjavascript\u002Fnetwork\u002F03-download-progress","03.javascript\u002F02.network\u002F03-download-progress",{"title":2151,"path":2152,"stem":2153},"Переривання fetch-запитів","\u002Fjavascript\u002Fnetwork\u002F04-abort-requests","03.javascript\u002F02.network\u002F04-abort-requests",{"title":2155,"path":2156,"stem":2157},"CORS - Запити між різними джерелами","\u002Fjavascript\u002Fnetwork\u002F05-cors","03.javascript\u002F02.network\u002F05-cors",{"title":2159,"path":2160,"stem":2161},"Fetch API - Повний довідник опцій","\u002Fjavascript\u002Fnetwork\u002F06-fetch-options","03.javascript\u002F02.network\u002F06-fetch-options",{"title":2163,"path":2164,"stem":2165},"URL Objects - Робота з посиланнями","\u002Fjavascript\u002Fnetwork\u002F07-url-objects","03.javascript\u002F02.network\u002F07-url-objects",{"title":2167,"path":2168,"stem":2169},"XMLHttpRequest - AJAX та низькорівневі запити","\u002Fjavascript\u002Fnetwork\u002F08-xmlhttprequest","03.javascript\u002F02.network\u002F08-xmlhttprequest",{"title":2171,"path":2172,"stem":2173},"Відновлюване завантаження файлів","\u002Fjavascript\u002Fnetwork\u002F09-resumable-upload","03.javascript\u002F02.network\u002F09-resumable-upload",{"title":2175,"path":2176,"stem":2177},"Cookies, document.cookie та світ після \"Cookiepocalypse\"","\u002Fjavascript\u002Fnetwork\u002F10-cookies","03.javascript\u002F02.network\u002F10-cookies",{"title":2179,"path":2180,"stem":2181},"js-cookie: Керування Cookies без Болю","\u002Fjavascript\u002Fnetwork\u002F11-js-cookie","03.javascript\u002F02.network\u002F11-js-cookie",{"title":2183,"path":2184,"stem":2185},"Axios: Потужний HTTP-клієнт для JavaScript","\u002Fjavascript\u002Fnetwork\u002F12-axios","03.javascript\u002F02.network\u002F12-axios",{"title":2187,"icon":2188,"path":2189,"stem":2190,"children":2191,"page":59},"Bom","i-lucide-monitor","\u002Fjavascript\u002Fbom","03.javascript\u002F03.bom",[2192,2196,2200,2204],{"title":2193,"path":2194,"stem":2195},"LocalStorage, SessionStorage та patterns збереження даних","\u002Fjavascript\u002Fbom\u002F01-localstorage","03.javascript\u002F03.bom\u002F01-localstorage",{"title":2197,"path":2198,"stem":2199},"Location Object - Керування адресою сторінки","\u002Fjavascript\u002Fbom\u002F02-location-object","03.javascript\u002F03.bom\u002F02-location-object",{"title":2201,"path":2202,"stem":2203},"History API - Керування історією браузера","\u002Fjavascript\u002Fbom\u002F03-history-api","03.javascript\u002F03.bom\u002F03-history-api",{"title":2205,"path":2206,"stem":2207},"Navigator Object - Ідентифікація та Можливості Пристрою","\u002Fjavascript\u002Fbom\u002F04-navigator-object","03.javascript\u002F03.bom\u002F04-navigator-object",{"title":2209,"icon":2210,"path":2211,"stem":2212,"children":2213},"React","i-devicon-react","\u002Fjavascript\u002Freact","03.javascript\u002F04.react\u002Findex",[2214,2215,2219,2223,2227,2231,2294,2329,2481],{"title":2209,"path":2211,"stem":2212},{"title":2216,"path":2217,"stem":2218},"Робота з Формами в React","\u002Fjavascript\u002Freact\u002Freact-forms","03.javascript\u002F04.react\u002F01.react-forms",{"title":2220,"path":2221,"stem":2222},"React Hook Form: Професійна Робота з Формами","\u002Fjavascript\u002Freact\u002Freact-hook-form","03.javascript\u002F04.react\u002F02.react-hook-form",{"title":2224,"path":2225,"stem":2226},"React Hook Form: Глибоке Розуміння Архітектури та Оптимізації","\u002Fjavascript\u002Freact\u002Freact-hook-form-new","03.javascript\u002F04.react\u002F02.react-hook-form-new",{"title":2228,"path":2229,"stem":2230},"Axios та React: Професійна Архітектура Запитів","\u002Fjavascript\u002Freact\u002Fdata-fetching-axios","03.javascript\u002F04.react\u002F03.data-fetching-axios",{"title":2232,"icon":132,"path":2233,"stem":2234,"children":2235},"Tanstack Query","\u002Fjavascript\u002Freact\u002Ftanstack-query","03.javascript\u002F04.react\u002F04.tanstack-query\u002Findex",[2236,2238,2242,2246,2250,2254,2258,2262,2266,2270,2274,2278,2282,2286,2290],{"title":2237,"path":2233,"stem":2234},"TanStack Query: Майстерність Керування Станом Сервера",{"title":2239,"path":2240,"stem":2241},"Парадигма Server State: Чому useEffect недостатньо","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fserver-state-paradigm","03.javascript\u002F04.react\u002F04.tanstack-query\u002F01.server-state-paradigm",{"title":2243,"path":2244,"stem":2245},"Встановлення та Налаштування: Фундамент","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Finstallation-and-devtools","03.javascript\u002F04.react\u002F04.tanstack-query\u002F02.installation-and-devtools",{"title":2247,"path":2248,"stem":2249},"Основи Запитів та Магія Ключів","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fquery-basics-and-keys","03.javascript\u002F04.react\u002F04.tanstack-query\u002F03.query-basics-and-keys",{"title":2251,"path":2252,"stem":2253},"Синхронізація Даних: Життєвий Цикл Запиту","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fdata-synchronization","03.javascript\u002F04.react\u002F04.tanstack-query\u002F04.data-synchronization",{"title":2255,"path":2256,"stem":2257},"Мутації та Інвалідація: Зміна Даних","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fmutations-and-invalidation","03.javascript\u002F04.react\u002F04.tanstack-query\u002F05.mutations-and-invalidation",{"title":2259,"path":2260,"stem":2261},"Оптимістичні Оновлення: Швидше за Світло","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Foptimistic-updates","03.javascript\u002F04.react\u002F04.tanstack-query\u002F06.optimistic-updates",{"title":2263,"path":2264,"stem":2265},"Пагінація та Infinite Scroll","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fpagination-and-load-more","03.javascript\u002F04.react\u002F04.tanstack-query\u002F07.pagination-and-load-more",{"title":2267,"path":2268,"stem":2269},"Просунуті Патерни та Оптимізація","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fadvanced-patterns","03.javascript\u002F04.react\u002F04.tanstack-query\u002F08.advanced-patterns",{"title":2271,"path":2272,"stem":2273},"Архітектура та Best Practices","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Farchitecture-and-best-practices","03.javascript\u002F04.react\u002F04.tanstack-query\u002F09.architecture-and-best-practices",{"title":2275,"path":2276,"stem":2277},"Server-Side Rendering (SSR) та Гідратація","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fserver-side-rendering","03.javascript\u002F04.react\u002F04.tanstack-query\u002F10.server-side-rendering",{"title":2279,"path":2280,"stem":2281},"Стратегії Тестування","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Ftesting-strategies","03.javascript\u002F04.react\u002F04.tanstack-query\u002F11.testing-strategies",{"title":2283,"path":2284,"stem":2285},"Аутентифікація та Обробка Помилок","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fauthentication-and-errors","03.javascript\u002F04.react\u002F04.tanstack-query\u002F12.authentication-and-errors",{"title":2287,"path":2288,"stem":2289},"React Suspense та Майбутнє","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Freact-suspense","03.javascript\u002F04.react\u002F04.tanstack-query\u002F13.react-suspense",{"title":2291,"path":2292,"stem":2293},"Глибоке Занурення в Продуктивність","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fperformance-deep-dive","03.javascript\u002F04.react\u002F04.tanstack-query\u002F14.performance-deep-dive",{"title":2295,"icon":2210,"path":2296,"stem":2297,"children":2298},"React Router","\u002Fjavascript\u002Freact\u002Freact-router","03.javascript\u002F04.react\u002F05.react-router\u002Findex",[2299,2301,2305,2309,2313,2317,2321,2325],{"title":2300,"path":2296,"stem":2297},"React Router: Навігаційна система сучасного вебу",{"title":2302,"path":2303,"stem":2304},"Налаштування та Базовий Роутинг","\u002Fjavascript\u002Freact\u002Freact-router\u002Fsetup-and-basic-routing","03.javascript\u002F04.react\u002F05.react-router\u002F01.setup-and-basic-routing",{"title":2306,"path":2307,"stem":2308},"Динамічна Навігація","\u002Fjavascript\u002Freact\u002Freact-router\u002Fnavigation-and-links","03.javascript\u002F04.react\u002F05.react-router\u002F02.navigation-and-links",{"title":2310,"path":2311,"stem":2312},"Вкладені Маршрути та Макети","\u002Fjavascript\u002Freact\u002Freact-router\u002Fnested-routes-and-layouts","03.javascript\u002F04.react\u002F05.react-router\u002F03.nested-routes-and-layouts",{"title":2314,"path":2315,"stem":2316},"Динамічні Маршрути та Параметри","\u002Fjavascript\u002Freact\u002Freact-router\u002Fdynamic-routing","03.javascript\u002F04.react\u002F05.react-router\u002F04.dynamic-routing",{"title":2318,"path":2319,"stem":2320},"Data APIs: Loaders та Actions","\u002Fjavascript\u002Freact\u002Freact-router\u002Fdata-loading","03.javascript\u002F04.react\u002F05.react-router\u002F05.data-loading",{"title":2322,"path":2323,"stem":2324},"Просунуті Патерни","\u002Fjavascript\u002Freact\u002Freact-router\u002Fadvanced-patterns","03.javascript\u002F04.react\u002F05.react-router\u002F06.advanced-patterns",{"title":2326,"path":2327,"stem":2328},"Legacy Routing: Компонентний підхід","\u002Fjavascript\u002Freact\u002Freact-router\u002Flegacy-routing","03.javascript\u002F04.react\u002F05.react-router\u002F07.legacy-routing",{"title":2330,"icon":132,"path":2331,"stem":2332,"children":2333},"Redux","\u002Fjavascript\u002Freact\u002Fredux","03.javascript\u002F04.react\u002F06.redux\u002Findex",[2334,2336,2352,2381,2390,2411,2427,2456],{"title":2335,"path":2331,"stem":2332},"Redux: Еволюція управління станом",{"title":14,"icon":15,"path":2337,"stem":2338,"children":2339,"page":59},"\u002Fjavascript\u002Freact\u002Fredux\u002Ffundamentals","03.javascript\u002F04.react\u002F06.redux\u002F01.fundamentals",[2340,2344,2348],{"title":2341,"path":2342,"stem":2343},"Вступ до State Management","\u002Fjavascript\u002Freact\u002Fredux\u002Ffundamentals\u002Fintro-state-management","03.javascript\u002F04.react\u002F06.redux\u002F01.fundamentals\u002F01.intro-state-management",{"title":2345,"path":2346,"stem":2347},"Філософія Redux та Три Принципи","\u002Fjavascript\u002Freact\u002Fredux\u002Ffundamentals\u002Fredux-philosophy","03.javascript\u002F04.react\u002F06.redux\u002F01.fundamentals\u002F02.redux-philosophy",{"title":2349,"path":2350,"stem":2351},"Чисті функції та Іммутабельність","\u002Fjavascript\u002Freact\u002Fredux\u002Ffundamentals\u002Fpure-functions-immutability","03.javascript\u002F04.react\u002F06.redux\u002F01.fundamentals\u002F03.pure-functions-immutability",{"title":2353,"icon":132,"path":2354,"stem":2355,"children":2356,"page":59},"Classic Redux","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux",[2357,2361,2365,2369,2373,2377],{"title":2358,"path":2359,"stem":2360},"Створення Store (Classic Redux)","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux\u002Fstore-setup","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux\u002F01.store-setup",{"title":2362,"path":2363,"stem":2364},"Actions, Constants та Action Creators","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux\u002Factions-constants","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux\u002F02.actions-constants",{"title":2366,"path":2367,"stem":2368},"Логіка Reducers","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux\u002Freducers","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux\u002F03.reducers",{"title":2370,"path":2371,"stem":2372},"Комбінування Reducers (Root Reducer)","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux\u002Fdata-flow","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux\u002F04.data-flow",{"title":2374,"path":2375,"stem":2376},"Підключення до React (React-Redux)","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux\u002Freact-redux-connection","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux\u002F05.react-redux-connection",{"title":2378,"path":2379,"stem":2380},"Middleware та Асинхронність (Redux Thunk)","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux\u002Fmiddleware-thunk","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux\u002F06.middleware-thunk",{"title":2382,"icon":132,"path":2383,"stem":2384,"children":2385,"page":59},"Transition To Rtk","\u002Fjavascript\u002Freact\u002Fredux\u002Ftransition-to-rtk","03.javascript\u002F04.react\u002F06.redux\u002F03.transition-to-rtk",[2386],{"title":2387,"path":2388,"stem":2389},"Проблеми класичного Redux","\u002Fjavascript\u002Freact\u002Fredux\u002Ftransition-to-rtk\u002Fproblems-with-classic","03.javascript\u002F04.react\u002F06.redux\u002F03.transition-to-rtk\u002F01.problems-with-classic",{"title":2391,"icon":132,"path":2392,"stem":2393,"children":2394,"page":59},"Redux Toolkit","\u002Fjavascript\u002Freact\u002Fredux\u002Fredux-toolkit","03.javascript\u002F04.react\u002F06.redux\u002F04.redux-toolkit",[2395,2399,2403,2407],{"title":2396,"path":2397,"stem":2398},"Налаштування Store з configureStore","\u002Fjavascript\u002Freact\u002Fredux\u002Fredux-toolkit\u002Fconfigure-store","03.javascript\u002F04.react\u002F06.redux\u002F04.redux-toolkit\u002F01.configure-store",{"title":2400,"path":2401,"stem":2402},"createSlice: Революція в Redux","\u002Fjavascript\u002Freact\u002Fredux\u002Fredux-toolkit\u002Fcreate-slice","03.javascript\u002F04.react\u002F06.redux\u002F04.redux-toolkit\u002F02.create-slice",{"title":2404,"path":2405,"stem":2406},"Асинхронність з createAsyncThunk","\u002Fjavascript\u002Freact\u002Fredux\u002Fredux-toolkit\u002Fasync-thunks","03.javascript\u002F04.react\u002F06.redux\u002F04.redux-toolkit\u002F03.async-thunks",{"title":2408,"path":2409,"stem":2410},"04. Entity Adapter: Керування нормалізованим станом","\u002Fjavascript\u002Freact\u002Fredux\u002Fredux-toolkit\u002Fentity-adapter","03.javascript\u002F04.react\u002F06.redux\u002F04.redux-toolkit\u002F04.entity-adapter",{"title":2412,"icon":92,"path":2413,"stem":2414,"children":2415,"page":59},"Advanced","\u002Fjavascript\u002Freact\u002Fredux\u002Fadvanced","03.javascript\u002F04.react\u002F06.redux\u002F05.advanced",[2416,2420,2424],{"title":2417,"path":2418,"stem":2419},"Мемоізація та Селектори: Повний Гайд по Reselect","\u002Fjavascript\u002Freact\u002Fredux\u002Fadvanced\u002Fselectors-reselect","03.javascript\u002F04.react\u002F06.redux\u002F05.advanced\u002F01.selectors-reselect",{"title":2421,"path":2422,"stem":2423},"RTK Query: Архітектура Серверного Кешу","\u002Fjavascript\u002Freact\u002Fredux\u002Fadvanced\u002Frtk-query-intro","03.javascript\u002F04.react\u002F06.redux\u002F05.advanced\u002F02.rtk-query-intro",{"title":2271,"path":2425,"stem":2426},"\u002Fjavascript\u002Freact\u002Fredux\u002Fadvanced\u002Farchitecture-best-practices","03.javascript\u002F04.react\u002F06.redux\u002F05.advanced\u002F03.architecture-best-practices",{"title":2428,"icon":132,"path":2429,"stem":2430,"children":2431,"page":59},"Project Kanban","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban",[2432,2436,2440,2444,2448,2452],{"title":2433,"path":2434,"stem":2435},"Проєкт: Kanban Board (Trello Clone)","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban\u002Fproject-overview","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban\u002F01.project-overview",{"title":2437,"path":2438,"stem":2439},"Налаштування та Типізація","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban\u002Fsetup-and-types","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban\u002F02.setup-and-types",{"title":2441,"path":2442,"stem":2443},"Board Slice: Серце Дошки","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban\u002Fboard-slice","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban\u002F03.board-slice",{"title":2445,"path":2446,"stem":2447},"Логіка Drag & Drop","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban\u002Fdrag-and-drop-logic","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban\u002F04.drag-and-drop-logic",{"title":2449,"path":2450,"stem":2451},"Інтеграція з RTK Query","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban\u002Frtk-query-integration","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban\u002F05.rtk-query-integration",{"title":2453,"path":2454,"stem":2455},"Optimistic Updates","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban\u002Foptimistic-updates","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban\u002F06.optimistic-updates",{"title":2457,"icon":132,"path":2458,"stem":2459,"children":2460,"page":59},"Testing","\u002Fjavascript\u002Freact\u002Fredux\u002Ftesting","03.javascript\u002F04.react\u002F06.redux\u002F07.testing",[2461,2465,2469,2473,2477],{"title":2462,"path":2463,"stem":2464},"Тестування Redux","\u002Fjavascript\u002Freact\u002Fredux\u002Ftesting\u002Fintro-testing","03.javascript\u002F04.react\u002F06.redux\u002F07.testing\u002F01.intro-testing",{"title":2466,"path":2467,"stem":2468},"Тестування Reducers","\u002Fjavascript\u002Freact\u002Fredux\u002Ftesting\u002Ftesting-reducers","03.javascript\u002F04.react\u002F06.redux\u002F07.testing\u002F02.testing-reducers",{"title":2470,"path":2471,"stem":2472},"Тестування Селекторів","\u002Fjavascript\u002Freact\u002Fredux\u002Ftesting\u002Ftesting-selectors","03.javascript\u002F04.react\u002F06.redux\u002F07.testing\u002F03.testing-selectors",{"title":2474,"path":2475,"stem":2476},"Тестування Компонентів (Integration)","\u002Fjavascript\u002Freact\u002Fredux\u002Ftesting\u002Ftesting-components","03.javascript\u002F04.react\u002F06.redux\u002F07.testing\u002F04.testing-components",{"title":2478,"path":2479,"stem":2480},"Тестування Async Thunks","\u002Fjavascript\u002Freact\u002Fredux\u002Ftesting\u002Ftesting-thunks","03.javascript\u002F04.react\u002F06.redux\u002F07.testing\u002F05.testing-thunks",{"title":2482,"icon":132,"path":2483,"stem":2484,"children":2485},"Ui Libraries","\u002Fjavascript\u002Freact\u002Fui-libraries","03.javascript\u002F04.react\u002F07.ui-libraries\u002Findex",[2486,2488,2492,2496,2500,2504,2508],{"title":2487,"path":2483,"stem":2484},"UI Бібліотеки в React",{"title":2489,"path":2490,"stem":2491},"Вступ до UI Бібліотек: Навіщо Винаходити Велосипед Двічі?","\u002Fjavascript\u002Freact\u002Fui-libraries\u002Fintroduction-to-ui-libraries","03.javascript\u002F04.react\u002F07.ui-libraries\u002F01.introduction-to-ui-libraries",{"title":2493,"path":2494,"stem":2495},"Філософія shadcn\u002Fui: \"Not a Component Library\"","\u002Fjavascript\u002Freact\u002Fui-libraries\u002Fshadcn-philosophy","03.javascript\u002F04.react\u002F07.ui-libraries\u002F02.shadcn-philosophy",{"title":2497,"path":2498,"stem":2499},"Установка та Налаштування shadcn\u002Fui","\u002Fjavascript\u002Freact\u002Fui-libraries\u002Fshadcn-installation","03.javascript\u002F04.react\u002F07.ui-libraries\u002F03.shadcn-installation",{"title":2501,"path":2502,"stem":2503},"Базові Компоненти shadcn\u002Fui: Фундамент Інтерфейсу","\u002Fjavascript\u002Freact\u002Fui-libraries\u002Fshadcn-components-basics","03.javascript\u002F04.react\u002F07.ui-libraries\u002F04.shadcn-components-basics",{"title":2505,"path":2506,"stem":2507},"Компоненти Форм: Побудова Інтерактивних Form","\u002Fjavascript\u002Freact\u002Fui-libraries\u002Fshadcn-components-forms","03.javascript\u002F04.react\u002F07.ui-libraries\u002F05.shadcn-components-forms",{"title":2509,"path":2510,"stem":2511},"Складні Компоненти: Dialog, Dropdown, Table та Command","\u002Fjavascript\u002Freact\u002Fui-libraries\u002Fshadcn-components-advanced","03.javascript\u002F04.react\u002F07.ui-libraries\u002F06.shadcn-components-advanced",{"title":2513,"icon":2514,"path":2515,"stem":2516,"children":2517,"page":59},"TypeScript","i-devicon-typescript","\u002Fjavascript\u002Ftypescript","03.javascript\u002F05.typescript",[2518,2522,2526,2530,2534,2538,2542,2546],{"title":2519,"path":2520,"stem":2521},"TypeScript: Броня для вашого коду","\u002Fjavascript\u002Ftypescript\u002Fintro-and-basic-types","03.javascript\u002F05.typescript\u002F01.intro-and-basic-types",{"title":2523,"path":2524,"stem":2525},"Майстерність Моделювання Даних: Інтерфейси та Просунуті Типи","\u002Fjavascript\u002Ftypescript\u002Finterfaces-and-advanced-types","03.javascript\u002F05.typescript\u002F02.interfaces-and-advanced-types",{"title":2527,"path":2528,"stem":2529},"Алхімія Типів: Generics та Utility Types","\u002Fjavascript\u002Ftypescript\u002Fgenerics-and-utilities","03.javascript\u002F05.typescript\u002F03.generics-and-utilities",{"title":2531,"path":2532,"stem":2533},"Архітектура та Шаблони: Класи в TypeScript","\u002Fjavascript\u002Ftypescript\u002Fclasses-and-oop","03.javascript\u002F05.typescript\u002F04.classes-and-oop",{"title":2535,"path":2536,"stem":2537},"Продакшн та Екосистема: Advanced Config & Workflow","\u002Fjavascript\u002Ftypescript\u002Fadvanced-patterns-and-config","03.javascript\u002F05.typescript\u002F05.advanced-patterns-and-config",{"title":2539,"path":2540,"stem":2541},"TypeScript у світі React","\u002Fjavascript\u002Ftypescript\u002Freact-basics","03.javascript\u002F05.typescript\u002F06.react-basics",{"title":2543,"path":2544,"stem":2545},"React + TypeScript: Продвинуті патерни","\u002Fjavascript\u002Ftypescript\u002Freact-advanced","03.javascript\u002F05.typescript\u002F07.react-advanced",{"title":2547,"path":2548,"stem":2549},"React + TypeScript: Екосистема та бібліотеки","\u002Fjavascript\u002Ftypescript\u002Freact-ecosystem","03.javascript\u002F05.typescript\u002F08.react-ecosystem",{"title":2551,"icon":2552,"path":2553,"stem":2554,"children":2555,"page":59},"Асинхронність","i-lucide-refresh-cw","\u002Fjavascript\u002Fasync-programming","03.javascript\u002F06.async-programming",[2556,2560,2564],{"title":2557,"path":2558,"stem":2559},"Event Loop: серце асинхронності в JavaScript","\u002Fjavascript\u002Fasync-programming\u002Fevent-loop-fundamentals","03.javascript\u002F06.async-programming\u002F01.event-loop-fundamentals",{"title":2561,"path":2562,"stem":2563},"Task Queue та Microtask Queue: пріоритети виконання","\u002Fjavascript\u002Fasync-programming\u002Ftask-queues","03.javascript\u002F06.async-programming\u002F02.task-queues",{"title":2565,"path":2566,"stem":2567},"Асинхронні патерни: від Callbacks до Async\u002FAwait","\u002Fjavascript\u002Fasync-programming\u002Fasync-patterns","03.javascript\u002F06.async-programming\u002F03.async-patterns",{"title":2569,"path":2570,"stem":2571},"Atomic Design","\u002Fjavascript\u002Fatomic-design","03.javascript\u002F2.atomic-design",{"title":2573,"icon":2574,"path":2575,"stem":2576,"children":2577,"page":59},"Java","i-devicon-java","\u002Fjava","04.java",[2578,2581,2584,2588,2592,2596,2600],{"title":162,"path":2579,"stem":2580},"\u002Fjava\u002Fdata-mapper-part1","04.java\u002F01.data-mapper-part1",{"title":166,"path":2582,"stem":2583},"\u002Fjava\u002Fdata-mapper-part2","04.java\u002F02.data-mapper-part2",{"title":2585,"path":2586,"stem":2587},"Service Layer: Організація бізнес-логіки","\u002Fjava\u002Fservice-layer","04.java\u002F03.service-layer",{"title":2589,"path":2590,"stem":2591},"Rich Domain Model та State Pattern","\u002Fjava\u002Frich-domain-model","04.java\u002F04.rich-domain-model",{"title":2593,"path":2594,"stem":2595},"Патерни для складної бізнес-логіки","\u002Fjava\u002Fbusiness-logic-patterns","04.java\u002F05.business-logic-patterns",{"title":2597,"path":2598,"stem":2599},"Обробка помилок та валідація","\u002Fjava\u002Ferror-handling-validation","04.java\u002F06.error-handling-validation",{"title":2601,"path":2602,"stem":2603,"children":2604,"page":59},"Проектування баз даних","\u002Fjava\u002Fpr2","04.java\u002Fpr2",[2605,2609,2613,2617,2621,2625,2629,2633,2637,2641,2645,2649,2653,2657,2661,2665,2669,2673,2677,2681,2685,2689,2693,2697,2701,2705,2709,2713,2717,2721,2725,2729,2733,2737,2741,2745,2749],{"title":2606,"path":2607,"stem":2608},"Концептуальне моделювання: Мистецтво розуміння предметної області","\u002Fjava\u002Fpr2\u002Fconceptual-modeling","04.java\u002Fpr2\u002F01.conceptual-modeling",{"title":2610,"path":2611,"stem":2612},"Логічне моделювання: Від бізнес-ідей до структур даних","\u002Fjava\u002Fpr2\u002Flogical-modeling","04.java\u002Fpr2\u002F02.logical-modeling",{"title":2614,"path":2615,"stem":2616},"Нормалізація: Гігієна даних та боротьба з аномаліями","\u002Fjava\u002Fpr2\u002Fnormalization","04.java\u002Fpr2\u002F03.normalization",{"title":2618,"path":2619,"stem":2620},"Фізична схема: Від абстракції до DDL","\u002Fjava\u002Fpr2\u002Fphysical-schema","04.java\u002Fpr2\u002F04.physical-schema",{"title":2622,"path":2623,"stem":2624},"Архітектурна класифікація таблиць","\u002Fjava\u002Fpr2\u002Ftable-classification","04.java\u002Fpr2\u002F05.table-classification",{"title":2626,"path":2627,"stem":2628},"Database Migrations: Версіонування схеми з Flyway","\u002Fjava\u002Fpr2\u002Fdatabase-migrations","04.java\u002Fpr2\u002F06.database-migrations",{"title":2630,"path":2631,"stem":2632},"А що, якби це була не реляційна БД?","\u002Fjava\u002Fpr2\u002Fbeyond-relational","04.java\u002Fpr2\u002F07.beyond-relational",{"title":2634,"path":2635,"stem":2636},"Object-Relational Impedance Mismatch: Два світи, що не хочуть дружити","\u002Fjava\u002Fpr2\u002Fimpedance-mismatch","04.java\u002Fpr2\u002F09.impedance-mismatch",{"title":2638,"path":2639,"stem":2640},"JDBC: Перший контакт із базою даних","\u002Fjava\u002Fpr2\u002Fjdbc-fundamentals","04.java\u002Fpr2\u002F10.jdbc-fundamentals",{"title":2642,"path":2643,"stem":2644},"Якість коду: Spotless, SpotBugs та SonarQube","\u002Fjava\u002Fpr2\u002F10a.code-quality","04.java\u002Fpr2\u002F10a.code-quality",{"title":2646,"path":2647,"stem":2648},"Connection Pool: Патерн Object Pool для JDBC-з'єднань","\u002Fjava\u002Fpr2\u002Fconnection-pool","04.java\u002Fpr2\u002F11.connection-pool",{"title":2650,"path":2651,"stem":2652},"Row Data Gateway: Об'єкт як обгортка рядка таблиці","\u002Fjava\u002Fpr2\u002Frow-data-gateway","04.java\u002Fpr2\u002F12.row-data-gateway",{"title":2654,"path":2655,"stem":2656},"Table Data Gateway: Фасад таблиці як архітектурний відступ","\u002Fjava\u002Fpr2\u002Ftable-data-gateway","04.java\u002Fpr2\u002F13.table-data-gateway",{"title":2658,"path":2659,"stem":2660},"Repository + Data Mapper: Правильна шарова архітектура з JDBC","\u002Fjava\u002Fpr2\u002Frepository-data-mapper","04.java\u002Fpr2\u002F14.repository-data-mapper",{"title":2662,"path":2663,"stem":2664},"Identity Map: Кешування сутностей у рамках сесії","\u002Fjava\u002Fpr2\u002Fidentity-map","04.java\u002Fpr2\u002F15.identity-map",{"title":2666,"path":2667,"stem":2668},"Unit of Work: Відстеження змін і координація JDBC-транзакцій","\u002Fjava\u002Fpr2\u002Funit-of-work","04.java\u002Fpr2\u002F16.unit-of-work",{"title":2670,"path":2671,"stem":2672},"Strategy: Замінювані SQL-стратегії для підтримки різних СУБД","\u002Fjava\u002Fpr2\u002Fstrategy-sql","04.java\u002Fpr2\u002F17.strategy-sql",{"title":2674,"path":2675,"stem":2676},"Proxy: Lazy Loading для One-To-Many колекцій","\u002Fjava\u002Fpr2\u002Fproxy-lazy-loading","04.java\u002Fpr2\u002F18.proxy-lazy-loading",{"title":2678,"path":2679,"stem":2680},"Generic Repository через Java Reflection: анотації та динамічний SQL","\u002Fjava\u002Fpr2\u002Fgeneric-repository-reflection","04.java\u002Fpr2\u002F19.generic-repository-reflection",{"title":2682,"path":2683,"stem":2684},"Specification Pattern: Композиція бізнес-правил для складних запитів","\u002Fjava\u002Fpr2\u002Fspecification-pattern","04.java\u002Fpr2\u002F20.specification-pattern",{"title":2686,"path":2687,"stem":2688},"Розширені можливості Specification Pattern: підзапити, агрегації та гібридний підхід","\u002Fjava\u002Fpr2\u002F20a.advanced-specifications","04.java\u002Fpr2\u002F20a.advanced-specifications",{"title":2690,"path":2691,"stem":2692},"Асинхронність у JDBC: Від блокуючих викликів до CompletableFuture","\u002Fjava\u002Fpr2\u002Fasynchronous-jdbc","04.java\u002Fpr2\u002F21.asynchronous-jdbc",{"title":2694,"path":2695,"stem":2696},"Інтеграційне тестування JDBC-репозиторіїв: Embedded H2 та патерн AAA","\u002Fjava\u002Fpr2\u002Fintegration-testing-h2","04.java\u002Fpr2\u002F22.integration-testing-h2",{"title":2698,"path":2699,"stem":2700},"Testcontainers: Тестування з реальною PostgreSQL у Docker-контейнерах","\u002Fjava\u002Fpr2\u002Fintegration-testing-testcontainers","04.java\u002Fpr2\u002F23.integration-testing-testcontainers",{"title":2702,"path":2703,"stem":2704},"Google Guice: Впровадження залежностей у JavaFX-проєкті","\u002Fjava\u002Fpr2\u002Fdependency-injection-guice","04.java\u002Fpr2\u002F24.dependency-injection-guice",{"title":2706,"path":2707,"stem":2708},"JavaFX: Основи побудови графічних інтерфейсів","\u002Fjava\u002Fpr2\u002Fjavafx-fundamentals","04.java\u002Fpr2\u002F25.javafx-fundamentals",{"title":2710,"path":2711,"stem":2712},"Properties та Bindings: Реактивність у JavaFX","\u002Fjava\u002Fpr2\u002Fjavafx-properties-bindings","04.java\u002Fpr2\u002F26.javafx-properties-bindings",{"title":2714,"path":2715,"stem":2716},"MVC vs MVP vs MVVM: Еволюція архітектурних патернів UI","\u002Fjava\u002Fpr2\u002Fui-architecture-patterns","04.java\u002Fpr2\u002F27.ui-architecture-patterns",{"title":2718,"path":2719,"stem":2720},"MVVM на практиці: Побудова ViewModel","\u002Fjava\u002Fpr2\u002Fmvvm-viewmodel-implementation","04.java\u002Fpr2\u002F28.mvvm-viewmodel-implementation",{"title":2722,"path":2723,"stem":2724},"View та Controller: Зв'язування з ViewModel через FXML","\u002Fjava\u002Fpr2\u002Fmvvm-view-controller","04.java\u002Fpr2\u002F29.mvvm-view-controller",{"title":2726,"path":2727,"stem":2728},"Інтеграція MVVM з Guice: Автоматична ін'єкція залежностей","\u002Fjava\u002Fpr2\u002Fmvvm-guice-integration","04.java\u002Fpr2\u002F30.mvvm-guice-integration",{"title":2730,"path":2731,"stem":2732},"Валідація та обробка помилок у MVVM","\u002Fjava\u002Fpr2\u002Fmvvm-validation-error-handling","04.java\u002Fpr2\u002F31.mvvm-validation-error-handling",{"title":2734,"path":2735,"stem":2736},"Навігація та управління екранами у JavaFX MVVM","\u002Fjava\u002Fpr2\u002Fmvvm-navigation-screen-management","04.java\u002Fpr2\u002F32.mvvm-navigation-screen-management",{"title":2738,"path":2739,"stem":2740},"Тестування JavaFX MVVM-додатків","\u002Fjava\u002Fpr2\u002Fmvvm-testing","04.java\u002Fpr2\u002F33.mvvm-testing",{"title":2742,"path":2743,"stem":2744},"Стилізація та теми у JavaFX: CSS та User Experience","\u002Fjava\u002Fpr2\u002Fjavafx-styling-themes","04.java\u002Fpr2\u002F34.javafx-styling-themes",{"title":2746,"path":2747,"stem":2748},"AtlantaFX: Сучасні теми для JavaFX додатків","\u002Fjava\u002Fpr2\u002Fatlantafx-modern-themes","04.java\u002Fpr2\u002F35.atlantafx-modern-themes",{"title":2750,"path":2751,"stem":2752},"Пакування та розповсюдження JavaFX-додатків","\u002Fjava\u002Fpr2\u002Fjar-packaging-distribution","04.java\u002Fpr2\u002F36.jar-packaging-distribution",{"title":2754,"icon":2755,"path":2756,"stem":2757,"children":2758,"page":59},"Python","i-devicon-python","\u002Fpython","05.python",[2759,2763,2766,2770,2774,2778,2782,2786,2790,2794,2798,2802,2806,2810,2814,2875],{"title":2760,"path":2761,"stem":2762},"Модулі, Пакети та Віртуальні Середовища","\u002Fpython\u002Fmodules-packages-venv","05.python\u002F00.modules-packages-venv",{"title":71,"path":2764,"stem":2765},"\u002Fpython\u002Fclasses-objects","05.python\u002F01.classes-objects",{"title":2767,"path":2768,"stem":2769},"Інкапсуляція, Керування Доступом та Властивості","\u002Fpython\u002Fencapsulation","05.python\u002F02.encapsulation",{"title":2771,"path":2772,"stem":2773},"Наслідування, MRO та суперсила super()","\u002Fpython\u002Finheritance-mro","05.python\u002F03.inheritance-mro",{"title":2775,"path":2776,"stem":2777},"Абстракція — ABC проти Статичних Протоколів (PEP 544)","\u002Fpython\u002Fabstraction-protocols","05.python\u002F04.abstraction-protocols",{"title":2779,"path":2780,"stem":2781},"Магічні методи (Dunder) та Емуляція протоколів","\u002Fpython\u002Fdunder-methods","05.python\u002F05.dunder-methods",{"title":2783,"path":2784,"stem":2785},"Декоратори та Керування життєвим циклом методів","\u002Fpython\u002Fdecorators-static-class","05.python\u002F06.decorators-static-class",{"title":2787,"path":2788,"stem":2789},"Дескриптори — Магія доступу до атрибутів","\u002Fpython\u002Fdescriptors","05.python\u002F07.descriptors",{"title":2791,"path":2792,"stem":2793},"Метакласи — Динамічне створення класів під капотом CPython","\u002Fpython\u002Fmetaclasses","05.python\u002F08.metaclasses",{"title":2795,"path":2796,"stem":2797},"Dataclasses, NamedTuple та сучасні контейнери Python","\u002Fpython\u002Fmodern-containers","05.python\u002F09.modern-containers",{"title":2799,"path":2800,"stem":2801},"GIL та модель конкурентності CPython — фундамент перед потоками і процесами","\u002Fpython\u002Fgil-concurrency-intro","05.python\u002F11.gil-concurrency-intro",{"title":2803,"path":2804,"stem":2805},"Threading — конкурентність для I\u002FO-bound задач","\u002Fpython\u002Fthreading","05.python\u002F12.threading",{"title":2807,"path":2808,"stem":2809},"Multiprocessing — справжній паралелізм для CPU-bound задач","\u002Fpython\u002Fmultiprocessing","05.python\u002F13.multiprocessing",{"title":2811,"path":2812,"stem":2813},"asyncio — кооперативна конкурентність та event loop","\u002Fpython\u002Fasyncio","05.python\u002F14.asyncio",{"title":2815,"icon":92,"path":2816,"stem":2817,"children":2818,"page":59},"FastAPI","\u002Fpython\u002Ffastapi","05.python\u002Ffastapi",[2819,2823,2827,2831,2835,2839,2843,2847,2851,2855,2859,2863,2867,2871],{"title":2820,"path":2821,"stem":2822},"Глибокий Typing та Pydantic v2 — від анотацій до валідації","\u002Fpython\u002Ffastapi\u002Ftyping-pydantic","05.python\u002Ffastapi\u002F15.typing-pydantic",{"title":2824,"path":2825,"stem":2826},"WSGI, ASGI та Python Web-екосистема","\u002Fpython\u002Ffastapi\u002Fwsgi-asgi-ecosystem","05.python\u002Ffastapi\u002F16.wsgi-asgi-ecosystem",{"title":2828,"path":2829,"stem":2830},"FastAPI: Перший додаток, Uvicorn та OpenAPI","\u002Fpython\u002Ffastapi\u002Ffastapi-intro","05.python\u002Ffastapi\u002F17.fastapi-intro",{"title":2832,"path":2833,"stem":2834},"Маршрутизація, параметри запитів та APIRouter","\u002Fpython\u002Ffastapi\u002Ffastapi-routing-params","05.python\u002Ffastapi\u002F18.fastapi-routing-params",{"title":2836,"path":2837,"stem":2838},"Pydantic v2 у FastAPI — схеми, валідація та серіалізація","\u002Fpython\u002Ffastapi\u002Ffastapi-pydantic-schemas","05.python\u002Ffastapi\u002F19.fastapi-pydantic-schemas",{"title":2840,"path":2841,"stem":2842},"Dependency Injection — серце архітектури FastAPI","\u002Fpython\u002Ffastapi\u002Ffastapi-dependency-injection","05.python\u002Ffastapi\u002F20.fastapi-dependency-injection",{"title":2844,"path":2845,"stem":2846},"Обробка помилок, Middleware та CORS у FastAPI","\u002Fpython\u002Ffastapi\u002Ffastapi-errors-middleware","05.python\u002Ffastapi\u002F21.fastapi-errors-middleware",{"title":2848,"path":2849,"stem":2850},"SQLAlchemy 2.0 — ORM, Core та Async Engine","\u002Fpython\u002Ffastapi\u002Fsqlalchemy-orm","05.python\u002Ffastapi\u002F22.sqlalchemy-orm",{"title":2852,"path":2853,"stem":2854},"Alembic — міграції бази даних","\u002Fpython\u002Ffastapi\u002Falembic-migrations","05.python\u002Ffastapi\u002F23.alembic-migrations",{"title":2856,"path":2857,"stem":2858},"Repository Pattern та Clean Architecture у FastAPI","\u002Fpython\u002Ffastapi\u002Ffastapi-repository-clean-arch","05.python\u002Ffastapi\u002F24.fastapi-repository-clean-arch",{"title":2860,"path":2861,"stem":2862},"Автентифікація та авторизація — JWT, OAuth2, RBAC","\u002Fpython\u002Ffastapi\u002Ffastapi-auth-security","05.python\u002Ffastapi\u002F25.fastapi-auth-security",{"title":2864,"path":2865,"stem":2866},"Тестування FastAPI — pytest, httpx, fixtures","\u002Fpython\u002Ffastapi\u002Ffastapi-testing","05.python\u002Ffastapi\u002F26.fastapi-testing",{"title":2868,"path":2869,"stem":2870},"Async на повну — Background Tasks, WebSockets, SSE та Celery","\u002Fpython\u002Ffastapi\u002Ffastapi-async-advanced","05.python\u002Ffastapi\u002F27.fastapi-async-advanced",{"title":2872,"path":2873,"stem":2874},"Deployment — Docker, CI\u002FCD, Monitoring","\u002Fpython\u002Ffastapi\u002Ffastapi-deployment","05.python\u002Ffastapi\u002F28.fastapi-deployment",{"title":2876,"path":2877,"stem":2878},"[object Object]","\u002Fpython\u002Foop-plan","05.python\u002Foop-plan",{"title":2880,"icon":2881,"path":2882,"stem":2883,"children":2884,"page":59},"Бази даних","i-lucide-database","\u002Fdatabases","06.databases",[2885,2915,2938,2975,3004,3022,3056,3068,3077],{"title":2886,"icon":2887,"path":2888,"stem":2889,"children":2890,"page":59},"Intro","i-lucide-play","\u002Fdatabases\u002Fintro","06.databases\u002F01.intro",[2891,2895,2899,2903,2907,2911],{"title":2892,"path":2893,"stem":2894},"Введення в теорію баз даних","\u002Fdatabases\u002Fintro\u002Fintroduction-to-databases","06.databases\u002F01.intro\u002F01.introduction-to-databases",{"title":2896,"path":2897,"stem":2898},"Реляційна модель даних","\u002Fdatabases\u002Fintro\u002Frelational-model-theory","06.databases\u002F01.intro\u002F02.relational-model-theory",{"title":2900,"path":2901,"stem":2902},"ER-моделювання","\u002Fdatabases\u002Fintro\u002Fer-modeling","06.databases\u002F01.intro\u002F03.er-modeling",{"title":2904,"path":2905,"stem":2906},"Логічне проектування БД","\u002Fdatabases\u002Fintro\u002Flogical-schema","06.databases\u002F01.intro\u002F04.logical-schema",{"title":2908,"path":2909,"stem":2910},"Класифікація таблиць","\u002Fdatabases\u002Fintro\u002Ftable-classification","06.databases\u002F01.intro\u002F05.table-classification",{"title":2912,"path":2913,"stem":2914},"PlantUML для баз даних","\u002Fdatabases\u002Fintro\u002Fplantuml-diagrams","06.databases\u002F01.intro\u002F06.plantuml-diagrams",{"title":2916,"icon":2881,"path":2917,"stem":2918,"children":2919,"page":59},"MS SQL Server Start","\u002Fdatabases\u002Fms-sql-server-start","06.databases\u002F02.ms-sql-server-start",[2920,2924,2930,2934],{"title":2921,"path":2922,"stem":2923},"Типи даних у MS SQL Server","\u002Fdatabases\u002Fms-sql-server-start\u002Fdata-types","06.databases\u002F02.ms-sql-server-start\u002F01.data-types",{"title":2925,"path":2926,"stem":2927,"children":2928},"Індекси у MS SQL Server","\u002Fdatabases\u002Fms-sql-server-start\u002Fsql-indexes","06.databases\u002F02.ms-sql-server-start\u002F02.sql-indexes",[2929],{"title":2925,"path":2926,"stem":2927},{"title":2931,"path":2932,"stem":2933},"Системні бази даних MS SQL Server","\u002Fdatabases\u002Fms-sql-server-start\u002Fsystem-databases","06.databases\u002F02.ms-sql-server-start\u002F03.system-databases",{"title":2935,"path":2936,"stem":2937},"Огляд мови SQL та запитів","\u002Fdatabases\u002Fms-sql-server-start\u002Fsql-queries-overview","06.databases\u002F02.ms-sql-server-start\u002F04.sql-queries-overview",{"title":2939,"icon":2881,"path":2940,"stem":2941,"children":2942,"page":59},"SQL","\u002Fdatabases\u002Fsql","06.databases\u002F03.sql",[2943,2947,2951,2955,2959,2963,2967,2971],{"title":2944,"path":2945,"stem":2946},"Налаштування демонстраційної бази даних","\u002Fdatabases\u002Fsql\u002Fsample-database-setup","06.databases\u002F03.sql\u002F00.sample-database-setup",{"title":2948,"path":2949,"stem":2950},"DDL - Створення таблиць (CREATE TABLE)","\u002Fdatabases\u002Fsql\u002Fddl-create-table","06.databases\u002F03.sql\u002F01.ddl-create-table",{"title":2952,"path":2953,"stem":2954},"DDL - Зміна та видалення таблиць (ALTER, DROP)","\u002Fdatabases\u002Fsql\u002Fddl-alter-drop-table","06.databases\u002F03.sql\u002F02.ddl-alter-drop-table",{"title":2956,"path":2957,"stem":2958},"SELECT запити - Основи","\u002Fdatabases\u002Fsql\u002Fselect-queries-fundamentals","06.databases\u002F03.sql\u002F03.select-queries-fundamentals",{"title":2960,"path":2961,"stem":2962},"SELECT запити - Розширені можливості","\u002Fdatabases\u002Fsql\u002Fselect-queries-advanced","06.databases\u002F03.sql\u002F04.select-queries-advanced",{"title":2964,"path":2965,"stem":2966},"INSERT запити - Додавання даних","\u002Fdatabases\u002Fsql\u002Finsert-queries","06.databases\u002F03.sql\u002F05.insert-queries",{"title":2968,"path":2969,"stem":2970},"UPDATE та DELETE запити","\u002Fdatabases\u002Fsql\u002Fupdate-delete-queries","06.databases\u002F03.sql\u002F06.update-delete-queries",{"title":2972,"path":2973,"stem":2974},"Транзакції в SQL","\u002Fdatabases\u002Fsql\u002Ftransactions","06.databases\u002F03.sql\u002F07.transactions",{"title":2976,"icon":2881,"path":2977,"stem":2978,"children":2979,"page":59},"Multi Table Databases","\u002Fdatabases\u002Fmulti-table-databases","06.databases\u002F04.multi-table-databases",[2980,2984,2988,2992,2996,3000],{"title":2981,"path":2982,"stem":2983},"Зв'язки та нормалізація БД","\u002Fdatabases\u002Fmulti-table-databases\u002Frelationships-and-normalization","06.databases\u002F04.multi-table-databases\u002F00.relationships-and-normalization",{"title":2985,"path":2986,"stem":2987},"INNER JOIN - З'єднання таблиць","\u002Fdatabases\u002Fmulti-table-databases\u002Finner-join","06.databases\u002F04.multi-table-databases\u002F01.inner-join",{"title":2989,"path":2990,"stem":2991},"OUTER JOINs - LEFT, RIGHT, FULL","\u002Fdatabases\u002Fmulti-table-databases\u002Fouter-joins","06.databases\u002F04.multi-table-databases\u002F02.outer-joins",{"title":2993,"path":2994,"stem":2995},"CROSS та SELF JOINs","\u002Fdatabases\u002Fmulti-table-databases\u002Fcross-self-joins","06.databases\u002F04.multi-table-databases\u002F03.cross-self-joins",{"title":2997,"path":2998,"stem":2999},"Підзапити (Subqueries)","\u002Fdatabases\u002Fmulti-table-databases\u002Fsubqueries","06.databases\u002F04.multi-table-databases\u002F04.subqueries",{"title":3001,"path":3002,"stem":3003},"Агрегації з JOIN","\u002Fdatabases\u002Fmulti-table-databases\u002Faggregations-with-joins","06.databases\u002F04.multi-table-databases\u002F05.aggregations-with-joins",{"title":3005,"icon":3006,"path":3007,"stem":3008,"children":3009,"page":59},"Aggregate Functions","i-lucide-calculator","\u002Fdatabases\u002Faggregate-functions","06.databases\u002F05.aggregate-functions",[3010,3014,3018],{"title":3011,"path":3012,"stem":3013},"Функції агрегування в MS SQL Server","\u002Fdatabases\u002Faggregate-functions\u002Fintroduction-aggregate-functions","06.databases\u002F05.aggregate-functions\u002F01.introduction-aggregate-functions",{"title":3015,"path":3016,"stem":3017},"Групування даних в MS SQL Server","\u002Fdatabases\u002Faggregate-functions\u002Fgrouping-data","06.databases\u002F05.aggregate-functions\u002F02.grouping-data",{"title":3019,"path":3020,"stem":3021},"Підзапити з агрегатними функціями","\u002Fdatabases\u002Faggregate-functions\u002Fsubqueries-aggregates","06.databases\u002F05.aggregate-functions\u002F03.subqueries-aggregates",{"title":3023,"icon":3024,"path":3025,"stem":3026,"children":3027,"page":59},"Тригери та зберігаємі процедури","i-lucide-database-zap","\u002Fdatabases\u002Ftriggers-stored-procedures","06.databases\u002F07.triggers-stored-procedures",[3028,3032,3036,3040,3044,3048,3052],{"title":3029,"path":3030,"stem":3031},"DML-тригери","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Fdml-triggers","06.databases\u002F07.triggers-stored-procedures\u002F01.dml-triggers",{"title":3033,"path":3034,"stem":3035},"DDL-тригери","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Fddl-triggers","06.databases\u002F07.triggers-stored-procedures\u002F02.ddl-triggers",{"title":3037,"path":3038,"stem":3039},"Transact-SQL розширення","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Ftransact-sql-extensions","06.databases\u002F07.triggers-stored-procedures\u002F03.transact-sql-extensions",{"title":3041,"path":3042,"stem":3043},"Транзакції","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Ftransactions","06.databases\u002F07.triggers-stored-procedures\u002F04.transactions",{"title":3045,"path":3046,"stem":3047},"Зберігаємі процедури","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Fstored-procedures","06.databases\u002F07.triggers-stored-procedures\u002F05.stored-procedures",{"title":3049,"path":3050,"stem":3051},"Користувацькі функції","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Fuser-defined-functions","06.databases\u002F07.triggers-stored-procedures\u002F06.user-defined-functions",{"title":3053,"path":3054,"stem":3055},"Безпека баз даних","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Fsecurity","06.databases\u002F07.triggers-stored-procedures\u002F08.security",{"title":3053,"icon":793,"path":3057,"stem":3058,"children":3059,"page":59},"\u002Fdatabases\u002Fsecurity","06.databases\u002F08.security",[3060,3064],{"title":3061,"path":3062,"stem":3063},"Вступ до безпеки баз даних","\u002Fdatabases\u002Fsecurity\u002Fintroduction","06.databases\u002F08.security\u002F01.introduction",{"title":3065,"path":3066,"stem":3067},"Системні представлення та метадані","\u002Fdatabases\u002Fsecurity\u002Fsystem-views","06.databases\u002F08.security\u002F02.system-views",{"title":3069,"icon":3070,"path":3071,"stem":3072,"children":3073,"page":59},"Резервне копіювання та відновлення","i-lucide-database-backup","\u002Fdatabases\u002Fbackup-recovery","06.databases\u002F09.backup-recovery",[3074],{"title":3069,"path":3075,"stem":3076},"\u002Fdatabases\u002Fbackup-recovery\u002Fbackup-restore","06.databases\u002F09.backup-recovery\u002F01.backup-restore",{"title":3078,"icon":3079,"path":3080,"stem":3081,"children":3082,"page":59},"Повнотекстовий пошук","i-lucide-search","\u002Fdatabases\u002Ffull-text-search","06.databases\u002F10.full-text-search",[3083],{"title":3078,"path":3084,"stem":3085},"\u002Fdatabases\u002Ffull-text-search\u002Ffull-text-search","06.databases\u002F10.full-text-search\u002F01.full-text-search",{"title":3087,"icon":3088,"path":3089,"stem":3090,"children":3091,"page":59},"Tools","i-lucide-wrench","\u002Ftools","07.tools",[3092,3168],{"title":3093,"icon":3094,"path":3095,"stem":3096,"children":3097},"Docker","i-simple-icons-docker","\u002Ftools\u002Fdocker","07.tools\u002F01.docker\u002Findex",[3098,3100,3104,3108,3112,3116,3120,3124,3128,3132,3136,3140,3144,3148,3152,3156,3160,3164],{"title":3099,"path":3095,"stem":3096},"Docker: від нуля до production",{"title":3101,"path":3102,"stem":3103},"Контейнеризація — від проблеми до рішення","\u002Ftools\u002Fdocker\u002Fcontainerization-concept","07.tools\u002F01.docker\u002F01.containerization-concept",{"title":3105,"path":3106,"stem":3107},"Docker — що це і навіщо?","\u002Ftools\u002Fdocker\u002Fdocker-what-and-why","07.tools\u002F01.docker\u002F02.docker-what-and-why",{"title":3109,"path":3110,"stem":3111},"Архітектура Docker Engine","\u002Ftools\u002Fdocker\u002Fdocker-architecture","07.tools\u002F01.docker\u002F03.docker-architecture",{"title":3113,"path":3114,"stem":3115},"Встановлення Docker","\u002Ftools\u002Fdocker\u002Finstallation","07.tools\u002F01.docker\u002F04.installation",{"title":3117,"path":3118,"stem":3119},"Перший контейнер — docker run","\u002Ftools\u002Fdocker\u002Ffirst-container","07.tools\u002F01.docker\u002F05.first-container",{"title":3121,"path":3122,"stem":3123},"Життєвий цикл контейнера","\u002Ftools\u002Fdocker\u002Fcontainer-lifecycle","07.tools\u002F01.docker\u002F06.container-lifecycle",{"title":3125,"path":3126,"stem":3127},"Docker Images — фундаментальні концепції","\u002Ftools\u002Fdocker\u002Fdocker-images-fundamentals","07.tools\u002F01.docker\u002F07.docker-images-fundamentals",{"title":3129,"path":3130,"stem":3131},"Dockerfile — основи","\u002Ftools\u002Fdocker\u002Fdockerfile-basics","07.tools\u002F01.docker\u002F08.dockerfile-basics",{"title":3133,"path":3134,"stem":3135},"Dockerfile — просунуті техніки","\u002Ftools\u002Fdocker\u002Fdockerfile-advanced","07.tools\u002F01.docker\u002F09.dockerfile-advanced",{"title":3137,"path":3138,"stem":3139},"Build Context та кешування шарів","\u002Ftools\u002Fdocker\u002Fbuild-context-and-cache","07.tools\u002F01.docker\u002F10.build-context-and-cache",{"title":3141,"path":3142,"stem":3143},"Реєстри Docker-образів","\u002Ftools\u002Fdocker\u002Fimage-registries","07.tools\u002F01.docker\u002F11.image-registries",{"title":3145,"path":3146,"stem":3147},"Контейнеризація .NET додатків","\u002Ftools\u002Fdocker\u002Fdotnet-containerization","07.tools\u002F01.docker\u002F12.dotnet-containerization",{"title":3149,"path":3150,"stem":3151},"Томи та збереження даних","\u002Ftools\u002Fdocker\u002Fvolumes-and-data","07.tools\u002F01.docker\u002F13.volumes-and-data",{"title":3153,"path":3154,"stem":3155},"Основи мережі в Docker","\u002Ftools\u002Fdocker\u002Fnetworking-basics","07.tools\u002F01.docker\u002F14.networking-basics",{"title":3157,"path":3158,"stem":3159},"Змінні оточення та конфігурація","\u002Ftools\u002Fdocker\u002Fenvironment-and-configuration","07.tools\u002F01.docker\u002F15.environment-and-configuration",{"title":3161,"path":3162,"stem":3163},"Docker Compose — оркестрація контейнерів","\u002Ftools\u002Fdocker\u002Fdocker-compose-basics","07.tools\u002F01.docker\u002F16.docker-compose-basics",{"title":3165,"path":3166,"stem":3167},"Docker Compose — Multi-Service застосунки","\u002Ftools\u002Fdocker\u002Fcompose-multi-service","07.tools\u002F01.docker\u002F17.compose-multi-service",{"title":3169,"icon":3170,"path":3171,"stem":3172,"children":3173},"Kubernetes","simple-icons:kubernetes","\u002Ftools\u002Fkubernetes","07.tools\u002F02.kubernetes\u002Findex",[3174,3176,3180,3184,3188,3192,3196,3200,3204],{"title":3175,"path":3171,"stem":3172},"Kubernetes: від розробки до production",{"title":3177,"path":3178,"stem":3179},"Kubernetes — коли Docker Compose більше не вистачає","\u002Ftools\u002Fkubernetes\u002Fwhy-kubernetes","07.tools\u002F02.kubernetes\u002F01.why-kubernetes",{"title":3181,"path":3182,"stem":3183},"Архітектура Kubernetes — анатомія кластера","\u002Ftools\u002Fkubernetes\u002Fkubernetes-architecture","07.tools\u002F02.kubernetes\u002F02.kubernetes-architecture",{"title":3185,"path":3186,"stem":3187},"Локальне середовище — minikube, kind та k3s","\u002Ftools\u002Fkubernetes\u002Flocal-environment","07.tools\u002F02.kubernetes\u002F03.local-environment",{"title":3189,"path":3190,"stem":3191},"Pod — атомарна одиниця Kubernetes","\u002Ftools\u002Fkubernetes\u002Fpods-and-containers","07.tools\u002F02.kubernetes\u002F04.pods-and-containers",{"title":3193,"path":3194,"stem":3195},"Патерни використання Pod","\u002Ftools\u002Fkubernetes\u002Fpod-patterns","07.tools\u002F02.kubernetes\u002F05.pod-patterns",{"title":3197,"path":3198,"stem":3199},"Deployment — декларативне управління Pod","\u002Ftools\u002Fkubernetes\u002Fdeployment-basics","07.tools\u002F02.kubernetes\u002F06.deployment-basics",{"title":3201,"path":3202,"stem":3203},"Rolling Updates та управління життєвим циклом Deployment","\u002Ftools\u002Fkubernetes\u002Fdeployment-rolling-updates","07.tools\u002F02.kubernetes\u002F07.deployment-rolling-updates",{"title":3205,"path":3206,"stem":3207},"Service — мережева абстракція для Pod","\u002Ftools\u002Fkubernetes\u002Fservices-networking","07.tools\u002F02.kubernetes\u002F08.services-networking",{"title":3209,"icon":3210,"path":3211,"stem":3212,"children":3213,"page":59},"Software Engineering","i-lucide-code-2","\u002Fsoftware-engineering","09.software-engineering",[3214,3218,3222,3226,3230,3234,3238,3242,3246,3250,3254],{"title":3215,"path":3216,"stem":3217},"1. Аналіз предметної області. Експертні знання та складність","\u002Fsoftware-engineering\u002Fintro-subdomains","09.software-engineering\u002F01.intro-subdomains",{"title":3219,"path":3220,"stem":3221},"2. Обмежені контексти. Інтеграція обмежених контекстів","\u002Fsoftware-engineering\u002Fintegrating-limited-contexts","09.software-engineering\u002F02.integrating-limited-contexts",{"title":3223,"path":3224,"stem":3225},"3. Реалізація простої бізнес-логіки","\u002Fsoftware-engineering\u002Fsimple","09.software-engineering\u002F03.simple",{"title":3227,"path":3228,"stem":3229},"4. Опрацювання складної бізнес-логіки","\u002Fsoftware-engineering\u002Fcomplex-business-logic","09.software-engineering\u002F04.complex-business-logic",{"title":3231,"path":3232,"stem":3233},"5. Моделювання фактора часу. Подієво-орієнтована архітектура.","\u002Fsoftware-engineering\u002Fmodelling-the-time-factor","09.software-engineering\u002F05.modelling-the-time-factor",{"title":3235,"path":3236,"stem":3237},"6. Архітектурні патерни","\u002Fsoftware-engineering\u002Farchitectural-patterns","09.software-engineering\u002F06.architectural-patterns",{"title":3239,"path":3240,"stem":3241},"Паттерни взаємодії","\u002Fsoftware-engineering\u002Fpatterns-of-interaction","09.software-engineering\u002F07.patterns-of-interaction",{"title":3243,"path":3244,"stem":3245},"Евристика проєктування","\u002Fsoftware-engineering\u002Fdesign-heuristics","09.software-engineering\u002F08.design-heuristics",{"title":3247,"path":3248,"stem":3249},"Еволюція проєктних рішень","\u002Fsoftware-engineering\u002Fevolution-of-design-solutions","09.software-engineering\u002F09.evolution-of-design-solutions",{"title":3251,"path":3252,"stem":3253},"EventStorming","\u002Fsoftware-engineering\u002Feventstorming","09.software-engineering\u002F10.eventstorming",{"title":3255,"path":3256,"stem":3257},"DDD на практиці","\u002Fsoftware-engineering\u002Fddd-in-practice","09.software-engineering\u002F11.ddd-in-practice",{"title":3259,"icon":943,"path":3260,"stem":3261,"children":3262,"page":59},"DDD","\u002Fddd","10.ddd",[3263,3267,3271,3275,3279,3283,3287,3291,3295,3299,3303,3307,3311],{"title":3264,"path":3265,"stem":3266},"Аналіз предметної області","\u002Fddd\u002Fdomain-analysis","10.ddd\u002F01.domain-analysis",{"title":3268,"path":3269,"stem":3270},"Експертні знання про предметну область","\u002Fddd\u002Fdomain-expert-knowledge","10.ddd\u002F02.domain-expert-knowledge",{"title":3272,"path":3273,"stem":3274},"Як осмислити складність предметної області","\u002Fddd\u002Fmanaging-domain-complexity","10.ddd\u002F03.managing-domain-complexity",{"title":3276,"path":3277,"stem":3278},"Інтеграція обмежених контекстів","\u002Fddd\u002Fbounded-context-integration","10.ddd\u002F04.bounded-context-integration",{"title":3280,"path":3281,"stem":3282},"Реалізація простої бізнес-логіки","\u002Fddd\u002Fsimple-business-logic","10.ddd\u002F05.simple-business-logic",{"title":3284,"path":3285,"stem":3286},"Обробка складної бізнес-логіки","\u002Fddd\u002Fcomplex-business-logic","10.ddd\u002F06.complex-business-logic",{"title":3288,"path":3289,"stem":3290},"Моделювання фактора часу","\u002Fddd\u002Ftime-modeling","10.ddd\u002F07.time-modeling",{"title":3292,"path":3293,"stem":3294},"Глава 8. Архітектурні Патерни","\u002Fddd\u002Farchitectural-patterns","10.ddd\u002F08.architectural-patterns",{"title":3296,"path":3297,"stem":3298},"Глава 9. Патерни Взаємодії","\u002Fddd\u002Finteraction-patterns","10.ddd\u002F09.interaction-patterns",{"title":3300,"path":3301,"stem":3302},"Глава 10. Проектні Евристики","\u002Fddd\u002Fdesign-heuristics","10.ddd\u002F10.design-heuristics",{"title":3304,"path":3305,"stem":3306},"Глава 11. Еволюція Проектних Рішень","\u002Fddd\u002Fevolution-of-design-decisions","10.ddd\u002F11.evolution-of-design-decisions",{"title":3308,"path":3309,"stem":3310},"Глава 12. EventStorming","\u002Fddd\u002Fevent-storming","10.ddd\u002F12.event-storming",{"title":3312,"path":3313,"stem":3314},"Глава 13. DDD на Практиці","\u002Fddd\u002Fddd-in-practice","10.ddd\u002F13.ddd-in-practice",{"title":3316,"icon":3317,"path":3318,"stem":3319,"children":3320,"page":59},"Media Streaming","i-lucide-video","\u002Fmedia-streaming","11.media-streaming",[3321,3325,3329,3333,3337,3341,3345],{"title":3322,"path":3323,"stem":3324},"01. Магія Стрімінгу: Що відбувається, коли ви натискаєте \"Play\"","\u002Fmedia-streaming\u002Fintroduction","11.media-streaming\u002F01.introduction",{"title":3326,"path":3327,"stem":3328},"02. Анатомія Медіа: Кодеки, Контейнери та Стиснення","\u002Fmedia-streaming\u002Faudio-video-anatomy","11.media-streaming\u002F02.audio-video-anatomy",{"title":3330,"path":3331,"stem":3332},"03. The Gym: FFmpeg Deep Dive","\u002Fmedia-streaming\u002Fffmpeg-gym","11.media-streaming\u002F03.ffmpeg-gym",{"title":3334,"path":3335,"stem":3336},"04. HLS Protocol: HTTP Live Streaming у Деталях","\u002Fmedia-streaming\u002Fhls-protocol","11.media-streaming\u002F04.hls-protocol",{"title":3338,"path":3339,"stem":3340},"05. DASH Protocol: Відкритий Стандарт","\u002Fmedia-streaming\u002Fdash-protocol","11.media-streaming\u002F05.dash-protocol",{"title":3342,"path":3343,"stem":3344},"06. Масштабування: CDN та Adaptive Bitrate","\u002Fmedia-streaming\u002Fcdn-and-adaptive-bitrate","11.media-streaming\u002F06.cdn-and-adaptive-bitrate",{"title":3346,"path":3347,"stem":3348},"07. Війна із Затримкою (Latency)","\u002Fmedia-streaming\u002Frealtime-latency","11.media-streaming\u002F07.realtime-latency",{"title":3350,"icon":3351,"path":3352,"stem":3353,"children":3354,"page":59},"HTML & CSS","i-devicon-html5","\u002Fhtml-css","12.html-css",[3355,3359,3363,3367,3371,3375,3379,3383,3387,3391,3395,3399,3403,3407,3411,3415,3419,3423,3427,3431,3435,3439,3443,3447,3451,3455,3459,3463,3467,3471],{"title":3356,"path":3357,"stem":3358},"Вступ до HTML. Структура документа","\u002Fhtml-css\u002Fintro-html-structure","12.html-css\u002F01.intro-html-structure",{"title":3360,"path":3361,"stem":3362},"Форматування тексту в HTML","\u002Fhtml-css\u002Fhtml-text-formatting","12.html-css\u002F02.html-text-formatting",{"title":3364,"path":3365,"stem":3366},"Посилання та зображення в HTML","\u002Fhtml-css\u002Fhtml-links-images","12.html-css\u002F03.html-links-images",{"title":3368,"path":3369,"stem":3370},"Списки та таблиці в HTML","\u002Fhtml-css\u002Fhtml-lists-tables","12.html-css\u002F04.html-lists-tables",{"title":3372,"path":3373,"stem":3374},"Форми в HTML","\u002Fhtml-css\u002Fhtml-forms","12.html-css\u002F05.html-forms",{"title":3376,"path":3377,"stem":3378},"Семантичні елементи HTML5","\u002Fhtml-css\u002Fhtml-semantic-elements","12.html-css\u002F06.html-semantic-elements",{"title":3380,"path":3381,"stem":3382},"Мультимедіа та розширені елементи HTML","\u002Fhtml-css\u002Fhtml-multimedia-advanced","12.html-css\u002F07.html-multimedia-advanced",{"title":3384,"path":3385,"stem":3386},"Мікророзмітка та SEO в HTML","\u002Fhtml-css\u002Fhtml-microdata-seo","12.html-css\u002F08.html-microdata-seo",{"title":3388,"path":3389,"stem":3390},"Вступ до CSS. Селектори та специфічність","\u002Fhtml-css\u002Fcss-intro-selectors","12.html-css\u002F09.css-intro-selectors",{"title":3392,"path":3393,"stem":3394},"Блокова модель CSS. Відступи. Box Sizing","\u002Fhtml-css\u002Fcss-box-model","12.html-css\u002F10.css-box-model",{"title":3396,"path":3397,"stem":3398},"Розміри у CSS: повний довідник одиниць і ключових слів","\u002Fhtml-css\u002F10a.css-sizing","12.html-css\u002F10a.css-sizing",{"title":3400,"path":3401,"stem":3402},"Типографіка в CSS. Шрифти та текст","\u002Fhtml-css\u002Fcss-typography","12.html-css\u002F11.css-typography",{"title":3404,"path":3405,"stem":3406},"Кольори та фони в CSS","\u002Fhtml-css\u002Fcss-colors-backgrounds","12.html-css\u002F12.css-colors-backgrounds",{"title":3408,"path":3409,"stem":3410},"Тіні та фільтри в CSS","\u002Fhtml-css\u002F12b.css-shadows-filters","12.html-css\u002F12b.css-shadows-filters",{"title":3412,"path":3413,"stem":3414},"CSS Flexbox: Фундамент гнучких макетів","\u002Fhtml-css\u002Fcss-flexbox-fundamentals","12.html-css\u002F13.css-flexbox-fundamentals",{"title":3416,"path":3417,"stem":3418},"CSS Flexbox: Вирівнювання та Позиціонування","\u002Fhtml-css\u002Fcss-flexbox-alignment-sizing-and-patterns","12.html-css\u002F14.css-flexbox-alignment-sizing-and-patterns",{"title":3420,"path":3421,"stem":3422},"CSS Grid. Двовимірний макет. Частина 1","\u002Fhtml-css\u002Fcss-layout-grid","12.html-css\u002F15.css-layout-grid",{"title":3424,"path":3425,"stem":3426},"CSS Grid. Двовимірний макет. Частина 2","\u002Fhtml-css\u002Fcss-layout-grid-advanced","12.html-css\u002F16.css-layout-grid-advanced",{"title":3428,"path":3429,"stem":3430},"Позиціонування в CSS. Z-index. Stacking Context","\u002Fhtml-css\u002Fcss-positioning","12.html-css\u002F17.css-positioning",{"title":3432,"path":3433,"stem":3434},"CSS Анімації та Переходи","\u002Fhtml-css\u002Fcss-animations-transitions","12.html-css\u002F18.css-animations-transitions",{"title":3436,"path":3437,"stem":3438},"Адаптивний дизайн. Media Queries. Частина 1","\u002Fhtml-css\u002Fcss-responsive-media-queries","12.html-css\u002F19.css-responsive-media-queries",{"title":3440,"path":3441,"stem":3442},"Адаптивний дизайн. Частина 2: clamp(), Container Queries, @layer","\u002Fhtml-css\u002Fcss-responsive-advanced","12.html-css\u002F20.css-responsive-advanced",{"title":3444,"path":3445,"stem":3446},"CSS Custom Properties. Методології. Сучасний CSS","\u002Fhtml-css\u002Fcss-variables-methodologies","12.html-css\u002F21.css-variables-methodologies",{"title":3448,"path":3449,"stem":3450},"Сучасний CSS 2023–2025: Нові можливості","\u002Fhtml-css\u002Fcss-modern-features","12.html-css\u002F22.css-modern-features",{"title":3452,"path":3453,"stem":3454},"CSS Nesting, @layer, @scope та @property: нативний препроцесор","\u002Fhtml-css\u002F22a.css-nesting-modern-syntax","12.html-css\u002F22a.css-nesting-modern-syntax",{"title":3456,"path":3457,"stem":3458},"CSS для форм та інтерактивних станів","\u002Fhtml-css\u002Fcss-forms-interactive-states","12.html-css\u002F23.css-forms-interactive-states",{"title":3460,"path":3461,"stem":3462},"Доступність у CSS (CSS Accessibility)","\u002Fhtml-css\u002Fcss-accessibility","12.html-css\u002F24.css-accessibility",{"title":3464,"path":3465,"stem":3466},"CSS-функції та сучасні sizing primitives","\u002Fhtml-css\u002Fcss-functions-sizing","12.html-css\u002F25.css-functions-sizing",{"title":3468,"path":3469,"stem":3470},"Rendering Pipeline і CSS Performance","\u002Fhtml-css\u002Fcss-rendering-performance","12.html-css\u002F26.css-rendering-performance",{"title":3472,"path":3473,"stem":3474},"CSS Best Practices: типові ситуації та правильні рішення","\u002Fhtml-css\u002Fcss-best-practices","12.html-css\u002F27.css-best-practices",{"title":3476,"path":3477,"stem":3478,"children":3479,"page":59},"AWS","\u002Faws","13.aws",[3480,3484,3488,3492,3496,3500,3504,3508,3512,3516,3520,3524,3528,3532,3536,3540,3544,3548],{"title":3481,"path":3482,"stem":3483},"Реєстрація AWS акаунту та студентські програми","\u002Faws\u002Faccount-registration","13.aws\u002F00.account-registration",{"title":3485,"path":3486,"stem":3487},"Вступ до хмарних обчислень та AWS","\u002Faws\u002Fintroduction-to-cloud","13.aws\u002F01.introduction-to-cloud",{"title":3489,"path":3490,"stem":3491},"AWS IAM — Identity and Access Management","\u002Faws\u002Fiam","13.aws\u002F02.iam",{"title":3493,"path":3494,"stem":3495},"AWS IAM CLI — Довідник команд","\u002Faws\u002F02a.iam-doc","13.aws\u002F02a.iam-doc",{"title":3497,"path":3498,"stem":3499},"Docker та контейнеризація в AWS — ECR, ECS та Fargate","\u002Faws\u002Fdocker-ecs","13.aws\u002F03.docker-ecs",{"title":3501,"path":3502,"stem":3503},"AWS ECR \u002F ECS CLI — Довідник команд","\u002Faws\u002F03a.docker-ecs-doc","13.aws\u002F03a.docker-ecs-doc",{"title":3505,"path":3506,"stem":3507},"Amazon EC2 — Elastic Compute Cloud","\u002Faws\u002Fec2","13.aws\u002F04.ec2",{"title":3509,"path":3510,"stem":3511},"AWS EC2 CLI — Довідник команд","\u002Faws\u002F04a.ec2-doc","13.aws\u002F04a.ec2-doc",{"title":3513,"path":3514,"stem":3515},"Elastic Load Balancing та Auto Scaling","\u002Faws\u002Falb-asg","13.aws\u002F05.alb-asg",{"title":3517,"path":3518,"stem":3519},"Amazon S3 — Simple Storage Service","\u002Faws\u002Fs3","13.aws\u002F06.s3",{"title":3521,"path":3522,"stem":3523},"Amazon CloudFront — Content Delivery Network","\u002Faws\u002Fcloudfront","13.aws\u002F07.cloudfront",{"title":3525,"path":3526,"stem":3527},"Amazon RDS — Relational Database Service","\u002Faws\u002Frds","13.aws\u002F08.rds",{"title":3529,"path":3530,"stem":3531},"Amazon DynamoDB — NoSQL Database","\u002Faws\u002Fdynamodb","13.aws\u002F09.dynamodb",{"title":3533,"path":3534,"stem":3535},"AWS Lambda та Serverless Compute","\u002Faws\u002Flambda","13.aws\u002F10.lambda",{"title":3537,"path":3538,"stem":3539},"Amazon Bedrock - Foundation Models, RAG та Agents","\u002Faws\u002Fbedrock","13.aws\u002F22.bedrock",{"title":3541,"path":3542,"stem":3543},"Amazon Rekognition - Комп'ютерний зір","\u002Faws\u002Frekognition","13.aws\u002F23.rekognition",{"title":3545,"path":3546,"stem":3547},"Amazon Textract - Інтелектуальний аналіз документів","\u002Faws\u002Ftextract","13.aws\u002F24.textract",{"title":3549,"path":3550,"stem":3551},"Amazon Polly, Transcribe, Comprehend та Translate","\u002Faws\u002Faudio-nlp-services","13.aws\u002F25.audio-nlp-services",{"title":3553,"path":3554,"stem":3555,"children":3556,"page":59},"Ai Development","\u002Fai-development","14.ai-development",[3557],{"title":3558,"path":3559,"stem":3560,"children":3561,"page":59},"Foundations","\u002Fai-development\u002Ffoundations","14.ai-development\u002F00.foundations",[3562],{"title":3563,"path":3564,"stem":3565},"Модуль 0.1. Що таке Large Language Model (LLM)","\u002Fai-development\u002Ffoundations\u002Fwhat-is-llm","14.ai-development\u002F00.foundations\u002F01.what-is-llm",{"title":3567,"path":3568,"stem":3569,"children":3570,"page":59},"React Native","\u002Freact-native","15.react-native",[3571,3592],{"title":3572,"path":3573,"stem":3574,"children":3575,"page":59},"Version1","\u002Freact-native\u002Fversion1","15.react-native\u002Fversion1",[3576,3580,3584,3588],{"title":3577,"path":3578,"stem":3579},"Що таке React Native","\u002Freact-native\u002Fversion1\u002Fwhat-is-react-native","15.react-native\u002Fversion1\u002F01.what-is-react-native",{"title":3581,"path":3582,"stem":3583},"Як влаштований React Native «під капотом»","\u002Freact-native\u002Fversion1\u002Freact-native-architecture","15.react-native\u002Fversion1\u002F02.react-native-architecture",{"title":3585,"path":3586,"stem":3587},"Від React до React Native: ключові відмінності","\u002Freact-native\u002Fversion1\u002Freact-native-vs-react","15.react-native\u002Fversion1\u002F03.react-native-vs-react",{"title":3589,"path":3590,"stem":3591},"View та Text — фундаментальні будівельні блоки","\u002Freact-native\u002Fversion1\u002Fview-and-text","15.react-native\u002Fversion1\u002F04.view-and-text",{"title":3593,"path":3594,"stem":3595,"children":3596,"page":59},"Version2","\u002Freact-native\u002Fversion2","15.react-native\u002Fversion2",[3597,3601,3605,3609,3613,3617,3621,3625,3629,3633,3637,3641,3645,3649,3653,3657,3661,3665,3669,3673,3677,3681,3685,3689,3693,3697,3701],{"title":3598,"path":3599,"stem":3600},"React Native — навіщо він потрібен","\u002Freact-native\u002Fversion2\u002Fwhy-react-native","15.react-native\u002Fversion2\u002F01.why-react-native",{"title":3602,"path":3603,"stem":3604},"Налаштування середовища розробки","\u002Freact-native\u002Fversion2\u002Fenvironment-setup","15.react-native\u002Fversion2\u002F02.environment-setup",{"title":3606,"path":3607,"stem":3608},"Expo і класичний React Native — два шляхи одного фреймворку","\u002Freact-native\u002Fversion2\u002Fexpo-vs-cli-landscape","15.react-native\u002Fversion2\u002F03.expo-vs-cli-landscape",{"title":3610,"path":3611,"stem":3612},"Середовище Expo — перший запуск","\u002Freact-native\u002Fversion2\u002Fexpo-setup-and-tooling","15.react-native\u002Fversion2\u002F04.expo-setup-and-tooling",{"title":3614,"path":3615,"stem":3616},"Структура проєкту та перші UI-примітиви","\u002Freact-native\u002Fversion2\u002Fproject-structure-and-conventions","15.react-native\u002Fversion2\u002F05.project-structure-and-conventions",{"title":3618,"path":3619,"stem":3620},"Базові компоненти React Native","\u002Freact-native\u002Fversion2\u002Fcore-components","15.react-native\u002Fversion2\u002F06.core-components",{"title":3622,"path":3623,"stem":3624},"Flexbox і layout у React Native","\u002Freact-native\u002Fversion2\u002Fflexbox-and-layout","15.react-native\u002Fversion2\u002F07.flexbox-and-layout",{"title":3626,"path":3627,"stem":3628},"StyleSheet і теми (light \u002F dark)","\u002Freact-native\u002Fversion2\u002Fstylesheet-and-theming","15.react-native\u002Fversion2\u002F08.stylesheet-and-theming",{"title":3630,"path":3631,"stem":3632},"Списки та віртуалізація","\u002Freact-native\u002Fversion2\u002Flists-and-virtualization","15.react-native\u002Fversion2\u002F09.lists-and-virtualization",{"title":3634,"path":3635,"stem":3636},"Форми, ввід і валідація","\u002Freact-native\u002Fversion2\u002Fforms-input-validation","15.react-native\u002Fversion2\u002F10.forms-input-validation",{"title":3638,"path":3639,"stem":3640},"Основи Expo Router","\u002Freact-native\u002Fversion2\u002Fexpo-router-basics","15.react-native\u002Fversion2\u002F11.expo-router-basics",{"title":3642,"path":3643,"stem":3644},"Вкладені навігатори та модалки","\u002Freact-native\u002Fversion2\u002Fnested-navigators-and-modals","15.react-native\u002Fversion2\u002F12.nested-navigators-and-modals",{"title":3646,"path":3647,"stem":3648},"Deep linking і параметри маршрутів","\u002Freact-native\u002Fversion2\u002Fdeep-linking-and-params","15.react-native\u002Fversion2\u002F13.deep-linking-and-params",{"title":3650,"path":3651,"stem":3652},"Робота з мережею та життєвий цикл застосунку","\u002Freact-native\u002Fversion2\u002Fnetworking-and-app-lifecycle","15.react-native\u002Fversion2\u002F14.networking-and-app-lifecycle",{"title":3654,"path":3655,"stem":3656},"Redux Toolkit на мобільних платформах","\u002Freact-native\u002Fversion2\u002Fredux-toolkit-on-mobile","15.react-native\u002Fversion2\u002F15.redux-toolkit-on-mobile",{"title":3658,"path":3659,"stem":3660},"RTK Query на мобільних платформах","\u002Freact-native\u002Fversion2\u002Frtk-query-mobile","15.react-native\u002Fversion2\u002F16.rtk-query-mobile",{"title":3662,"path":3663,"stem":3664},"Автентифікація та Безпечне Зберігання","\u002Freact-native\u002Fversion2\u002Fauth-secure-storage","15.react-native\u002Fversion2\u002F18.auth-secure-storage",{"title":3666,"path":3667,"stem":3668},"Локальне сховище — AsyncStorage, MMKV, SQLite","\u002Freact-native\u002Fversion2\u002Flocal-storage-mmkv-sqlite","15.react-native\u002Fversion2\u002F19.local-storage-mmkv-sqlite",{"title":3670,"path":3671,"stem":3672},"Офлайн-First і синхронізація","\u002Freact-native\u002Fversion2\u002Foffline-first-sync","15.react-native\u002Fversion2\u002F20.offline-first-sync",{"title":3674,"path":3675,"stem":3676},"Камера, медіа та файлова система","\u002Freact-native\u002Fversion2\u002Fcamera-media-filesystem","15.react-native\u002Fversion2\u002F21.camera-media-filesystem",{"title":3678,"path":3679,"stem":3680},"Карти та геолокація","\u002Freact-native\u002Fversion2\u002Fmaps-and-location","15.react-native\u002Fversion2\u002F22.maps-and-location",{"title":3682,"path":3683,"stem":3684},"Жести та дотики","\u002Freact-native\u002Fversion2\u002Fgestures-and-touch","15.react-native\u002Fversion2\u002F23.gestures-and-touch",{"title":3686,"path":3687,"stem":3688},"Анімації з Reanimated","\u002Freact-native\u002Fversion2\u002Freanimated-animations","15.react-native\u002Fversion2\u002F24.reanimated-animations",{"title":3690,"path":3691,"stem":3692},"Push і локальні сповіщення","\u002Freact-native\u002Fversion2\u002Fpush-and-local-notifications","15.react-native\u002Fversion2\u002F25.push-and-local-notifications",{"title":3694,"path":3695,"stem":3696},"Інтернаціоналізація та доступність","\u002Freact-native\u002Fversion2\u002Faccessibility-and-i18n","15.react-native\u002Fversion2\u002F26.accessibility-and-i18n",{"title":3698,"path":3699,"stem":3700},"EAS Build та профілі збірки","\u002Freact-native\u002Fversion2\u002Feas-build-and-profiles","15.react-native\u002Fversion2\u002F29.eas-build-and-profiles",{"title":3702,"path":3703,"stem":3704},"Публікація в App Store та Google Play","\u002Freact-native\u002Fversion2\u002Fapp-store-play-release","15.react-native\u002Fversion2\u002F30.app-store-play-release",{"title":3706,"path":3707,"stem":3708,"children":3709,"page":59},"Ai Python","\u002Fai-python","16.ai-python",[3710,3719,3728,3737,3766,3792,3817,3850,3867,3880,3889,3902,3911,3932,3945,3966],{"title":3711,"path":3712,"stem":3713,"children":3714,"page":59},"Intro To Ai","\u002Fai-python\u002Fintro-to-ai","16.ai-python\u002F01.intro-to-ai",[3715],{"title":3716,"path":3717,"stem":3718},"Вступ до штучного інтелекту та машинного навчання","\u002Fai-python\u002Fintro-to-ai\u002Fintro-to-ai","16.ai-python\u002F01.intro-to-ai\u002F01.intro-to-ai",{"title":3720,"path":3721,"stem":3722,"children":3723,"page":59},"Jupyter Notebook","\u002Fai-python\u002Fjupyter-notebook","16.ai-python\u002F02.jupyter-notebook",[3724],{"title":3725,"path":3726,"stem":3727},"Знайомство з Jupyter Notebook та JupyterLab","\u002Fai-python\u002Fjupyter-notebook\u002Fjupyter-notebook","16.ai-python\u002F02.jupyter-notebook\u002F02.jupyter-notebook",{"title":3729,"path":3730,"stem":3731,"children":3732,"page":59},"Numpy Pandas","\u002Fai-python\u002Fnumpy-pandas","16.ai-python\u002F03.numpy-pandas",[3733],{"title":3734,"path":3735,"stem":3736},"Робота з даними з використанням NumPy і pandas","\u002Fai-python\u002Fnumpy-pandas\u002Fnumpy-pandas","16.ai-python\u002F03.numpy-pandas\u002F03.numpy-pandas",{"title":3738,"path":3739,"stem":3740,"children":3741,"page":59},"Statistics Basics","\u002Fai-python\u002Fstatistics-basics","16.ai-python\u002F04.statistics-basics",[3742,3746,3750,3754,3758,3762],{"title":3743,"path":3744,"stem":3745},"Випадкові величини та їх типи","\u002Fai-python\u002Fstatistics-basics\u002Frandom-variables","16.ai-python\u002F04.statistics-basics\u002F01.random-variables",{"title":3747,"path":3748,"stem":3749},"Міри центральної тенденції","\u002Fai-python\u002Fstatistics-basics\u002Fcentral-tendency","16.ai-python\u002F04.statistics-basics\u002F02.central-tendency",{"title":3751,"path":3752,"stem":3753},"Міри варіації (розсіювання)","\u002Fai-python\u002Fstatistics-basics\u002Fvariability","16.ai-python\u002F04.statistics-basics\u002F03.variability",{"title":3755,"path":3756,"stem":3757},"Розподіли випадкових величин","\u002Fai-python\u002Fstatistics-basics\u002Fdistributions","16.ai-python\u002F04.statistics-basics\u002F04.distributions",{"title":3759,"path":3760,"stem":3761},"Кореляція та взаємозв'язки","\u002Fai-python\u002Fstatistics-basics\u002Fcorrelation","16.ai-python\u002F04.statistics-basics\u002F05.correlation",{"title":3763,"path":3764,"stem":3765},"Викиди та аномалії","\u002Fai-python\u002Fstatistics-basics\u002Foutliers","16.ai-python\u002F04.statistics-basics\u002F06.outliers",{"title":3767,"path":3768,"stem":3769,"children":3770},"Візуалізація даних за допомогою matplotlib","\u002Fai-python\u002Fdata-visualization","16.ai-python\u002F05.data-visualization\u002Findex",[3771,3772,3776,3780,3784,3788],{"title":3767,"path":3768,"stem":3769},{"title":3773,"path":3774,"stem":3775},"Основи matplotlib — Figure, Axes та перший графік","\u002Fai-python\u002Fdata-visualization\u002Fmatplotlib-basics","16.ai-python\u002F05.data-visualization\u002F01.matplotlib-basics",{"title":3777,"path":3778,"stem":3779},"Візуалізація розподілів — гістограми та box plots","\u002Fai-python\u002Fdata-visualization\u002Fdistributions","16.ai-python\u002F05.data-visualization\u002F02.distributions",{"title":3781,"path":3782,"stem":3783},"Візуалізація залежностей — scatter plots та кореляція","\u002Fai-python\u002Fdata-visualization\u002Frelationships","16.ai-python\u002F05.data-visualization\u002F03.relationships",{"title":3785,"path":3786,"stem":3787},"Візуалізація категоріальних даних — bar charts та pie charts","\u002Fai-python\u002Fdata-visualization\u002Fcategorical","16.ai-python\u002F05.data-visualization\u002F04.categorical",{"title":3789,"path":3790,"stem":3791},"Композиції та стилізація — subplots та багатопанельні дашборди","\u002Fai-python\u002Fdata-visualization\u002Fsubplots-styling","16.ai-python\u002F05.data-visualization\u002F05.subplots-styling",{"title":3793,"path":3794,"stem":3795,"children":3796,"page":59},"Linear Regression","\u002Fai-python\u002Flinear-regression","16.ai-python\u002F06.linear-regression",[3797,3801,3805,3809,3813],{"title":3798,"path":3799,"stem":3800},"Регресійна задача та лінійна регресія з однією змінною","\u002Fai-python\u002Flinear-regression\u002Fregression-task","16.ai-python\u002F06.linear-regression\u002F01.regression-task",{"title":3802,"path":3803,"stem":3804},"Метрики якості регресії — як оцінити модель","\u002Fai-python\u002Flinear-regression\u002Fquality-metrics","16.ai-python\u002F06.linear-regression\u002F02.quality-metrics",{"title":3806,"path":3807,"stem":3808},"Градієнтний спуск — як модель навчається","\u002Fai-python\u002Flinear-regression\u002Fgradient-descent","16.ai-python\u002F06.linear-regression\u002F03.gradient-descent",{"title":3810,"path":3811,"stem":3812},"Множинна лінійна регресія — модель з багатьма ознаками","\u002Fai-python\u002Flinear-regression\u002Fmultiple-regression","16.ai-python\u002F06.linear-regression\u002F04.multiple-regression",{"title":3814,"path":3815,"stem":3816},"Практичні завдання та резюме модуля","\u002Fai-python\u002Flinear-regression\u002Fpractice","16.ai-python\u002F06.linear-regression\u002F05.practice",{"title":3818,"path":3819,"stem":3820,"children":3821,"page":59},"Practical Regression","\u002Fai-python\u002Fpractical-regression","16.ai-python\u002F07.practical-regression",[3822,3826,3830,3834,3838,3842,3846],{"title":3823,"path":3824,"stem":3825},"Знайомство з scikit-learn","\u002Fai-python\u002Fpractical-regression\u002Fintro-scikit-learn","16.ai-python\u002F07.practical-regression\u002F01.intro-scikit-learn",{"title":3827,"path":3828,"stem":3829},"Exploratory Data Analysis датасету Housing Prices","\u002Fai-python\u002Fpractical-regression\u002Fhousing-dataset-eda","16.ai-python\u002F07.practical-regression\u002F02.housing-dataset-eda",{"title":3831,"path":3832,"stem":3833},"Попередня обробка даних (Data Preprocessing)","\u002Fai-python\u002Fpractical-regression\u002Fdata-preprocessing","16.ai-python\u002F07.practical-regression\u002F03.data-preprocessing",{"title":3835,"path":3836,"stem":3837},"Train\u002FTest Split та перша повноцінна модель","\u002Fai-python\u002Fpractical-regression\u002Ftrain-test-split","16.ai-python\u002F07.practical-regression\u002F04.train-test-split",{"title":3839,"path":3840,"stem":3841},"Перенавчання та недонавчання","\u002Fai-python\u002Fpractical-regression\u002Foverfitting-underfitting","16.ai-python\u002F07.practical-regression\u002F05.overfitting-underfitting",{"title":3843,"path":3844,"stem":3845},"Крос-валідація (Cross-Validation)","\u002Fai-python\u002Fpractical-regression\u002Fcross-validation","16.ai-python\u002F07.practical-regression\u002F06.cross-validation",{"title":3847,"path":3848,"stem":3849},"Гіперпараметри та їх оптимізація","\u002Fai-python\u002Fpractical-regression\u002Fhyperparameter-tuning","16.ai-python\u002F07.practical-regression\u002F07.hyperparameter-tuning",{"title":3851,"path":3852,"stem":3853,"children":3854,"page":59},"Polynomial Regression","\u002Fai-python\u002Fpolynomial-regression","16.ai-python\u002F08.polynomial-regression",[3855,3859,3863],{"title":3856,"path":3857,"stem":3858},"Нелінійні залежності та поліноміальна регресія","\u002Fai-python\u002Fpolynomial-regression\u002Fnonlinear-patterns","16.ai-python\u002F08.polynomial-regression\u002F01.nonlinear-patterns",{"title":3860,"path":3861,"stem":3862},"Регуляризація в регресії — Ridge та Lasso","\u002Fai-python\u002Fpolynomial-regression\u002Fregularization-methods","16.ai-python\u002F08.polynomial-regression\u002F02.regularization-methods",{"title":3864,"path":3865,"stem":3866},"Практика — поліноміальна регресія та регуляризація на Housing Prices","\u002Fai-python\u002Fpolynomial-regression\u002Fhousing-prices-practice","16.ai-python\u002F08.polynomial-regression\u002F03.housing-prices-practice",{"title":3868,"path":3869,"stem":3870,"children":3871,"page":59},"Decision Trees Random Forest","\u002Fai-python\u002Fdecision-trees-random-forest","16.ai-python\u002F09.decision-trees-random-forest",[3872,3876],{"title":3873,"path":3874,"stem":3875},"Дерева рішень — моделі з прозорою та зрозумілою логікою","\u002Fai-python\u002Fdecision-trees-random-forest\u002Fdecision-trees","16.ai-python\u002F09.decision-trees-random-forest\u002F01.decision-trees",{"title":3877,"path":3878,"stem":3879},"Random Forest — ансамблі дерев рішень","\u002Fai-python\u002Fdecision-trees-random-forest\u002Frandom-forest","16.ai-python\u002F09.decision-trees-random-forest\u002F02.random-forest",{"title":3881,"path":3882,"stem":3883,"children":3884,"page":59},"Gradient Boosting","\u002Fai-python\u002Fgradient-boosting","16.ai-python\u002F10.gradient-boosting",[3885],{"title":3886,"path":3887,"stem":3888},"Градієнтний бустинг та XGBoost — послідовне виправлення помилок","\u002Fai-python\u002Fgradient-boosting\u002Fgradient-boosting-xgboost","16.ai-python\u002F10.gradient-boosting\u002F01.gradient-boosting-xgboost",{"title":3890,"path":3891,"stem":3892,"children":3893,"page":59},"Logistic Regression Classification","\u002Fai-python\u002Flogistic-regression-classification","16.ai-python\u002F11.logistic-regression-classification",[3894,3898],{"title":3895,"path":3896,"stem":3897},"Основи класифікації та логістична регресія","\u002Fai-python\u002Flogistic-regression-classification\u002Fclassification-basics","16.ai-python\u002F11.logistic-regression-classification\u002F01.classification-basics",{"title":3899,"path":3900,"stem":3901},"Метрики якості класифікації","\u002Fai-python\u002Flogistic-regression-classification\u002Fclassification-metrics","16.ai-python\u002F11.logistic-regression-classification\u002F02.classification-metrics",{"title":3903,"path":3904,"stem":3905,"children":3906,"page":59},"Neural Networks Basics","\u002Fai-python\u002Fneural-networks-basics","16.ai-python\u002F12.neural-networks-basics",[3907],{"title":3908,"path":3909,"stem":3910},"Вступ до нейронних мереж — від персептрона до багатошарових мереж","\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp","16.ai-python\u002F12.neural-networks-basics\u002F01.perceptron-to-mlp",{"title":3912,"path":3913,"stem":3914,"children":3915,"page":59},"Pytorch Intro","\u002Fai-python\u002Fpytorch-intro","16.ai-python\u002F13.pytorch-intro",[3916,3920,3924,3928],{"title":3917,"path":3918,"stem":3919},"Тензори та автоматичне диференціювання в PyTorch","\u002Fai-python\u002Fpytorch-intro\u002Ftensors-and-autograd","16.ai-python\u002F13.pytorch-intro\u002F01.tensors-and-autograd",{"title":3921,"path":3922,"stem":3923},"Побудова та тренування нейронних мереж у PyTorch","\u002Fai-python\u002Fpytorch-intro\u002Fbuilding-and-training","16.ai-python\u002F13.pytorch-intro\u002F02.building-and-training",{"title":3925,"path":3926,"stem":3927},"Робота з даними та регуляризація в PyTorch","\u002Fai-python\u002Fpytorch-intro\u002Fdata-and-regularization","16.ai-python\u002F13.pytorch-intro\u002F03.data-and-regularization",{"title":3929,"path":3930,"stem":3931},"Просунуті теми PyTorch — GPU, оптимізація та deployment","\u002Fai-python\u002Fpytorch-intro\u002Fadvanced-topics","16.ai-python\u002F13.pytorch-intro\u002F04.advanced-topics",{"title":3933,"path":3934,"stem":3935,"children":3936,"page":59},"Activation Functions Heart Disease","\u002Fai-python\u002Factivation-functions-heart-disease","16.ai-python\u002F14.activation-functions-heart-disease",[3937,3941],{"title":3938,"path":3939,"stem":3940},"Функції активації та побудова нейронної мережі для передбачення вад серця","\u002Fai-python\u002Factivation-functions-heart-disease\u002Fheart-disease-prediction","16.ai-python\u002F14.activation-functions-heart-disease\u002F01.heart-disease-prediction",{"title":3942,"path":3943,"stem":3944},"Бонус — Повний приклад Student Performance Prediction","\u002Fai-python\u002Factivation-functions-heart-disease\u002Fstudent-performance-bonus","16.ai-python\u002F14.activation-functions-heart-disease\u002F02.student-performance-bonus",{"title":3946,"path":3947,"stem":3948,"children":3949,"page":59},"Cnn Image Classification","\u002Fai-python\u002Fcnn-image-classification","16.ai-python\u002F15.cnn-image-classification",[3950,3954,3958,3962],{"title":3951,"path":3952,"stem":3953},"Основи згорткових нейронних мереж — чому не MLP?","\u002Fai-python\u002Fcnn-image-classification\u002Fcnn-fundamentals","16.ai-python\u002F15.cnn-image-classification\u002F01.cnn-fundamentals",{"title":3955,"path":3956,"stem":3957},"Практична імплементація CNN для класифікації MNIST","\u002Fai-python\u002Fcnn-image-classification\u002Fmnist-classification","16.ai-python\u002F15.cnn-image-classification\u002F02.mnist-classification",{"title":3959,"path":3960,"stem":3961},"Глибші CNN та аугментація даних для CIFAR-10","\u002Fai-python\u002Fcnn-image-classification\u002Fcifar10-and-data-augmentation","16.ai-python\u002F15.cnn-image-classification\u002F03.cifar10-and-data-augmentation",{"title":3963,"path":3964,"stem":3965},"Transfer Learning та візуалізація внутрішніх представлень CNN","\u002Fai-python\u002Fcnn-image-classification\u002Ftransfer-learning-and-visualization","16.ai-python\u002F15.cnn-image-classification\u002F04.transfer-learning-and-visualization",{"title":3967,"path":3968,"stem":3969,"children":3970,"page":59},"Batching Normalization Deep Networks","\u002Fai-python\u002Fbatching-normalization-deep-networks","16.ai-python\u002F16.batching-normalization-deep-networks",[3971,3975,3979,3983,3987,3991,3995],{"title":3972,"path":3973,"stem":3974},"Mini-batch Gradient Descent та ефективна обробка даних","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Fmini-batch-gradient-descent","16.ai-python\u002F16.batching-normalization-deep-networks\u002F01.mini-batch-gradient-descent",{"title":3976,"path":3977,"stem":3978},"Ініціалізація ваг — фундамент стабільного навчання","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Fweight-initialization","16.ai-python\u002F16.batching-normalization-deep-networks\u002F02.weight-initialization",{"title":3980,"path":3981,"stem":3982},"Batch Normalization — прорив у глибокому навчанні","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Fbatch-normalization","16.ai-python\u002F16.batching-normalization-deep-networks\u002F03.batch-normalization",{"title":3984,"path":3985,"stem":3986},"Dropout та комбіновані стратегії регуляризації","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Fdropout-and-regularization","16.ai-python\u002F16.batching-normalization-deep-networks\u002F04.dropout-and-regularization",{"title":3988,"path":3989,"stem":3990},"Проєктування глибоких мереж — від теорії до практики","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Fdeep-networks-architectures","16.ai-python\u002F16.batching-normalization-deep-networks\u002F05.deep-networks-architectures",{"title":3992,"path":3993,"stem":3994},"Планування learning rate — коли та як зменшувати крок навчання","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Flearning-rate-scheduling","16.ai-python\u002F16.batching-normalization-deep-networks\u002F06.learning-rate-scheduling",{"title":3996,"path":3997,"stem":3998},"Підсумковий проєкт — побудова сучасного класифікатора зображень","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Ffinal-project-deep-classifier","16.ai-python\u002F16.batching-normalization-deep-networks\u002F07.final-project-deep-classifier",{"title":4000,"icon":658,"path":4001,"stem":4002,"children":4003,"page":59},"Клієнт-серверна архітектура","\u002Fclient-server-architecture","17.client-server-architecture",[4004,4008,4012,4016,4020,4024,4028,4032,4036,4040,4044,4048,4052,4056,4060,4064,4068,4072],{"title":4005,"path":4006,"stem":4007},"Архітектура клієнт-серверних систем та основи Go","\u002Fclient-server-architecture\u002Fclient-server-architecture-and-go","17.client-server-architecture\u002F01.client-server-architecture-and-go",{"title":4009,"path":4010,"stem":4011},"Система типів та модель пам’яті мови Go","\u002Fclient-server-architecture\u002Ftype-system-and-memory-model","17.client-server-architecture\u002F02.type-system-and-memory-model",{"title":4013,"path":4014,"stem":4015},"Інтерфейси та модель конкурентності мови Go","\u002Fclient-server-architecture\u002Finterfaces-and-concurrency-model","17.client-server-architecture\u002F03.interfaces-and-concurrency-model",{"title":4017,"path":4018,"stem":4019},"Сокетне програмування та протокол TCP у Go","\u002Fclient-server-architecture\u002Ftcp-socket-programming","17.client-server-architecture\u002F04.tcp-socket-programming",{"title":4021,"path":4022,"stem":4023},"Протокол UDP та датаграмна передача даних","\u002Fclient-server-architecture\u002Fudp-datagram-transmission","17.client-server-architecture\u002F05.udp-datagram-transmission",{"title":4025,"path":4026,"stem":4027},"Криптографічний захист каналів зв","\u002Fclient-server-architecture\u002Ftls-cryptographic-channel-protection","17.client-server-architecture\u002F06.tls-cryptographic-channel-protection",{"title":4029,"path":4030,"stem":4031},"Прикладні мережеві протоколи DNS та SMTP","\u002Fclient-server-architecture\u002Fdns-smtp-application-protocols","17.client-server-architecture\u002F07.dns-smtp-application-protocols",{"title":4033,"path":4034,"stem":4035},"Протокол HTTP та стандартний вебсервер Go","\u002Fclient-server-architecture\u002Fhttp-protocol-and-web-server","17.client-server-architecture\u002F08.http-protocol-and-web-server",{"title":4037,"path":4038,"stem":4039},"Проєктування REST API та маршрутизація засобами Chi","\u002Fclient-server-architecture\u002Frest-api-design-and-chi-routing","17.client-server-architecture\u002F09.rest-api-design-and-chi-routing",{"title":4041,"path":4042,"stem":4043},"Лекція 10. Шарувата архітектура та конвеєри обробки запитів","\u002Fclient-server-architecture\u002Flayered-architecture-and-middleware-pipelines","17.client-server-architecture\u002F10.layered-architecture-and-middleware-pipelines",{"title":4045,"path":4046,"stem":4047},"Лекція 11. Архітектура та маршрутизація фреймворку Gin","\u002Fclient-server-architecture\u002Fgin-framework-architecture-and-routing","17.client-server-architecture\u002F11.gin-framework-architecture-and-routing",{"title":4049,"path":4050,"stem":4051},"Лекція 12. Валідація даних, безпека та документування у Gin","\u002Fclient-server-architecture\u002Fdata-validation-security-and-documentation-in-gin","17.client-server-architecture\u002F12.data-validation-security-and-documentation-in-gin",{"title":4053,"path":4054,"stem":4055},"Лекція 13. Взаємодія з реляційними СУБД та технології ORM","\u002Fclient-server-architecture\u002Frelational-databases-and-orm","17.client-server-architecture\u002F13.relational-databases-and-orm",{"title":4057,"path":4058,"stem":4059},"Потокова передача даних та протокол WebSocket","\u002Fclient-server-architecture\u002Fstreaming-data-and-websockets","17.client-server-architecture\u002F14.streaming-data-and-websockets",{"title":4061,"path":4062,"stem":4063},"Міжсервісна взаємодія на основі протоколу gRPC","\u002Fclient-server-architecture\u002Fgrpc-inter-service-communication","17.client-server-architecture\u002F15.grpc-inter-service-communication",{"title":4065,"path":4066,"stem":4067},"Асинхронний обмін повідомленнями та протоколи черг","\u002Fclient-server-architecture\u002Fasynchronous-message-exchange-and-queue-protocols","17.client-server-architecture\u002F16.asynchronous-message-exchange-and-queue-protocols",{"title":4069,"path":4070,"stem":4071},"Протоколи потокового медіа та технологія WebRTC","\u002Fclient-server-architecture\u002Fstreaming-media-protocols-and-webrtc","17.client-server-architecture\u002F17.streaming-media-protocols-and-webrtc",{"title":4073,"path":4074,"stem":4075},"Моніторинг, безпека та контейнеризація застосунків","\u002Fclient-server-architecture\u002Fmonitoring-security-and-containerization","17.client-server-architecture\u002F18.monitoring-security-and-containerization",{"title":4077,"icon":2134,"path":4078,"stem":4079,"children":4080,"page":59},"Розробка WEB-застосувань","\u002Fweb-development","18.web-development",[4081,4126,4164,4193,4222,4279,4329,4423,4489,4571,4604,4632,4674,4720,4763],{"title":4082,"icon":658,"path":4083,"stem":4084,"children":4085,"page":59},"Архітектура комп'ютерних мереж та мережеві протоколи","\u002Fweb-development\u002Fnetwork-architecture-and-protocols","18.web-development\u002F01.network-architecture-and-protocols",[4086,4090,4094,4098,4102,4106,4110,4114,4118,4122],{"title":4087,"path":4088,"stem":4089},"Еволюція веброзробки та модель клієнт-сервер","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fweb-evolution-client-server","18.web-development\u002F01.network-architecture-and-protocols\u002F01.web-evolution-client-server",{"title":4091,"path":4092,"stem":4093},"Еталонна модель OSI","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fosi-model","18.web-development\u002F01.network-architecture-and-protocols\u002F02.osi-model",{"title":4095,"path":4096,"stem":4097},"Стек протоколів TCP\u002FIP","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Ftcp-ip-stack","18.web-development\u002F01.network-architecture-and-protocols\u002F03.tcp-ip-stack",{"title":4099,"path":4100,"stem":4101},"IP-адресація, порти та сокети","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fip-addressing-ports-sockets","18.web-development\u002F01.network-architecture-and-protocols\u002F04.ip-addressing-ports-sockets",{"title":4103,"path":4104,"stem":4105},"Протоколи TCP та UDP","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Ftcp-udp-protocols","18.web-development\u002F01.network-architecture-and-protocols\u002F05.tcp-udp-protocols",{"title":4107,"path":4108,"stem":4109},"Система доменних імен DNS","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fdns-system","18.web-development\u002F01.network-architecture-and-protocols\u002F06.dns-system",{"title":4111,"path":4112,"stem":4113},"Протокол SMTP та поштові протоколи","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fsmtp-email-protocols","18.web-development\u002F01.network-architecture-and-protocols\u002F07.smtp-email-protocols",{"title":4115,"path":4116,"stem":4117},"Протокол WebSocket","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fwebsocket-protocol","18.web-development\u002F01.network-architecture-and-protocols\u002F08.websocket-protocol",{"title":4119,"path":4120,"stem":4121},"Протокол SSH","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fssh-protocol","18.web-development\u002F01.network-architecture-and-protocols\u002F09.ssh-protocol",{"title":4123,"path":4124,"stem":4125},"Огляд сучасних серверних технологій","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fmodern-backend-technologies","18.web-development\u002F01.network-architecture-and-protocols\u002F10.modern-backend-technologies",{"title":4127,"icon":4128,"path":4129,"stem":4130,"children":4131,"page":59},"Протокол HTTP та захищена передача даних HTTPS","i-lucide-lock","\u002Fweb-development\u002Fhttp-and-https","18.web-development\u002F02.http-and-https",[4132,4136,4140,4144,4148,4152,4156,4160],{"title":4133,"path":4134,"stem":4135},"Вступ до протоколу HTTP та еволюція веб-технологій","\u002Fweb-development\u002Fhttp-and-https\u002Fintroduction-and-evolution","18.web-development\u002F02.http-and-https\u002F01.introduction-and-evolution",{"title":4137,"path":4138,"stem":4139},"Анатомія HTTP-запиту","\u002Fweb-development\u002Fhttp-and-https\u002Fhttp-request-structure","18.web-development\u002F02.http-and-https\u002F02.http-request-structure",{"title":4141,"path":4142,"stem":4143},"Анатомія HTTP-відповіді","\u002Fweb-development\u002Fhttp-and-https\u002Fhttp-response-structure","18.web-development\u002F02.http-and-https\u002F03.http-response-structure",{"title":4145,"path":4146,"stem":4147},"Методи HTTP та їхня семантика","\u002Fweb-development\u002Fhttp-and-https\u002Fhttp-methods","18.web-development\u002F02.http-and-https\u002F04.http-methods",{"title":4149,"path":4150,"stem":4151},"Коди статусу HTTP та їхнє призначення","\u002Fweb-development\u002Fhttp-and-https\u002Fhttp-status-codes","18.web-development\u002F02.http-and-https\u002F05.http-status-codes",{"title":4153,"path":4154,"stem":4155},"HTTP-заголовки та їхнє призначення","\u002Fweb-development\u002Fhttp-and-https\u002Fhttp-headers","18.web-development\u002F02.http-and-https\u002F06.http-headers",{"title":4157,"path":4158,"stem":4159},"CORS та механізми безпеки HTTP","\u002Fweb-development\u002Fhttp-and-https\u002Fcors-and-security","18.web-development\u002F02.http-and-https\u002F07.cors-and-security",{"title":4161,"path":4162,"stem":4163},"HTTPS та криптографічні основи TLS","\u002Fweb-development\u002Fhttp-and-https\u002Fhttps-and-tls","18.web-development\u002F02.http-and-https\u002F08.https-and-tls",{"title":4165,"icon":2514,"path":4166,"stem":4167,"children":4168,"page":59},"Система типів мови TypeScript","\u002Fweb-development\u002Ftypescript-type-system","18.web-development\u002F03.typescript-type-system",[4169,4173,4177,4181,4185,4189],{"title":4170,"path":4171,"stem":4172},"Знайомство з TypeScript Compiler","\u002Fweb-development\u002Ftypescript-type-system\u002Fintroduction-compiler-config","18.web-development\u002F03.typescript-type-system\u002F01.introduction-compiler-config",{"title":4174,"path":4175,"stem":4176},"Примітивні типи даних: string, number, boolean","\u002Fweb-development\u002Ftypescript-type-system\u002Fprimitive-special-types","18.web-development\u002F03.typescript-type-system\u002F02.primitive-special-types",{"title":4178,"path":4179,"stem":4180},"Масиви, кортежі та об","\u002Fweb-development\u002Ftypescript-type-system\u002Farrays-tuples-objects","18.web-development\u002F03.typescript-type-system\u002F03.arrays-tuples-objects",{"title":4182,"path":4183,"stem":4184},"Псевдоніми типів, Union типи, Intersection типи та літеральні типи","\u002Fweb-development\u002Ftypescript-type-system\u002Funion-intersection-literals","18.web-development\u002F03.typescript-type-system\u002F04.union-intersection-literals",{"title":4186,"path":4187,"stem":4188},"Type Narrowing (звуження типів)","\u002Fweb-development\u002Ftypescript-type-system\u002Ftype-narrowing","18.web-development\u002F03.typescript-type-system\u002F05.type-narrowing",{"title":4190,"path":4191,"stem":4192},"Типізація функцій","\u002Fweb-development\u002Ftypescript-type-system\u002Ffunctions-typing","18.web-development\u002F03.typescript-type-system\u002F06.functions-typing",{"title":4194,"icon":2514,"path":4195,"stem":4196,"children":4197,"page":59},"Розширені засоби мови TypeScript","\u002Fweb-development\u002Ftypescript-advanced","18.web-development\u002F04.typescript-advanced",[4198,4202,4206,4210,4214,4218],{"title":4199,"path":4200,"stem":4201},"Interfaces та Classes","\u002Fweb-development\u002Ftypescript-advanced\u002Finterfaces-classes","18.web-development\u002F04.typescript-advanced\u002F01.interfaces-classes",{"title":4203,"path":4204,"stem":4205},"Основи Generic типів","\u002Fweb-development\u002Ftypescript-advanced\u002Fgenerics-fundamentals","18.web-development\u002F04.typescript-advanced\u002F02.generics-fundamentals",{"title":4207,"path":4208,"stem":4209},"Enums та Decorators","\u002Fweb-development\u002Ftypescript-advanced\u002Fenums-decorators","18.web-development\u002F04.typescript-advanced\u002F03.enums-decorators",{"title":4211,"path":4212,"stem":4213},"Utility Types","\u002Fweb-development\u002Ftypescript-advanced\u002Futility-types","18.web-development\u002F04.typescript-advanced\u002F04.utility-types",{"title":4215,"path":4216,"stem":4217},"Mapped та Conditional Types","\u002Fweb-development\u002Ftypescript-advanced\u002Fmapped-conditional-types","18.web-development\u002F04.typescript-advanced\u002F05.mapped-conditional-types",{"title":4219,"path":4220,"stem":4221},"Модулі та Strict Mode","\u002Fweb-development\u002Ftypescript-advanced\u002Fmodules-strict-mode","18.web-development\u002F04.typescript-advanced\u002F06.modules-strict-mode",{"title":4223,"icon":4224,"path":4225,"stem":4226,"children":4227,"page":59},"Платформа Node.js як середовище виконання","i-devicon-nodejs","\u002Fweb-development\u002Fnodejs-platform","18.web-development\u002F05.nodejs-platform",[4228,4232,4236,4240,4244,4248,4252,4256,4260,4264,4268,4271,4275],{"title":4229,"path":4230,"stem":4231},"Що таке Node.js та його архітектура","\u002Fweb-development\u002Fnodejs-platform\u002Fwhat-is-nodejs","18.web-development\u002F05.nodejs-platform\u002F01.what-is-nodejs",{"title":4233,"path":4234,"stem":4235},"Event Loop — серце Node.js","\u002Fweb-development\u002Fnodejs-platform\u002Fevent-loop","18.web-development\u002F05.nodejs-platform\u002F02.event-loop",{"title":4237,"path":4238,"stem":4239},"Модульні системи: CommonJS vs ES Modules","\u002Fweb-development\u002Fnodejs-platform\u002Fmodule-systems","18.web-development\u002F05.nodejs-platform\u002F03.module-systems",{"title":4241,"path":4242,"stem":4243},"npm та package.json","\u002Fweb-development\u002Fnodejs-platform\u002Fnpm-package-json","18.web-development\u002F05.nodejs-platform\u002F04.npm-package-json",{"title":4245,"path":4246,"stem":4247},"Глобальні об\\","\u002Fweb-development\u002Fnodejs-platform\u002Fglobal-objects","18.web-development\u002F05.nodejs-platform\u002F05.global-objects",{"title":4249,"path":4250,"stem":4251},"Вбудований модуль fs (File System)","\u002Fweb-development\u002Fnodejs-platform\u002Fbuilt-in-modules-fs","18.web-development\u002F05.nodejs-platform\u002F06.built-in-modules-fs",{"title":4253,"path":4254,"stem":4255},"Вбудований модуль path","\u002Fweb-development\u002Fnodejs-platform\u002Fbuilt-in-modules-path","18.web-development\u002F05.nodejs-platform\u002F07.built-in-modules-path",{"title":4257,"path":4258,"stem":4259},"Вбудований модуль http","\u002Fweb-development\u002Fnodejs-platform\u002Fbuilt-in-modules-http","18.web-development\u002F05.nodejs-platform\u002F08.built-in-modules-http",{"title":4261,"path":4262,"stem":4263},"Streams — потоки даних у Node.js","\u002Fweb-development\u002Fnodejs-platform\u002Fstreams","18.web-development\u002F05.nodejs-platform\u002F09.streams",{"title":4265,"path":4266,"stem":4267},"Вбудований модуль util (Utilities)","\u002Fweb-development\u002Fnodejs-platform\u002Fbuilt-in-modules-util","18.web-development\u002F05.nodejs-platform\u002F10.built-in-modules-util",{"title":3157,"path":4269,"stem":4270},"\u002Fweb-development\u002Fnodejs-platform\u002Fenvironment-variables","18.web-development\u002F05.nodejs-platform\u002F11.environment-variables",{"title":4272,"path":4273,"stem":4274},"Інструменти налагодження та розробки","\u002Fweb-development\u002Fnodejs-platform\u002Fdebugging-tools","18.web-development\u002F05.nodejs-platform\u002F12.debugging-tools",{"title":4276,"path":4277,"stem":4278},"Продуктивність та Best Practices","\u002Fweb-development\u002Fnodejs-platform\u002Fperformance-best-practices","18.web-development\u002F05.nodejs-platform\u002F13.performance-best-practices",{"title":4280,"icon":4281,"path":4282,"stem":4283,"children":4284,"page":59},"Асинхронне програмування у Node.js","i-lucide-clock","\u002Fweb-development\u002Fasync-programming-nodejs","18.web-development\u002F06.async-programming-nodejs",[4285,4289,4293,4297,4301,4305,4309,4313,4317,4321,4325],{"title":4286,"path":4287,"stem":4288},"Синхронний vs асинхронний код","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fsync-vs-async","18.web-development\u002F06.async-programming-nodejs\u002F01.sync-vs-async",{"title":4290,"path":4291,"stem":4292},"Callbacks — перша парадигма асинхронності","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fcallbacks","18.web-development\u002F06.async-programming-nodejs\u002F02.callbacks",{"title":4294,"path":4295,"stem":4296},"Promises — стандарт асинхронності","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fpromises","18.web-development\u002F06.async-programming-nodejs\u002F03.promises",{"title":4298,"path":4299,"stem":4300},"Promise комбінатори","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fpromise-combinators","18.web-development\u002F06.async-programming-nodejs\u002F04.promise-combinators",{"title":4302,"path":4303,"stem":4304},"Async\u002FAwait — синтаксичний цукор над Promises","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fasync-await","18.web-development\u002F06.async-programming-nodejs\u002F05.async-await",{"title":4306,"path":4307,"stem":4308},"Паралельне vs послідовне виконання","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fparallel-vs-sequential","18.web-development\u002F06.async-programming-nodejs\u002F06.parallel-vs-sequential",{"title":4310,"path":4311,"stem":4312},"EventEmitter — подієва модель Node.js","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fevent-emitter","18.web-development\u002F06.async-programming-nodejs\u002F07.event-emitter",{"title":4314,"path":4315,"stem":4316},"Worker Threads — багатопотоковість у Node.js","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fworker-threads","18.web-development\u002F06.async-programming-nodejs\u002F08.worker-threads",{"title":4318,"path":4319,"stem":4320},"Child Processes — запуск зовнішніх процесів","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fchild-processes","18.web-development\u002F06.async-programming-nodejs\u002F09.child-processes",{"title":4322,"path":4323,"stem":4324},"Обробка помилок у асинхронному коді","\u002Fweb-development\u002Fasync-programming-nodejs\u002Ferror-handling","18.web-development\u002F06.async-programming-nodejs\u002F10.error-handling",{"title":4326,"path":4327,"stem":4328},"Порівняння Node.js фреймворків","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fnodejs-frameworks","18.web-development\u002F06.async-programming-nodejs\u002F11.nodejs-frameworks",{"title":4330,"icon":4331,"path":4332,"stem":4333,"children":4334,"page":59},"Тема 7. Фреймворк NestJS. Контролери та маршрутизація","i-lucide-route","\u002Fweb-development\u002Fnestjs-controllers-routing","18.web-development\u002F07.nestjs-controllers-routing",[4335,4339,4343,4347,4351,4355,4359,4363,4367,4371,4375,4379,4383,4387,4391,4395,4399,4403,4407,4411,4415,4419],{"title":4336,"path":4337,"stem":4338},"Філософія та архітектура NestJS","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fnestjs-philosophy","18.web-development\u002F07.nestjs-controllers-routing\u002F01.nestjs-philosophy",{"title":4340,"path":4341,"stem":4342},"Три стовпи архітектури: модулі, контролери, провайдери","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fthree-pillars","18.web-development\u002F07.nestjs-controllers-routing\u002F02.three-pillars",{"title":4344,"path":4345,"stem":4346},"Інверсія керування (IoC) та ін","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fioc-and-di","18.web-development\u002F07.nestjs-controllers-routing\u002F03.ioc-and-di",{"title":4348,"path":4349,"stem":4350},"Встановлення NestJS CLI та створення проєкту","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fnestjs-cli-setup","18.web-development\u002F07.nestjs-controllers-routing\u002F04.nestjs-cli-setup",{"title":4352,"path":4353,"stem":4354},"Структура проєкту NestJS та конвенції","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fproject-structure","18.web-development\u002F07.nestjs-controllers-routing\u002F05.project-structure",{"title":4356,"path":4357,"stem":4358},"Контролери: основи маршрутизації","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fcontrollers-basics","18.web-development\u002F07.nestjs-controllers-routing\u002F06.controllers-basics",{"title":4360,"path":4361,"stem":4362},"Декоратори маршрутизації HTTP-методів","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Froute-decorators","18.web-development\u002F07.nestjs-controllers-routing\u002F07.route-decorators",{"title":4364,"path":4365,"stem":4366},"Параметри маршруту та декоратор @Param","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Froute-parameters","18.web-development\u002F07.nestjs-controllers-routing\u002F08.route-parameters",{"title":4368,"path":4369,"stem":4370},"Query-параметри та декоратор @Query","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fquery-parameters","18.web-development\u002F07.nestjs-controllers-routing\u002F09.query-parameters",{"title":4372,"path":4373,"stem":4374},"Тіло запиту та декоратор @Body","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Frequest-body","18.web-development\u002F07.nestjs-controllers-routing\u002F10.request-body",{"title":4376,"path":4377,"stem":4378},"Робота з заголовками запиту та відповіді","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fheaders-decorators","18.web-development\u002F07.nestjs-controllers-routing\u002F11.headers-decorators",{"title":4380,"path":4381,"stem":4382},"Data Transfer Objects (DTO): визначення та призначення","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fdto-introduction","18.web-development\u002F07.nestjs-controllers-routing\u002F12.dto-introduction",{"title":4384,"path":4385,"stem":4386},"Об'єкти Request та Response","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Frequest-response-objects","18.web-development\u002F07.nestjs-controllers-routing\u002F13.request-response-objects",{"title":4388,"path":4389,"stem":4390},"HTTP-статус коди та декоратор @HttpCode","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fhttp-status-codes","18.web-development\u002F07.nestjs-controllers-routing\u002F14.http-status-codes",{"title":4392,"path":4393,"stem":4394},"Перенаправлення (Redirects) та декоратор @Redirect","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fredirects","18.web-development\u002F07.nestjs-controllers-routing\u002F15.redirects",{"title":4396,"path":4397,"stem":4398},"Асинхронні обробники та Observables","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fasync-handlers","18.web-development\u002F07.nestjs-controllers-routing\u002F16.async-handlers",{"title":4400,"path":4401,"stem":4402},"Маршрутизація за піддоменами та версіонування API","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fsub-domain-routing","18.web-development\u002F07.nestjs-controllers-routing\u002F17.sub-domain-routing",{"title":4404,"path":4405,"stem":4406},"Області видимості контролерів (Scopes)","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fcontroller-scopes","18.web-development\u002F07.nestjs-controllers-routing\u002F18.controller-scopes",{"title":4408,"path":4409,"stem":4410},"Основні команди NestJS CLI","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fnestjs-cli-commands","18.web-development\u002F07.nestjs-controllers-routing\u002F19.nestjs-cli-commands",{"title":4412,"path":4413,"stem":4414},"Практичний приклад: створення CRUD-контролера","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fcrud-example","18.web-development\u002F07.nestjs-controllers-routing\u002F20.crud-example",{"title":4416,"path":4417,"stem":4418},"Тестування контролерів","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Ftesting-controllers","18.web-development\u002F07.nestjs-controllers-routing\u002F21.testing-controllers",{"title":4420,"path":4421,"stem":4422},"Best Practices для контролерів та маршрутизації","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fbest-practices","18.web-development\u002F07.nestjs-controllers-routing\u002F22.best-practices",{"title":4424,"icon":4425,"path":4426,"stem":4427,"children":4428,"page":59},"Тема 8. Провайдери, сервіси та модульна система NestJS","i-lucide-package","\u002Fweb-development\u002Fnestjs-providers-modules","18.web-development\u002F08.nestjs-providers-modules",[4429,4433,4437,4441,4445,4449,4453,4457,4461,4465,4469,4473,4477,4481,4485],{"title":4430,"path":4431,"stem":4432},"Концепція провайдерів у NestJS","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fproviders-concept","18.web-development\u002F08.nestjs-providers-modules\u002F01.providers-concept",{"title":4434,"path":4435,"stem":4436},"Сервіси: інкапсуляція бізнес-логіки","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fservices-business-logic","18.web-development\u002F08.nestjs-providers-modules\u002F02.services-business-logic",{"title":4438,"path":4439,"stem":4440},"Практика ін","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fdependency-injection-practice","18.web-development\u002F08.nestjs-providers-modules\u002F03.dependency-injection-practice",{"title":4442,"path":4443,"stem":4444},"Custom Providers: useValue, useClass, useFactory, useExisting","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fcustom-providers","18.web-development\u002F08.nestjs-providers-modules\u002F04.custom-providers",{"title":4446,"path":4447,"stem":4448},"Injection Tokens: рядкові та символьні токени","\u002Fweb-development\u002Fnestjs-providers-modules\u002Finjection-tokens","18.web-development\u002F08.nestjs-providers-modules\u002F05.injection-tokens",{"title":4450,"path":4451,"stem":4452},"Опціональні провайдери та декоратор @Optional","\u002Fweb-development\u002Fnestjs-providers-modules\u002Foptional-providers","18.web-development\u002F08.nestjs-providers-modules\u002F07.optional-providers",{"title":4454,"path":4455,"stem":4456},"Структура модулів: imports, controllers, providers, exports","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fmodules-structure","18.web-development\u002F08.nestjs-providers-modules\u002F08.modules-structure",{"title":4458,"path":4459,"stem":4460},"Feature Modules: ізоляція функціональності","\u002Fweb-development\u002Fnestjs-providers-modules\u002Ffeature-modules","18.web-development\u002F08.nestjs-providers-modules\u002F09.feature-modules",{"title":4462,"path":4463,"stem":4464},"Shared Modules: перевикористання провайдерів","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fshared-modules","18.web-development\u002F08.nestjs-providers-modules\u002F10.shared-modules",{"title":4466,"path":4467,"stem":4468},"Global Modules та декоратор @Global","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fglobal-modules","18.web-development\u002F08.nestjs-providers-modules\u002F11.global-modules",{"title":4470,"path":4471,"stem":4472},"Dynamic Modules: конфігурація під час виконання","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fdynamic-modules","18.web-development\u002F08.nestjs-providers-modules\u002F12.dynamic-modules",{"title":4474,"path":4475,"stem":4476},"Циклічні залежності та forwardRef","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fcircular-dependencies","18.web-development\u002F08.nestjs-providers-modules\u002F13.circular-dependencies",{"title":4478,"path":4479,"stem":4480},"Lifecycle Hooks: хуки життєвого циклу","\u002Fweb-development\u002Fnestjs-providers-modules\u002Flifecycle-hooks","18.web-development\u002F08.nestjs-providers-modules\u002F14.lifecycle-hooks",{"title":4482,"path":4483,"stem":4484},"ModuleRef: динамічний доступ до провайдерів","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fmodule-reference","18.web-development\u002F08.nestjs-providers-modules\u002F15.module-reference",{"title":4486,"path":4487,"stem":4488},"Тестування сервісів та провайдерів","\u002Fweb-development\u002Fnestjs-providers-modules\u002Ftesting-services","18.web-development\u002F08.nestjs-providers-modules\u002F16.testing-services",{"title":4490,"icon":4491,"path":4492,"stem":4493,"children":4494,"page":59},"Тема 9. Валідація даних та конвеєр обробки запитів у NestJS","i-lucide-filter","\u002Fweb-development\u002Fnestjs-validation-pipeline","18.web-development\u002F09.nestjs-validation-pipeline",[4495,4499,4503,4507,4511,4515,4519,4523,4527,4531,4535,4539,4543,4547,4551,4555,4559,4563,4567],{"title":4496,"path":4497,"stem":4498},"Request Pipeline: конвеєр обробки запитів","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Frequest-pipeline","18.web-development\u002F09.nestjs-validation-pipeline\u002F01.request-pipeline",{"title":4500,"path":4501,"stem":4502},"Pipes: концепція трансформації та валідації","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fpipes-concept","18.web-development\u002F09.nestjs-validation-pipeline\u002F02.pipes-concept",{"title":4504,"path":4505,"stem":4506},"Вбудовані pipes: ParseIntPipe, ParseBoolPipe, ParseUUIDPipe","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fbuilt-in-pipes","18.web-development\u002F09.nestjs-validation-pipeline\u002F03.built-in-pipes",{"title":4508,"path":4509,"stem":4510},"ValidationPipe: автоматична валідація DTO","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fvalidation-pipe","18.web-development\u002F09.nestjs-validation-pipeline\u002F04.validation-pipe",{"title":4512,"path":4513,"stem":4514},"Декоратори class-validator для DTO","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fclass-validator-decorators","18.web-development\u002F09.nestjs-validation-pipeline\u002F05.class-validator-decorators",{"title":4516,"path":4517,"stem":4518},"Створення кастомних валідаторів","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fcustom-validators","18.web-development\u002F09.nestjs-validation-pipeline\u002F06.custom-validators",{"title":4520,"path":4521,"stem":4522},"Створення власних Pipes","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fcustom-pipes","18.web-development\u002F09.nestjs-validation-pipeline\u002F07.custom-pipes",{"title":4524,"path":4525,"stem":4526},"Основи Middleware","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fmiddleware-basics","18.web-development\u002F09.nestjs-validation-pipeline\u002F08.middleware-basics",{"title":4528,"path":4529,"stem":4530},"Практичні приклади Middleware","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fmiddleware-examples","18.web-development\u002F09.nestjs-validation-pipeline\u002F09.middleware-examples",{"title":4532,"path":4533,"stem":4534},"Guards: захисні перехоплювачі доступу","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fguards-concept","18.web-development\u002F09.nestjs-validation-pipeline\u002F10.guards-concept",{"title":4536,"path":4537,"stem":4538},"Створення кастомних Guards","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fcustom-guards","18.web-development\u002F09.nestjs-validation-pipeline\u002F11.custom-guards",{"title":4540,"path":4541,"stem":4542},"Interceptors: перехоплення та трансформація відповідей","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Finterceptors-concept","18.web-development\u002F09.nestjs-validation-pipeline\u002F12.interceptors-concept",{"title":4544,"path":4545,"stem":4546},"Практичні приклади Interceptors","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Finterceptor-examples","18.web-development\u002F09.nestjs-validation-pipeline\u002F13.interceptor-examples",{"title":4548,"path":4549,"stem":4550},"Exception Filters: обробка виключень","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fexception-filters","18.web-development\u002F09.nestjs-validation-pipeline\u002F14.exception-filters",{"title":4552,"path":4553,"stem":4554},"Custom Exception Filters: спеціалізовані фільтри","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fcustom-exception-filters","18.web-development\u002F09.nestjs-validation-pipeline\u002F15.custom-exception-filters",{"title":4556,"path":4557,"stem":4558},"Execution Context: контекст виконання","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fexecution-context","18.web-development\u002F09.nestjs-validation-pipeline\u002F16.execution-context",{"title":4560,"path":4561,"stem":4562},"Custom Decorators: власні декоратори","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fcustom-decorators","18.web-development\u002F09.nestjs-validation-pipeline\u002F17.custom-decorators",{"title":4564,"path":4565,"stem":4566},"Global Components: глобальні компоненти","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fglobal-components","18.web-development\u002F09.nestjs-validation-pipeline\u002F18.global-components",{"title":4568,"path":4569,"stem":4570},"Pipeline Best Practices: найкращі практики","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fpipeline-best-practices","18.web-development\u002F09.nestjs-validation-pipeline\u002F19.pipeline-best-practices",{"title":4572,"icon":2881,"path":4573,"stem":4574,"children":4575,"page":59},"Інтеграція реляційних баз даних засобами TypeORM","\u002Fweb-development\u002Ftypeorm-integration","18.web-development\u002F10.typeorm-integration",[4576,4580,4584,4588,4592,4596,4600],{"title":4577,"path":4578,"stem":4579},"Робота з базами даних у Node.js через нативні драйвери","\u002Fweb-development\u002Ftypeorm-integration\u002F01-nodejs-database-drivers","18.web-development\u002F10.typeorm-integration\u002F01-nodejs-database-drivers",{"title":4581,"path":4582,"stem":4583},"ORM та знайомство з TypeORM","\u002Fweb-development\u002Ftypeorm-integration\u002F02-orm-and-typeorm-intro","18.web-development\u002F10.typeorm-integration\u002F02-orm-and-typeorm-intro",{"title":4585,"path":4586,"stem":4587},"Налаштування TypeORM у NestJS проєкті","\u002Fweb-development\u002Ftypeorm-integration\u002F03-typeorm-setup-nestjs","18.web-development\u002F10.typeorm-integration\u002F03-typeorm-setup-nestjs",{"title":4589,"path":4590,"stem":4591},"Entity класи та декоратори TypeORM","\u002Fweb-development\u002Ftypeorm-integration\u002F04-entities-and-decorators","18.web-development\u002F10.typeorm-integration\u002F04-entities-and-decorators",{"title":4593,"path":4594,"stem":4595},"Repository Pattern та CRUD операції","\u002Fweb-development\u002Ftypeorm-integration\u002F05-repository-pattern-crud","18.web-development\u002F10.typeorm-integration\u002F05-repository-pattern-crud",{"title":4597,"path":4598,"stem":4599},"Пагінація та фільтрація даних","\u002Fweb-development\u002Ftypeorm-integration\u002F06-pagination-filtering","18.web-development\u002F10.typeorm-integration\u002F06-pagination-filtering",{"title":4601,"path":4602,"stem":4603},"QueryBuilder для складних запитів","\u002Fweb-development\u002Ftypeorm-integration\u002F07-query-builder","18.web-development\u002F10.typeorm-integration\u002F07-query-builder",{"title":4605,"icon":4606,"path":4607,"stem":4608,"children":4609,"page":59},"Зв'язки між сутностями, міграції та оптимізація запитів","i-lucide-git-branch","\u002Fweb-development\u002Fentity-relations-migrations","18.web-development\u002F11.entity-relations-migrations",[4610,4614,4618,4622,4626],{"title":4611,"path":4612,"stem":4613},"Зв'язки One-to-Many та Many-to-One","\u002Fweb-development\u002Fentity-relations-migrations\u002F01-one-to-many-many-to-one","18.web-development\u002F11.entity-relations-migrations\u002F01-one-to-many-many-to-one",{"title":4615,"path":4616,"stem":4617},"Зв'язки One-to-One та Many-to-Many","\u002Fweb-development\u002Fentity-relations-migrations\u002F02-one-to-one-many-to-many","18.web-development\u002F11.entity-relations-migrations\u002F02-one-to-one-many-to-many",{"title":4619,"path":4620,"stem":4621},"Керування міграціями бази даних","\u002Fweb-development\u002Fentity-relations-migrations\u002F03-migrations-management","18.web-development\u002F11.entity-relations-migrations\u002F03-migrations-management",{"title":4623,"path":4624,"stem":4625},"Транзакції у TypeORM","\u002Fweb-development\u002Fentity-relations-migrations\u002F04-transactions","18.web-development\u002F11.entity-relations-migrations\u002F04-transactions",{"title":4627,"path":4628,"stem":4629,"children":4630},"Індекси та оптимізація запитів","\u002Fweb-development\u002Fentity-relations-migrations\u002F05-indexes-optimization","18.web-development\u002F11.entity-relations-migrations\u002F05-indexes-optimization",[4631],{"title":4627,"path":4628,"stem":4629},{"title":4633,"icon":4634,"path":4635,"stem":4636,"children":4637,"page":59},"Механізми автентифікації у вебзастосунках","i-lucide-key","\u002Fweb-development\u002Fauthentication","18.web-development\u002F12.authentication",[4638,4642,4646,4650,4654,4658,4662,4666,4670],{"title":4639,"path":4640,"stem":4641},"Автентифікація vs Авторизація","\u002Fweb-development\u002Fauthentication\u002F01-authentication-vs-authorization","18.web-development\u002F12.authentication\u002F01-authentication-vs-authorization",{"title":4643,"path":4644,"stem":4645},"Стратегії автентифікації","\u002Fweb-development\u002Fauthentication\u002F02-authentication-strategies","18.web-development\u002F12.authentication\u002F02-authentication-strategies",{"title":4647,"path":4648,"stem":4649},"Автентифікація на основі сесій","\u002Fweb-development\u002Fauthentication\u002F03-session-based-authentication","18.web-development\u002F12.authentication\u002F03-session-based-authentication",{"title":4651,"path":4652,"stem":4653},"Структура JSON Web Token (JWT)","\u002Fweb-development\u002Fauthentication\u002F04-jwt-structure","18.web-development\u002F12.authentication\u002F04-jwt-structure",{"title":4655,"path":4656,"stem":4657},"Інтеграція JWT у NestJS","\u002Fweb-development\u002Fauthentication\u002F05-nestjs-jwt-integration","18.web-development\u002F12.authentication\u002F05-nestjs-jwt-integration",{"title":4659,"path":4660,"stem":4661},"Passport.js стратегії у NestJS","\u002Fweb-development\u002Fauthentication\u002F06-passport-strategies","18.web-development\u002F12.authentication\u002F06-passport-strategies",{"title":4663,"path":4664,"stem":4665},"Безпечне зберігання паролів: хешування та криптографічний захист","\u002Fweb-development\u002Fauthentication\u002F07-password-hashing","18.web-development\u002F12.authentication\u002F07-password-hashing",{"title":4667,"path":4668,"stem":4669},"Refresh Token та безпечне оновлення доступу","\u002Fweb-development\u002Fauthentication\u002F08-refresh-tokens","18.web-development\u002F12.authentication\u002F08-refresh-tokens",{"title":4671,"path":4672,"stem":4673},"OAuth 2.0 та OpenID Connect: делегована автентифікація","\u002Fweb-development\u002Fauthentication\u002F09-oauth2-openid","18.web-development\u002F12.authentication\u002F09-oauth2-openid",{"title":4675,"icon":4676,"path":4677,"stem":4678,"children":4679,"page":59},"Авторизація та безпека серверних застосунків","i-lucide-shield","\u002Fweb-development\u002Fauthorization-security","18.web-development\u002F13.authorization-security",[4680,4684,4688,4692,4696,4700,4704,4708,4712,4716],{"title":4681,"path":4682,"stem":4683},"Моделі авторизації","\u002Fweb-development\u002Fauthorization-security\u002F01-authorization-models","18.web-development\u002F13.authorization-security\u002F01-authorization-models",{"title":4685,"path":4686,"stem":4687},"Реалізація RBAC у NestJS","\u002Fweb-development\u002Fauthorization-security\u002F02-rbac-implementation","18.web-development\u002F13.authorization-security\u002F02-rbac-implementation",{"title":4689,"path":4690,"stem":4691},"Permission-Based Access Control","\u002Fweb-development\u002Fauthorization-security\u002F03-permission-based-access","18.web-development\u002F13.authorization-security\u002F03-permission-based-access",{"title":4693,"path":4694,"stem":4695},"ABAC та бібліотека CASL","\u002Fweb-development\u002Fauthorization-security\u002F04-abac-casl","18.web-development\u002F13.authorization-security\u002F04-abac-casl",{"title":4697,"path":4698,"stem":4699},"Кастомні декоратори та метадані","\u002Fweb-development\u002Fauthorization-security\u002F05-custom-decorators-metadata","18.web-development\u002F13.authorization-security\u002F05-custom-decorators-metadata",{"title":4701,"path":4702,"stem":4703},"Конфігурація CORS","\u002Fweb-development\u002Fauthorization-security\u002F06-cors-configuration","18.web-development\u002F13.authorization-security\u002F06-cors-configuration",{"title":4705,"path":4706,"stem":4707},"Захист через HTTP Security Headers (Helmet)","\u002Fweb-development\u002Fauthorization-security\u002F07-helmet-security-headers","18.web-development\u002F13.authorization-security\u002F07-helmet-security-headers",{"title":4709,"path":4710,"stem":4711},"Rate Limiting та Throttling","\u002Fweb-development\u002Fauthorization-security\u002F08-rate-limiting-throttling","18.web-development\u002F13.authorization-security\u002F08-rate-limiting-throttling",{"title":4713,"path":4714,"stem":4715},"Захист від поширених атак","\u002Fweb-development\u002Fauthorization-security\u002F09-common-attacks-protection","18.web-development\u002F13.authorization-security\u002F09-common-attacks-protection",{"title":4717,"path":4718,"stem":4719},"HTTPS у продакшені","\u002Fweb-development\u002Fauthorization-security\u002F10-https-production","18.web-development\u002F13.authorization-security\u002F10-https-production",{"title":4721,"icon":871,"path":4722,"stem":4723,"children":4724,"page":59},"Комунікація у реальному часі, нотифікації та фонові задачі","\u002Fweb-development\u002Frealtime-notifications-jobs","18.web-development\u002F14.realtime-notifications-jobs",[4725,4729,4733,4737,4741,4745,4748,4751,4755,4759],{"title":4726,"path":4727,"stem":4728},"Методи комунікації у реальному часі","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F01-realtime-communication-methods","18.web-development\u002F14.realtime-notifications-jobs\u002F01-realtime-communication-methods",{"title":4730,"path":4731,"stem":4732},"WebSocket Gateway у NestJS","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F02-websocket-gateway","18.web-development\u002F14.realtime-notifications-jobs\u002F02-websocket-gateway",{"title":4734,"path":4735,"stem":4736},"Lifecycle та Rooms у WebSocket","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F03-websocket-lifecycle-rooms","18.web-development\u002F14.realtime-notifications-jobs\u002F03-websocket-lifecycle-rooms",{"title":4738,"path":4739,"stem":4740},"Server-Sent Events (SSE)","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F04-server-sent-events","18.web-development\u002F14.realtime-notifications-jobs\u002F04-server-sent-events",{"title":4742,"path":4743,"stem":4744},"Архітектура системи нотифікацій","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F05-notification-system","18.web-development\u002F14.realtime-notifications-jobs\u002F05-notification-system",{"title":904,"path":4746,"stem":4747},"\u002Fweb-development\u002Frealtime-notifications-jobs\u002F06-email-notifications","18.web-development\u002F14.realtime-notifications-jobs\u002F06-email-notifications",{"title":900,"path":4749,"stem":4750},"\u002Fweb-development\u002Frealtime-notifications-jobs\u002F07-web-push-notifications","18.web-development\u002F14.realtime-notifications-jobs\u002F07-web-push-notifications",{"title":4752,"path":4753,"stem":4754},"Фонові задачі та черги","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F08-background-jobs-queues","18.web-development\u002F14.realtime-notifications-jobs\u002F08-background-jobs-queues",{"title":4756,"path":4757,"stem":4758},"Планувальники та Cron jobs","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F09-schedulers-cron","18.web-development\u002F14.realtime-notifications-jobs\u002F09-schedulers-cron",{"title":4760,"path":4761,"stem":4762},"Практичні сценарії застосування","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F10-practical-scenarios","18.web-development\u002F14.realtime-notifications-jobs\u002F10-practical-scenarios",{"title":4764,"icon":4765,"path":4766,"stem":4767,"children":4768,"page":59},"Тестування, документування та розгортання застосунків","i-lucide-rocket","\u002Fweb-development\u002Ftesting-documentation-deployment","18.web-development\u002F15.testing-documentation-deployment",[4769,4773,4777,4781,4785,4789,4793,4797,4801,4805],{"title":4770,"path":4771,"stem":4772},"Піраміда тестування та стратегія","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F01-testing-pyramid-strategy","18.web-development\u002F15.testing-documentation-deployment\u002F01-testing-pyramid-strategy",{"title":4774,"path":4775,"stem":4776},"Основи Jest у NestJS","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F02-jest-nestjs-basics","18.web-development\u002F15.testing-documentation-deployment\u002F02-jest-nestjs-basics",{"title":4778,"path":4779,"stem":4780},"Unit-тестування сервісів","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F03-unit-testing-services","18.web-development\u002F15.testing-documentation-deployment\u002F03-unit-testing-services",{"title":4782,"path":4783,"stem":4784},"E2E тестування та покриття коду","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F04-e2e-testing-coverage","18.web-development\u002F15.testing-documentation-deployment\u002F04-e2e-testing-coverage",{"title":4786,"path":4787,"stem":4788},"Swagger, OpenAPI, Scalar та Arazzo","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F05-swagger-openapi","18.web-development\u002F15.testing-documentation-deployment\u002F05-swagger-openapi",{"title":4790,"path":4791,"stem":4792},"Керування конфігурацією","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F06-configuration-management","18.web-development\u002F15.testing-documentation-deployment\u002F06-configuration-management",{"title":4794,"path":4795,"stem":4796},"Docker та контейнеризація","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F07-docker-containerization","18.web-development\u002F15.testing-documentation-deployment\u002F07-docker-containerization",{"title":4798,"path":4799,"stem":4800},"CI\u002FCD Pipelines","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F08-cicd-pipelines","18.web-development\u002F15.testing-documentation-deployment\u002F08-cicd-pipelines",{"title":4802,"path":4803,"stem":4804},"Логування та моніторинг","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F09-logging-monitoring","18.web-development\u002F15.testing-documentation-deployment\u002F09-logging-monitoring",{"title":4806,"path":4807,"stem":4808},"Серіалізація та компресія","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F10-serialization-compression","18.web-development\u002F15.testing-documentation-deployment\u002F10-serialization-compression",{"title":4810,"icon":4811,"path":4812,"stem":4813,"children":4814,"page":59},"AI Core: мислення AI","i-lucide-brain","\u002Fai-core","19.ai-core",[4815,4856,4905,4943],{"title":4816,"icon":4765,"path":4817,"stem":4818,"children":4819,"page":59},"Вхід у професію AI Native Developer","\u002Fai-core\u002Fai-native-developer","19.ai-core\u002F01.ai-native-developer",[4820,4824,4828,4832,4836,4840,4844,4848,4852],{"title":4821,"path":4822,"stem":4823},"Вступ до професії розробника цифрових продуктів","\u002Fai-core\u002Fai-native-developer\u002Fdigital-products","19.ai-core\u002F01.ai-native-developer\u002F01.digital-products",{"title":4825,"path":4826,"stem":4827},"Професія розробника програмного забезпечення","\u002Fai-core\u002Fai-native-developer\u002Fsoftware-developer","19.ai-core\u002F01.ai-native-developer\u002F02.software-developer",{"title":4829,"path":4830,"stem":4831},"Професія AI Native Developer","\u002Fai-core\u002Fai-native-developer\u002Fai-native-developer","19.ai-core\u002F01.ai-native-developer\u002F03.ai-native-developer",{"title":4833,"path":4834,"stem":4835},"Вплив AI на розробку програмного забезпечення","\u002Fai-core\u002Fai-native-developer\u002Fai-impact-on-development","19.ai-core\u002F01.ai-native-developer\u002F04.ai-impact-on-development",{"title":4837,"path":4838,"stem":4839},"Життєвий цикл цифрового продукту","\u002Fai-core\u002Fai-native-developer\u002Fproduct-lifecycle","19.ai-core\u002F01.ai-native-developer\u002F05.product-lifecycle",{"title":4841,"path":4842,"stem":4843},"Застосування AI на етапах створення цифрового продукту","\u002Fai-core\u002Fai-native-developer\u002Fai-in-product-creation","19.ai-core\u002F01.ai-native-developer\u002F06.ai-in-product-creation",{"title":4845,"path":4846,"stem":4847},"Розподіл завдань між людиною та AI","\u002Fai-core\u002Fai-native-developer\u002Fhuman-vs-ai-tasks","19.ai-core\u002F01.ai-native-developer\u002F07.human-vs-ai-tasks",{"title":4849,"path":4850,"stem":4851},"Компетенції AI Native Developer","\u002Fai-core\u002Fai-native-developer\u002Fcompetencies","19.ai-core\u002F01.ai-native-developer\u002F08.competencies",{"title":4853,"path":4854,"stem":4855},"Карта професійного розвитку AI Native Developer","\u002Fai-core\u002Fai-native-developer\u002Fcareer-roadmap","19.ai-core\u002F01.ai-native-developer\u002F09.career-roadmap",{"title":4857,"icon":255,"path":4858,"stem":4859,"children":4860,"page":59},"Штучний інтелект і машинне навчання","\u002Fai-core\u002Fai-and-machine-learning","19.ai-core\u002F02.ai-and-machine-learning",[4861,4865,4869,4873,4877,4881,4885,4889,4893,4897,4901],{"title":4862,"path":4863,"stem":4864},"Штучний інтелект","\u002Fai-core\u002Fai-and-machine-learning\u002Fwhat-is-ai","19.ai-core\u002F02.ai-and-machine-learning\u002F01.what-is-ai",{"title":4866,"path":4867,"stem":4868},"Відмінність AI від інших програмних систем","\u002Fai-core\u002Fai-and-machine-learning\u002Fai-vs-automation","19.ai-core\u002F02.ai-and-machine-learning\u002F02.ai-vs-automation",{"title":4870,"path":4871,"stem":4872},"Завдання штучного інтелекту","\u002Fai-core\u002Fai-and-machine-learning\u002Fai-tasks","19.ai-core\u002F02.ai-and-machine-learning\u002F03.ai-tasks",{"title":4874,"path":4875,"stem":4876},"Machine Learning","\u002Fai-core\u002Fai-and-machine-learning\u002Fmachine-learning","19.ai-core\u002F02.ai-and-machine-learning\u002F04.machine-learning",{"title":4878,"path":4879,"stem":4880},"Machine Learning Workflow","\u002Fai-core\u002Fai-and-machine-learning\u002Fml-workflow","19.ai-core\u002F02.ai-and-machine-learning\u002F05.ml-workflow",{"title":4882,"path":4883,"stem":4884},"Типи машинного навчання","\u002Fai-core\u002Fai-and-machine-learning\u002Fml-types","19.ai-core\u002F02.ai-and-machine-learning\u002F06.ml-types",{"title":4886,"path":4887,"stem":4888},"Generative AI","\u002Fai-core\u002Fai-and-machine-learning\u002Fgenerative-ai","19.ai-core\u002F02.ai-and-machine-learning\u002F07.generative-ai",{"title":4890,"path":4891,"stem":4892},"Типи контенту, створюваного AI","\u002Fai-core\u002Fai-and-machine-learning\u002Fai-content-types","19.ai-core\u002F02.ai-and-machine-learning\u002F08.ai-content-types",{"title":4894,"path":4895,"stem":4896},"Великі мовні моделі","\u002Fai-core\u002Fai-and-machine-learning\u002Flarge-language-models","19.ai-core\u002F02.ai-and-machine-learning\u002F09.large-language-models",{"title":4898,"path":4899,"stem":4900},"Можливості та обмеження Generative AI","\u002Fai-core\u002Fai-and-machine-learning\u002Fcapabilities-and-limitations","19.ai-core\u002F02.ai-and-machine-learning\u002F10.capabilities-and-limitations",{"title":4902,"path":4903,"stem":4904},"Сучасні AI-асистенти","\u002Fai-core\u002Fai-and-machine-learning\u002Fmodern-ai-assistants","19.ai-core\u002F02.ai-and-machine-learning\u002F11.modern-ai-assistants",{"title":4906,"icon":4907,"path":4908,"stem":4909,"children":4910,"page":59},"Постановка завдань для AI: принципи створення промптів","i-lucide-message-square-text","\u002Fai-core\u002Fprompt-engineering","19.ai-core\u002F03.prompt-engineering",[4911,4915,4919,4923,4927,4931,4935,4939],{"title":4912,"path":4913,"stem":4914},"Промпт як інструмент","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-as-tool","19.ai-core\u002F03.prompt-engineering\u002F01.prompt-as-tool",{"title":4916,"path":4917,"stem":4918},"Принципи створення промптів","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-principles","19.ai-core\u002F03.prompt-engineering\u002F02.prompt-principles",{"title":4920,"path":4921,"stem":4922},"Структура промпта","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-structure","19.ai-core\u002F03.prompt-engineering\u002F03.prompt-structure",{"title":4924,"path":4925,"stem":4926},"Види промптів за типом задачі","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-types","19.ai-core\u002F03.prompt-engineering\u002F04.prompt-types",{"title":4928,"path":4929,"stem":4930},"Прийоми посилення промпта","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-enhancement","19.ai-core\u002F03.prompt-engineering\u002F05.prompt-enhancement",{"title":4932,"path":4933,"stem":4934},"Розбір і покращення промпта","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-analysis","19.ai-core\u002F03.prompt-engineering\u002F06.prompt-analysis",{"title":4936,"path":4937,"stem":4938},"Типові помилки під час створення промптів","\u002Fai-core\u002Fprompt-engineering\u002Fcommon-mistakes","19.ai-core\u002F03.prompt-engineering\u002F07.common-mistakes",{"title":4940,"path":4941,"stem":4942},"Практикум: особиста бібліотека промптів","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-library","19.ai-core\u002F03.prompt-engineering\u002F08.prompt-library",{"title":4944,"icon":793,"path":4945,"stem":4946,"children":4947,"page":59},"Перевірка результатів, безпека та AI Native Workflow","\u002Fai-core\u002Fverification-security-workflow","19.ai-core\u002F04.verification-security-workflow",[4948,4952,4956,4960,4964,4968,4972,4976,4980],{"title":4949,"path":4950,"stem":4951},"Межі можливостей AI","\u002Fai-core\u002Fverification-security-workflow\u002Fai-limitations","19.ai-core\u002F04.verification-security-workflow\u002F01.ai-limitations",{"title":4953,"path":4954,"stem":4955},"Галюцинації AI","\u002Fai-core\u002Fverification-security-workflow\u002Fai-hallucinations","19.ai-core\u002F04.verification-security-workflow\u002F02.ai-hallucinations",{"title":4957,"path":4958,"stem":4959},"Критичне мислення під час роботи з AI","\u002Fai-core\u002Fverification-security-workflow\u002Fcritical-thinking","19.ai-core\u002F04.verification-security-workflow\u002F03.critical-thinking",{"title":4961,"path":4962,"stem":4963},"Перевірка результатів роботи AI","\u002Fai-core\u002Fverification-security-workflow\u002Fresult-verification","19.ai-core\u002F04.verification-security-workflow\u002F04.result-verification",{"title":4965,"path":4966,"stem":4967},"Захист даних під час роботи з AI","\u002Fai-core\u002Fverification-security-workflow\u002Fdata-protection","19.ai-core\u002F04.verification-security-workflow\u002F05.data-protection",{"title":4969,"path":4970,"stem":4971},"Авторське право та навчальна доброчесність","\u002Fai-core\u002Fverification-security-workflow\u002Fcopyright-integrity","19.ai-core\u002F04.verification-security-workflow\u002F06.copyright-integrity",{"title":4973,"path":4974,"stem":4975},"Відповідальне використання AI","\u002Fai-core\u002Fverification-security-workflow\u002Fresponsible-use","19.ai-core\u002F04.verification-security-workflow\u002F07.responsible-use",{"title":4977,"path":4978,"stem":4979},"AI Native Workflow","\u002Fai-core\u002Fverification-security-workflow\u002Fai-native-workflow","19.ai-core\u002F04.verification-security-workflow\u002F08.ai-native-workflow",{"title":4981,"path":4982,"stem":4983},"Застосування AI Native Workflow під час створення цифрового продукту","\u002Fai-core\u002Fverification-security-workflow\u002Fworkflow-in-practice","19.ai-core\u002F04.verification-security-workflow\u002F09.workflow-in-practice",{"title":4985,"icon":4986,"path":4987,"stem":4988,"children":4989,"page":59},"AI Developer: Vibe Coding Sprint","i-lucide-code-xml","\u002Fai-developer","20.ai-developer",[4990,5016,5038,5059],{"title":4991,"icon":4992,"path":4993,"stem":4994,"children":4995,"page":59},"Проєктування і чорнова версія","i-lucide-pencil-ruler","\u002Fai-developer\u002Fdraft-creation","20.ai-developer\u002F01.draft-creation",[4996,5000,5004,5008,5012],{"title":4997,"path":4998,"stem":4999},"Парадигма Vibe Coding Workflow","\u002Fai-developer\u002Fdraft-creation\u002Fvibe-coding-workflow","20.ai-developer\u002F01.draft-creation\u002F01.vibe-coding-workflow",{"title":5001,"path":5002,"stem":5003},"AI-середовище швидкої розробки","\u002Fai-developer\u002Fdraft-creation\u002Fai-ide-environment","20.ai-developer\u002F01.draft-creation\u002F02.ai-ide-environment",{"title":5005,"path":5006,"stem":5007},"Користувацьке завдання та межі першої версії","\u002Fai-developer\u002Fdraft-creation\u002Fproduct-scope-and-mvp","20.ai-developer\u002F01.draft-creation\u002F03.product-scope-and-mvp",{"title":5009,"path":5010,"stem":5011},"Архітектура інтерфейсу та стани застосунку","\u002Fai-developer\u002Fdraft-creation\u002Fapplication-architecture-and-states","20.ai-developer\u002F01.draft-creation\u002F04.application-architecture-and-states",{"title":5013,"path":5014,"stem":5015},"Генерація та фіксація чорнової версії","\u002Fai-developer\u002Fdraft-creation\u002Fgenerating-draft-version","20.ai-developer\u002F01.draft-creation\u002F05.generating-draft-version",{"title":5017,"icon":5018,"path":5019,"stem":5020,"children":5021,"page":59},"Перша робоча версія","i-lucide-play-circle","\u002Fai-developer\u002Ffirst-working-version","20.ai-developer\u002F02.first-working-version",[5022,5026,5030,5034],{"title":5023,"path":5024,"stem":5025},"Уточнення контексту проєкту для AI","\u002Fai-developer\u002Ffirst-working-version\u002Frefining-project-context","20.ai-developer\u002F02.first-working-version\u002F01.refining-project-context",{"title":5027,"path":5028,"stem":5029},"Стратегія завдань для AI-розробки","\u002Fai-developer\u002Ffirst-working-version\u002Fai-prompting-strategy","20.ai-developer\u002F02.first-working-version\u002F02.ai-prompting-strategy",{"title":5031,"path":5032,"stem":5033},"Доопрацювання до першої робочої версії","\u002Fai-developer\u002Ffirst-working-version\u002Frefining-to-working-version","20.ai-developer\u002F02.first-working-version\u002F03.refining-to-working-version",{"title":5035,"path":5036,"stem":5037},"Перевірка першої робочої версії","\u002Fai-developer\u002Ffirst-working-version\u002Ftesting-first-working-version","20.ai-developer\u002F02.first-working-version\u002F04.testing-first-working-version",{"title":5039,"icon":3088,"path":5040,"stem":5041,"children":5042,"page":59},"Ітерації, дебагінг та відновлення","\u002Fai-developer\u002Fiteration-debugging-recovery","20.ai-developer\u002F03.iteration-debugging-recovery",[5043,5047,5051,5055],{"title":5044,"path":5045,"stem":5046},"Управління точковими змінами продукту","\u002Fai-developer\u002Fiteration-debugging-recovery\u002Fchange-management","20.ai-developer\u002F03.iteration-debugging-recovery\u002F01.change-management",{"title":5048,"path":5049,"stem":5050},"Надійність інтерфейсу та обробка помилок","\u002Fai-developer\u002Fiteration-debugging-recovery\u002Fscenario-reliability-and-errors","20.ai-developer\u002F03.iteration-debugging-recovery\u002F02.scenario-reliability-and-errors",{"title":5052,"path":5053,"stem":5054},"Керування контекстом і збереження версій","\u002Fai-developer\u002Fiteration-debugging-recovery\u002Fproject-context-and-versions","20.ai-developer\u002F03.iteration-debugging-recovery\u002F03.project-context-and-versions",{"title":5056,"path":5057,"stem":5058},"Збої AI-розробки, ліміти та аварійне відновлення","\u002Fai-developer\u002Fiteration-debugging-recovery\u002Fai-breakdowns-and-recovery","20.ai-developer\u002F03.iteration-debugging-recovery\u002F04.ai-breakdowns-and-recovery",{"title":5060,"icon":5061,"path":5062,"stem":5063,"children":5064,"page":59},"Перевірка та завершення продукту","i-lucide-check-check","\u002Fai-developer\u002Fverification-and-completion","20.ai-developer\u002F04.verification-and-completion",[5065,5069,5073],{"title":5066,"path":5067,"stem":5068},"Комплексний аудит та підсумкове тестування","\u002Fai-developer\u002Fverification-and-completion\u002Ffinal-product-testing","20.ai-developer\u002F04.verification-and-completion\u002F01.final-product-testing",{"title":5070,"path":5071,"stem":5072},"Підготовка підсумкової версії коду","\u002Fai-developer\u002Fverification-and-completion\u002Fpreparing-release-version","20.ai-developer\u002F04.verification-and-completion\u002F02.preparing-release-version",{"title":5074,"path":5075,"stem":5076},"Демонстрація, публікація та критерії оцінювання","\u002Fai-developer\u002Fverification-and-completion\u002Fproduct-showcase-and-publishing","20.ai-developer\u002F04.verification-and-completion\u002F03.product-showcase-and-publishing",{"title":5078,"path":5079,"stem":5080,"children":5081,"page":59},"Tailwind","\u002Ftailwind","21.tailwind",[5082,5086,5090,5094,5098,5102,5106,5110,5114,5118,5122,5126],{"title":5083,"path":5084,"stem":5085},"Що таке Tailwind CSS і навіщо він потрібен","\u002Ftailwind\u002Ftailwind-intro-philosophy","21.tailwind\u002F01.tailwind-intro-philosophy",{"title":5087,"path":5088,"stem":5089},"Встановлення та налаштування Tailwind CSS v4","\u002Ftailwind\u002Ftailwind-installation-setup","21.tailwind\u002F02.tailwind-installation-setup",{"title":5091,"path":5092,"stem":5093},"Utility-класи: основи та система Tailwind","\u002Ftailwind\u002Ftailwind-utility-classes-core","21.tailwind\u002F03.tailwind-utility-classes-core",{"title":5095,"path":5096,"stem":5097},"Layout: Flexbox та Grid через Tailwind","\u002Ftailwind\u002Ftailwind-flexbox-grid","21.tailwind\u002F04.tailwind-flexbox-grid",{"title":5099,"path":5100,"stem":5101},"Кастомізація теми через @theme у Tailwind v4","\u002Ftailwind\u002Ftailwind-theme-customization","21.tailwind\u002F05.tailwind-theme-customization",{"title":5103,"path":5104,"stem":5105},"Варіанти: hover, focus, responsive, dark mode та нові v4","\u002Ftailwind\u002Ftailwind-variants-states","21.tailwind\u002F06.tailwind-variants-states",{"title":5107,"path":5108,"stem":5109},"Типографіка та система кольорів у Tailwind v4","\u002Ftailwind\u002Ftailwind-typography-colors","21.tailwind\u002F07.tailwind-typography-colors",{"title":5111,"path":5112,"stem":5113},"Компоненти та повторюваність: @apply, @utility та патерни","\u002Ftailwind\u002Ftailwind-components-patterns","21.tailwind\u002F08.tailwind-components-patterns",{"title":5115,"path":5116,"stem":5117},"Темна тема та система дизайн-токенів у Tailwind v4","\u002Ftailwind\u002Ftailwind-dark-mode-theming","21.tailwind\u002F09.tailwind-dark-mode-theming",{"title":5119,"path":5120,"stem":5121},"Довільні значення та контейнерні запити у Tailwind v4","\u002Ftailwind\u002Ftailwind-arbitrary-container-queries","21.tailwind\u002F10.tailwind-arbitrary-container-queries",{"title":5123,"path":5124,"stem":5125},"Анімації, трансформації та 3D у Tailwind v4","\u002Ftailwind\u002Ftailwind-animations-transforms","21.tailwind\u002F11.tailwind-animations-transforms",{"title":5127,"path":5128,"stem":5129},"Tailwind CLI, PostCSS та інтеграція з фреймворками","\u002Ftailwind\u002Ftailwind-cli-tooling","21.tailwind\u002F12.tailwind-cli-tooling",{"title":5131,"path":5132,"stem":5133,"children":5134,"page":59},"React Typescript","\u002Freact-typescript","22.react-typescript",[5135,5160,5164,5168,5172,5176,5180,5184,5188,5192,5222,5226,5230,5234,5238],{"title":5136,"path":5137,"stem":5138,"children":5139,"page":59},"From Html To Project","\u002Freact-typescript\u002Ffrom-html-to-project","22.react-typescript\u002F01.from-html-to-project",[5140,5144,5148,5152,5156],{"title":5141,"path":5142,"stem":5143},"Від одного HTML-файлу до повноцінного проєкту","\u002Freact-typescript\u002Ffrom-html-to-project\u002Fevolution","22.react-typescript\u002F01.from-html-to-project\u002F01.evolution",{"title":5145,"path":5146,"stem":5147},"Що таке React","\u002Freact-typescript\u002Ffrom-html-to-project\u002Fwhat-is-react","22.react-typescript\u002F01.from-html-to-project\u002F02.what-is-react",{"title":5149,"path":5150,"stem":5151},"JSX та TSX — синтаксичний цукор, а не магія","\u002Freact-typescript\u002Ffrom-html-to-project\u002Fjsx-tsx-syntax","22.react-typescript\u002F01.from-html-to-project\u002F03.jsx-tsx-syntax",{"title":5153,"path":5154,"stem":5155},"Компоненти — будівельні блоки інтерфейсу","\u002Freact-typescript\u002Ffrom-html-to-project\u002Fcomponents","22.react-typescript\u002F01.from-html-to-project\u002F04.components",{"title":5157,"path":5158,"stem":5159},"JSX — розмітка всередині TypeScript","\u002Freact-typescript\u002Ffrom-html-to-project\u002Fjsx-expressions","22.react-typescript\u002F01.from-html-to-project\u002F05.jsx-expressions",{"title":5161,"path":5162,"stem":5163},"Хук useReducer: структуроване управління складним станом","\u002Freact-typescript\u002Fuse-reducer","22.react-typescript\u002F23.use-reducer",{"title":5165,"path":5166,"stem":5167},"Context API: передавання даних без «пропс-дрілінгу»","\u002Freact-typescript\u002Fcontext-api","22.react-typescript\u002F24.context-api",{"title":5169,"path":5170,"stem":5171},"Синхронізація з ефектами: хук useEffect та функції очищення","\u002Freact-typescript\u002Fuse-effect","22.react-typescript\u002F27.use-effect",{"title":5173,"path":5174,"stem":5175},"Можливо, вам не потрібен ефект: антипатерни та альтернативи","\u002Freact-typescript\u002Fyou-might-not-need-effect","22.react-typescript\u002F28.you-might-not-need-effect",{"title":5177,"path":5178,"stem":5179},"Життєвий цикл реактивних ефектів: мислення процесами синхронізації","\u002Freact-typescript\u002Flifecycle-of-reactive-effects","22.react-typescript\u002F29.lifecycle-of-reactive-effects",{"title":5181,"path":5182,"stem":5183},"Розділення подій та ефектів: реактивна проти нереактивної логіки","\u002Freact-typescript\u002Fseparating-events-from-effects","22.react-typescript\u002F30.separating-events-from-effects",{"title":5185,"path":5186,"stem":5187},"Видалення зайвих залежностей ефектів та оптимізація синхронізації","\u002Freact-typescript\u002Fremoving-effect-dependencies","22.react-typescript\u002F31.removing-effect-dependencies",{"title":5189,"path":5190,"stem":5191},"Кастомні хуки: повторне використання та композиція реактивної логіки","\u002Freact-typescript\u002Fcustom-hooks","22.react-typescript\u002F32.custom-hooks",{"title":5193,"path":5194,"stem":5195,"children":5196},"React Router v7: Маршрутизація в SPA","\u002Freact-typescript\u002Freact-router-v7","22.react-typescript\u002F33.react-router-v7\u002Findex",[5197,5198,5202,5206,5210,5214,5218],{"title":5193,"path":5194,"stem":5195},{"title":5199,"path":5200,"stem":5201},"Встановлення та базова конфігурація React Router v7","\u002Freact-typescript\u002Freact-router-v7\u002Finstallation-setup","22.react-typescript\u002F33.react-router-v7\u002F01.installation-setup",{"title":5203,"path":5204,"stem":5205},"Вкладені маршрути та Outlet: архітектура складних макетів","\u002Freact-typescript\u002Freact-router-v7\u002Fnested-routes-outlet","22.react-typescript\u002F33.react-router-v7\u002F02.nested-routes-outlet",{"title":5207,"path":5208,"stem":5209},"Динамічні маршрути та параметри URL","\u002Freact-typescript\u002Freact-router-v7\u002Fdynamic-routes-params","22.react-typescript\u002F33.react-router-v7\u002F03.dynamic-routes-params",{"title":5211,"path":5212,"stem":5213},"Навігація та корисні хуки React Router","\u002Freact-typescript\u002Freact-router-v7\u002Fnavigation-hooks","22.react-typescript\u002F33.react-router-v7\u002F04.navigation-hooks",{"title":5215,"path":5216,"stem":5217},"Обробка помилок та 404: ErrorBoundary і fallback-маршрути","\u002Freact-typescript\u002Freact-router-v7\u002Ferror-handling-404","22.react-typescript\u002F33.react-router-v7\u002F05.error-handling-404",{"title":5219,"path":5220,"stem":5221},"Data Router API: альтернативний синтаксис через createBrowserRouter","\u002Freact-typescript\u002Freact-router-v7\u002Fdata-router-api-examples","22.react-typescript\u002F33.react-router-v7\u002F06.data-router-api-examples",{"title":5223,"path":5224,"stem":5225},"Axios: HTTP-клієнт із розширеними можливостями","\u002Freact-typescript\u002Faxios","22.react-typescript\u002F34.axios",{"title":5227,"path":5228,"stem":5229},"Redux: класичний підхід до глобального стану","\u002Freact-typescript\u002Fredux-classic","22.react-typescript\u002F35.redux-classic",{"title":5231,"path":5232,"stem":5233},"Redux Toolkit: сучасний стандарт Redux","\u002Freact-typescript\u002Fredux-toolkit","22.react-typescript\u002F36.redux-toolkit",{"title":5235,"path":5236,"stem":5237},"RTK Query: запити до сервера без болю","\u002Freact-typescript\u002Frtk-query-tanstack-query","22.react-typescript\u002F38.rtk-query-tanstack-query",{"title":5239,"path":5240,"stem":5241},"React Hook Form + Zod: типобезпечна валідація форм","\u002Freact-typescript\u002Freact-hook-form-zod","22.react-typescript\u002F39.react-hook-form-zod",{"title":5243,"path":5244,"stem":5245},"Тестування компонентів діаграм та пісочниць","\u002Ftest-components","98.test-components",{"id":5247,"title":2077,"body":5248,"description":13690,"extension":13691,"links":13692,"meta":13693,"navigation":5565,"path":2078,"seo":13694,"stem":2079,"__hash__":13695},"docs\u002F02.cpp\u002F91.binary-search-tree.md",{"type":5249,"value":5250,"toc":13652},"minimark",[5251,5255,5381,5384,5389,5404,5419,5429,5439,5453,5460,5476,5485,5515,5526,5736,5746,5748,5752,5757,5774,5779,5960,5979,5983,6001,6013,6051,6056,6064,6096,6101,6107,6123,6139,6143,6153,6170,6180,6190,6196,6221,6223,6227,6231,6242,6384,6394,6400,6404,7110,7122,7144,7148,7377,7389,7391,7395,7402,7407,7454,7799,7825,8063,8068,8070,8074,8080,8084,8358,8362,8365,8575,8580,8597,8599,8603,8613,8617,8622,8628,8632,8635,8641,8645,8650,8668,8681,8687,8691,9381,9392,9397,9399,9403,9412,9416,9426,9616,9624,9630,9634,9640,9823,9828,9834,9838,9843,10026,10030,10036,10207,10212,10214,10218,10227,10438,10445,10450,10452,10456,11162,11298,11300,11304,11308,11315,11399,11404,11409,11415,11442,11446,11458,11463,11494,11512,11514,11518,11623,11637,11639,11643,11652,11657,11688,11739,11741,11745,13626,13628,13648],[5252,5253,2077],"h1",{"id":5254},"власні-структури-даних-бінарне-дерево-пошуку",[5256,5257,5258,5338],"card-group",{},[5259,5260,5263],"card",{"icon":5261,"title":5262},"i-lucide-target","🎯 Мета лекції",[5264,5265,5266,5279,5291,5318,5328],"ul",{},[5267,5268,5269,5270,5274,5275,5278],"li",{},"Перейти від ",[5271,5272,5273],"strong",{},"лінійних структур"," (масиви, списки) до ",[5271,5276,5277],{},"ієрархічних"," (дерева): вузли організовані у багаторівневу структуру з відношенням батько-діти.",[5267,5280,5281,5282,5285,5286,5290],{},"Опанувати концепцію ",[5271,5283,5284],{},"бінарного дерева пошуку"," (",[5287,5288,5289],"em",{},"Binary Search Tree, BST","): кожен вузол має не більше двох дітей, ліве піддерево містить менші значення, праве — більші.",[5267,5292,5293,5294,5285,5297,5300,5301,5285,5304,5300,5307,5285,5310,5313,5314,5317],{},"Реалізувати ключові операції: ",[5271,5295,5296],{},"вставка",[5287,5298,5299],{},"insert","), ",[5271,5302,5303],{},"пошук",[5287,5305,5306],{},"search",[5271,5308,5309],{},"видалення",[5287,5311,5312],{},"delete",") — всі з очікуваною складністю ",[5271,5315,5316],{},"O(log n)"," для збалансованого дерева.",[5267,5319,5320,5321,5285,5324,5327],{},"Дослідити ",[5271,5322,5323],{},"обходи дерева",[5287,5325,5326],{},"tree traversals","): in-order (впорядкований), pre-order (префіксний), post-order (постфіксний) — рекурсивні та ітеративні варіанти.",[5267,5329,5330,5331,5285,5334,5337],{},"Зрозуміти проблему ",[5271,5332,5333],{},"виродження",[5287,5335,5336],{},"degeneration","): у гіршому випадку BST перетворюється на однозв'язаний список з O(n) операціями.",[5259,5339,5341],{"icon":4634,"title":5340},"🔑 Ключові терміни",[5264,5342,5343,5357,5363,5369,5375],{},[5267,5344,5345,5348,5349,5352,5353,5356],{},[5271,5346,5347],{},"Tree (Дерево):"," нелінійна ієрархічна структура з кореневим вузлом (",[5287,5350,5351],{},"root",") та нащадками (",[5287,5354,5355],{},"children","), без циклів.",[5267,5358,5359,5362],{},[5271,5360,5361],{},"Binary Search Tree (BST):"," бінарне дерево з властивістю впорядкування: для кожного вузла всі значення лівого піддерева менші за значення вузла, всі значення правого піддерева більші.",[5267,5364,5365,5368],{},[5271,5366,5367],{},"Height (Висота дерева):"," найбільша відстань від кореня до листа; збалансоване дерево має висоту O(log n).",[5267,5370,5371,5374],{},[5271,5372,5373],{},"Traversal (Обхід):"," процес відвідування всіх вузлів дерева у певному порядку (in-order, pre-order, post-order).",[5267,5376,5377,5380],{},[5271,5378,5379],{},"Degenerate Tree (Вироджене дерево):"," дерево, що вироджується у лінійний ланцюжок (кожен вузол має лише одну дитину) — складність операцій деградує до O(n).",[5382,5383],"hr",{},[5385,5386,5388],"h2",{"id":5387},"hook-коли-лінійність-стає-вузьким-місцем","Hook: коли лінійність стає вузьким місцем",[5390,5391,5392,5393,5396,5397,5285,5400,5403],"p",{},"Уявіть словник з 1 мільйоном слів, збережений у ",[5271,5394,5395],{},"відсортованому масиві",". Щоб знайти слово \"algorithm\", ви використовуєте ",[5271,5398,5399],{},"бінарний пошук",[5287,5401,5402],{},"binary search","):",[5405,5406,5407,5410,5413,5416],"ol",{},[5267,5408,5409],{},"Перевірити середній елемент масиву (500 000-й).",[5267,5411,5412],{},"Якщо \"algorithm\" менше за нього — шукати в лівій половині (елементи 0–499 999).",[5267,5414,5415],{},"Інакше — у правій половині (елементи 500 001–999 999).",[5267,5417,5418],{},"Повторити для половини, що залишилася.",[5390,5420,5421,5424,5425,5428],{},[5271,5422,5423],{},"Складність:"," O(log n) — для 1 мільйона елементів достатньо ",[5271,5426,5427],{},"~20 порівнянь"," (log₂(1 000 000) ≈ 20). Це фантастично швидко порівняно з лінійним пошуком (O(n) — до 1 мільйона порівнянь у гіршому випадку).",[5390,5430,5431,5434,5435,5438],{},[5271,5432,5433],{},"Проблема:"," Тепер уявімо, що користувач хоче ",[5271,5436,5437],{},"додати нове слово"," \"abstraction\" на позицію 5000 (за алфавітом). У масиві це катастрофа:",[5405,5440,5441,5444,5450],{},[5267,5442,5443],{},"Знайти позицію вставки — O(log n) через бінарний пошук.",[5267,5445,5446,5449],{},[5271,5447,5448],{},"Зсунути 995 000 елементів"," на одну позицію праворуч — O(n).",[5267,5451,5452],{},"Вставити елемент.",[5390,5454,5455,5456,5459],{},"Загальна складність: ",[5271,5457,5458],{},"O(n)"," через зсув. Для динамічного словника з частими вставками це неприйнятно.",[5461,5462,5463,5464,5467,5468,5471,5472,5475],"note",{},"У попередній лекції (стаття 90) ми бачили, що ",[5271,5465,5466],{},"однозв'язаний список"," дозволяє вставку на початок за O(1), але пошук — O(n). Бінарний пошук у списку неможливий (немає довільного доступу). Чи існує структура, що поєднує ",[5271,5469,5470],{},"швидкий пошук"," (O(log n)) і ",[5271,5473,5474],{},"швидку вставку"," (O(log n))?",[5390,5477,5478,5479,5285,5482,5484],{},"Відповідь — ",[5271,5480,5481],{},"бінарне дерево пошуку",[5287,5483,5289],{},"). Це ієрархічна структура, де:",[5264,5486,5487,5501],{},[5267,5488,5489,5492,5493,5496,5497,5500],{},[5271,5490,5491],{},"Кожен вузол"," має не більше двох дітей: ліву (",[5287,5494,5495],{},"left",") та праву (",[5287,5498,5499],{},"right",").",[5267,5502,5503,5506,5507,5510,5511,5514],{},[5271,5504,5505],{},"Властивість впорядкування BST:"," для будь-якого вузла всі значення у лівому піддереві ",[5271,5508,5509],{},"менші"," за значення цього вузла, всі значення у правому піддереві — ",[5271,5512,5513],{},"більші",".",[5390,5516,5517,5518,5521,5522,5525],{},"Ця властивість дозволяє виконувати ",[5271,5519,5520],{},"бінарний пошук безпосередньо у структурі дерева",": на кожному кроці ми вибираємо ліву або праву гілку, відкидаючи половину можливостей. Вставка та видалення також виконуються за O(log n) у ",[5271,5523,5524],{},"збалансованому"," дереві, оскільки ми рухаємося вниз по одній гілці, не зсуваючи інші елементи.",[5527,5528,5530],"plant-uml",{"alt":5529},"Приклад бінарного дерева пошуку",[5531,5532,5537],"pre",{"className":5533,"code":5534,"language":5535,"meta":5536,"style":5536},"language-plantuml shiki shiki-themes light-plus dark-plus dark-plus","@startuml\nskinparam style plain\nskinparam backgroundColor #FFFFFF\n\npackage \"BST: [50, 30, 70, 20, 40, 60, 80]\" #F1F5F9 {\n    circle \"50\" as root #DBEAFE\n    circle \"30\" as left1 #DCFCE7\n    circle \"70\" as right1 #DCFCE7\n    circle \"20\" as left2 #E2E8F0\n    circle \"40\" as right2 #E2E8F0\n    circle \"60\" as left3 #E2E8F0\n    circle \"80\" as right3 #E2E8F0\n}\n\nroot -down-> left1 : \u003C 50\nroot -down-> right1 : > 50\nleft1 -down-> left2 : \u003C 30\nleft1 -down-> right2 : > 30\nright1 -down-> left3 : \u003C 70\nright1 -down-> right3 : > 70\n\nnote right of root #FEF3C7\n  Корінь дерева\n  Ліве піддерево: всі \u003C 50\n  Праве піддерево: всі > 50\nend note\n\nnote bottom of left2 #E2E8F0\n  Листки дерева\n  (вузли без дітей)\nend note\n\n@enduml\n","plantuml","",[5538,5539,5540,5548,5554,5560,5567,5573,5579,5585,5591,5597,5603,5609,5615,5621,5626,5632,5638,5644,5650,5656,5662,5667,5673,5679,5685,5691,5697,5702,5708,5714,5720,5725,5730],"code",{"__ignoreMap":5536},[5541,5542,5545],"span",{"class":5543,"line":5544},"line",1,[5541,5546,5547],{},"@startuml\n",[5541,5549,5551],{"class":5543,"line":5550},2,[5541,5552,5553],{},"skinparam style plain\n",[5541,5555,5557],{"class":5543,"line":5556},3,[5541,5558,5559],{},"skinparam backgroundColor #FFFFFF\n",[5541,5561,5563],{"class":5543,"line":5562},4,[5541,5564,5566],{"emptyLinePlaceholder":5565},true,"\n",[5541,5568,5570],{"class":5543,"line":5569},5,[5541,5571,5572],{},"package \"BST: [50, 30, 70, 20, 40, 60, 80]\" #F1F5F9 {\n",[5541,5574,5576],{"class":5543,"line":5575},6,[5541,5577,5578],{},"    circle \"50\" as root #DBEAFE\n",[5541,5580,5582],{"class":5543,"line":5581},7,[5541,5583,5584],{},"    circle \"30\" as left1 #DCFCE7\n",[5541,5586,5588],{"class":5543,"line":5587},8,[5541,5589,5590],{},"    circle \"70\" as right1 #DCFCE7\n",[5541,5592,5594],{"class":5543,"line":5593},9,[5541,5595,5596],{},"    circle \"20\" as left2 #E2E8F0\n",[5541,5598,5600],{"class":5543,"line":5599},10,[5541,5601,5602],{},"    circle \"40\" as right2 #E2E8F0\n",[5541,5604,5606],{"class":5543,"line":5605},11,[5541,5607,5608],{},"    circle \"60\" as left3 #E2E8F0\n",[5541,5610,5612],{"class":5543,"line":5611},12,[5541,5613,5614],{},"    circle \"80\" as right3 #E2E8F0\n",[5541,5616,5618],{"class":5543,"line":5617},13,[5541,5619,5620],{},"}\n",[5541,5622,5624],{"class":5543,"line":5623},14,[5541,5625,5566],{"emptyLinePlaceholder":5565},[5541,5627,5629],{"class":5543,"line":5628},15,[5541,5630,5631],{},"root -down-> left1 : \u003C 50\n",[5541,5633,5635],{"class":5543,"line":5634},16,[5541,5636,5637],{},"root -down-> right1 : > 50\n",[5541,5639,5641],{"class":5543,"line":5640},17,[5541,5642,5643],{},"left1 -down-> left2 : \u003C 30\n",[5541,5645,5647],{"class":5543,"line":5646},18,[5541,5648,5649],{},"left1 -down-> right2 : > 30\n",[5541,5651,5653],{"class":5543,"line":5652},19,[5541,5654,5655],{},"right1 -down-> left3 : \u003C 70\n",[5541,5657,5659],{"class":5543,"line":5658},20,[5541,5660,5661],{},"right1 -down-> right3 : > 70\n",[5541,5663,5665],{"class":5543,"line":5664},21,[5541,5666,5566],{"emptyLinePlaceholder":5565},[5541,5668,5670],{"class":5543,"line":5669},22,[5541,5671,5672],{},"note right of root #FEF3C7\n",[5541,5674,5676],{"class":5543,"line":5675},23,[5541,5677,5678],{},"  Корінь дерева\n",[5541,5680,5682],{"class":5543,"line":5681},24,[5541,5683,5684],{},"  Ліве піддерево: всі \u003C 50\n",[5541,5686,5688],{"class":5543,"line":5687},25,[5541,5689,5690],{},"  Праве піддерево: всі > 50\n",[5541,5692,5694],{"class":5543,"line":5693},26,[5541,5695,5696],{},"end note\n",[5541,5698,5700],{"class":5543,"line":5699},27,[5541,5701,5566],{"emptyLinePlaceholder":5565},[5541,5703,5705],{"class":5543,"line":5704},28,[5541,5706,5707],{},"note bottom of left2 #E2E8F0\n",[5541,5709,5711],{"class":5543,"line":5710},29,[5541,5712,5713],{},"  Листки дерева\n",[5541,5715,5717],{"class":5543,"line":5716},30,[5541,5718,5719],{},"  (вузли без дітей)\n",[5541,5721,5723],{"class":5543,"line":5722},31,[5541,5724,5696],{},[5541,5726,5728],{"class":5543,"line":5727},32,[5541,5729,5566],{"emptyLinePlaceholder":5565},[5541,5731,5733],{"class":5543,"line":5732},33,[5541,5734,5735],{},"@enduml\n",[5390,5737,5738,5739,5742,5743,5500],{},"У цій лекції ми спроєктуємо та реалізуємо повнофункціональне бінарне дерево пошуку з нуля, дослідимо його переваги та обмеження, та підготуємо грунт для вивчення збалансованих дерев (AVL, Red-Black) та стандартних контейнерів STL (",[5538,5740,5741],{},"std::set",", ",[5538,5744,5745],{},"std::map",[5382,5747],{},[5385,5749,5751],{"id":5750},"фундаментальні-концепції-дерев","Фундаментальні концепції дерев",[5753,5754,5756],"h3",{"id":5755},"термінологія-ієрархічних-структур","Термінологія ієрархічних структур",[5390,5758,5759,5285,5762,5765,5766,5769,5770,5773],{},[5271,5760,5761],{},"Дерево",[5287,5763,5764],{},"tree",") у комп'ютерних науках — це ",[5271,5767,5768],{},"нелінійна структура даних",", що моделює ієрархічні відношення. На відміну від масивів та списків (лінійні: A → B → C), дерево має ",[5271,5771,5772],{},"розгалужену структуру"," (A → B, C; B → D, E).",[5390,5775,5776],{},[5271,5777,5778],{},"Основні терміни:",[5780,5781,5782,5798],"table",{},[5783,5784,5785],"thead",{},[5786,5787,5788,5792,5795],"tr",{},[5789,5790,5791],"th",{"align":5495},"Термін",[5789,5793,5794],{"align":5495},"Визначення",[5789,5796,5797],{"align":5495},"Приклад",[5799,5800,5801,5818,5831,5853,5872,5896,5915,5928,5944],"tbody",{},[5786,5802,5803,5809,5812],{},[5804,5805,5806],"td",{"align":5495},[5271,5807,5808],{},"Root (Корінь)",[5804,5810,5811],{"align":5495},"Верхній вузол дерева, єдиний вузол без батька",[5804,5813,5814,5817],{"align":5495},[5538,5815,5816],{},"50"," на діаграмі вище",[5786,5819,5820,5825,5828],{},[5804,5821,5822],{"align":5495},[5271,5823,5824],{},"Node (Вузол)",[5804,5826,5827],{"align":5495},"Базовий елемент дерева, містить дані та покажчики на дітей",[5804,5829,5830],{"align":5495},"Кожен круг на діаграмі",[5786,5832,5833,5838,5841],{},[5804,5834,5835],{"align":5495},[5271,5836,5837],{},"Child (Дитина)",[5804,5839,5840],{"align":5495},"Вузол, що безпосередньо походить від іншого вузла",[5804,5842,5843,5846,5847,5850,5851],{"align":5495},[5538,5844,5845],{},"30"," і ",[5538,5848,5849],{},"70"," — діти вузла ",[5538,5852,5816],{},[5786,5854,5855,5860,5863],{},[5804,5856,5857],{"align":5495},[5271,5858,5859],{},"Parent (Батько)",[5804,5861,5862],{"align":5495},"Вузол, що має нащадків",[5804,5864,5865,5867,5868,5846,5870],{"align":5495},[5538,5866,5816],{}," — батько ",[5538,5869,5845],{},[5538,5871,5849],{},[5786,5873,5874,5879,5882],{},[5804,5875,5876],{"align":5495},[5271,5877,5878],{},"Leaf (Лист)",[5804,5880,5881],{"align":5495},"Вузол без дітей (кінцевий вузол)",[5804,5883,5884,5742,5887,5742,5890,5742,5893],{"align":5495},[5538,5885,5886],{},"20",[5538,5888,5889],{},"40",[5538,5891,5892],{},"60",[5538,5894,5895],{},"80",[5786,5897,5898,5903,5906],{},[5804,5899,5900],{"align":5495},[5271,5901,5902],{},"Subtree (Піддерево)",[5804,5904,5905],{"align":5495},"Дерево, що складається з вузла та всіх його нащадків",[5804,5907,5908,5909,5911,5912],{"align":5495},"Ліве піддерево ",[5538,5910,5816],{}," — це ",[5538,5913,5914],{},"[30, 20, 40]",[5786,5916,5917,5922,5925],{},[5804,5918,5919],{"align":5495},[5271,5920,5921],{},"Height (Висота)",[5804,5923,5924],{"align":5495},"Найбільша відстань від кореня до листа (кількість ребер)",[5804,5926,5927],{"align":5495},"Висота дерева вище — 2",[5786,5929,5930,5935,5938],{},[5804,5931,5932],{"align":5495},[5271,5933,5934],{},"Depth (Глибина вузла)",[5804,5936,5937],{"align":5495},"Відстань від кореня до вузла",[5804,5939,5940,5941,5943],{"align":5495},"Глибина ",[5538,5942,5886],{}," — 2",[5786,5945,5946,5951,5954],{},[5804,5947,5948],{"align":5495},[5271,5949,5950],{},"Level (Рівень)",[5804,5952,5953],{"align":5495},"Множина вузлів на однаковій глибині",[5804,5955,5956,5957],{"align":5495},"Рівень 1: ",[5538,5958,5959],{},"[30, 70]",[5961,5962,5964,5965,5968,5969,5971,5972,5974,5975,5978],"tip",{"title":5963},"Дерево як рекурсивна структура","Ключова властивість дерев: ",[5271,5966,5967],{},"кожне піддерево само є деревом",". Ліве піддерево вузла ",[5538,5970,5816],{}," — це окреме дерево з коренем ",[5538,5973,5845],{},". Це робить ",[5271,5976,5977],{},"рекурсію"," природною парадигмою для роботи з деревами: операція на дереві зводиться до операції на кореневому вузлі та рекурсивних викликів на лівому та правому піддеревах.",[5753,5980,5982],{"id":5981},"бінарне-дерево-vs-бінарне-дерево-пошуку","Бінарне дерево vs бінарне дерево пошуку",[5390,5984,5985,5285,5988,5991,5992,5995,5996,5496,5998,6000],{},[5271,5986,5987],{},"Бінарне дерево",[5287,5989,5990],{},"binary tree",") — це дерево, де ",[5271,5993,5994],{},"кожен вузол має не більше двох дітей",": ліву (",[5287,5997,5495],{},[5287,5999,5499],{},"). Це структурне обмеження, без додаткових вимог до значень.",[5390,6002,6003,5285,6006,6008,6009,6012],{},[5271,6004,6005],{},"Бінарне дерево пошуку",[5287,6007,5289],{},") — це бінарне дерево з додатковою ",[5271,6010,6011],{},"властивістю впорядкування",":",[6014,6015,6016,6029],"blockquote",{},[5390,6017,6018,6021,6022,6025,6026,6012],{},[5271,6019,6020],{},"BST-інваріант:"," Для будь-якого вузла ",[5538,6023,6024],{},"N"," з значенням ",[5538,6027,6028],{},"value",[5264,6030,6031,6040,6048],{},[5267,6032,6033,6034,6036,6037,5514],{},"Всі значення у лівому піддереві ",[5538,6035,6024],{}," ",[5271,6038,6039],{},"\u003C value",[5267,6041,6042,6043,6036,6045,5514],{},"Всі значення у правому піддереві ",[5538,6044,6024],{},[5271,6046,6047],{},"> value",[5267,6049,6050],{},"Обидва піддерева також є BST (рекурсивна властивість).",[5390,6052,6053],{},[5271,6054,6055],{},"Приклад валідного BST:",[5531,6057,6062],{"className":6058,"code":6060,"language":6061},[6059],"language-text","       50\n      \u002F  \\\n    30    70\n   \u002F \\   \u002F \\\n  20 40 60 80\n","text",[5538,6063,6060],{"__ignoreMap":5536},[5264,6065,6066,6075,6084],{},[5267,6067,5908,6068,6070,6071,6074],{},[5538,6069,5816],{},": ",[5541,6072,6073],{},"30, 20, 40"," — всі \u003C 50 ✅",[5267,6076,6077,6078,6070,6080,6083],{},"Праве піддерево ",[5538,6079,5816],{},[5541,6081,6082],{},"70, 60, 80"," — всі > 50 ✅",[5267,6085,6086,6087,6089,6090,6092,6093,6095],{},"Рекурсивно: піддерево ",[5538,6088,5845],{}," — ",[5541,6091,5886],{}," \u003C 30 \u003C ",[5541,6094,5889],{}," ✅",[5390,6097,6098],{},[5271,6099,6100],{},"Приклад невалідного BST:",[5531,6102,6105],{"className":6103,"code":6104,"language":6061},[6059],"       50\n      \u002F  \\\n    30    70\n   \u002F \\\n  20 60  ❌ 60 має бути у правому піддереві 50, а не в лівому!\n",[5538,6106,6104],{"__ignoreMap":5536},[5390,6108,6109,6110,6113,6114,6116,6117,6119,6120,5514],{},"Хоча ",[5538,6111,6112],{},"60 > 30",", властивість порушена на рівні кореня: ",[5538,6115,5892],{}," знаходиться у лівому піддереві ",[5538,6118,5816],{},", але ",[5538,6121,6122],{},"60 > 50",[6124,6125,6127,6128,6131,6132,6135,6136,6138],"warning",{"title":6126},"Глобальна властивість, а не локальна","BST-інваріант — це ",[5271,6129,6130],{},"глобальна"," умова: потрібно порівнювати не лише з безпосереднім батьком, а з ",[5271,6133,6134],{},"усіма предками",". Вузол ",[5538,6137,5892],{}," має бути меншим за всіх предків справа від нього у шляху до кореня. Саме це робить BST складним для підтримки при вставці та видаленні.",[5753,6140,6142],{"id":6141},"чому-olog-n-висота-збалансованого-дерева","Чому O(log n)? Висота збалансованого дерева",[5390,6144,6145,6148,6149,6152],{},[5271,6146,6147],{},"Інтуїція:"," У збалансованому BST кожен рівень має ",[5271,6150,6151],{},"удвічі більше вузлів",", ніж попередній:",[5264,6154,6155,6158,6161,6164,6167],{},[5267,6156,6157],{},"Рівень 0 (корінь): 1 вузол",[5267,6159,6160],{},"Рівень 1: 2 вузли",[5267,6162,6163],{},"Рівень 2: 4 вузли",[5267,6165,6166],{},"Рівень 3: 8 вузлів",[5267,6168,6169],{},"Рівень h: 2ʰ вузлів",[5390,6171,6172,6173,6176,6177,5514],{},"Загальна кількість вузлів: ",[5538,6174,6175],{},"n = 1 + 2 + 4 + ... + 2ʰ = 2^(h+1) - 1",". Звідси висота: ",[5538,6178,6179],{},"h = log₂(n+1) - 1 ≈ log₂(n)",[5390,6181,6182,6185,6186,6189],{},[5271,6183,6184],{},"Складність операцій:"," Пошук, вставка, видалення у BST зводяться до ",[5271,6187,6188],{},"руху вниз від кореня до листа"," по одній гілці. Кількість кроків = висота дерева = O(log n).",[5390,6191,6192,6195],{},[5271,6193,6194],{},"Для 1 мільйона вузлів:"," log₂(1 000 000) ≈ 20 — максимум 20 порівнянь для будь-якої операції. Порівняйте з O(n) = 1 000 000 у списку.",[6197,6198,6200,6209,6215],"caution",{"title":6199},"Гірший випадок: вироджене дерево",[5390,6201,6202,6203,6206,6207,6012],{},"Якщо вставляти елементи у ",[5271,6204,6205],{},"відсортованому порядку"," (10, 20, 30, 40, 50), BST вироджується у ",[5271,6208,5466],{},[5531,6210,6213],{"className":6211,"code":6212,"language":6061},[6059],"10\n  \\\n   20\n     \\\n      30\n        \\\n         40\n           \\\n            50\n",[5538,6214,6212],{"__ignoreMap":5536},[5390,6216,6217,6218,6220],{},"Висота = n - 1, складність операцій = ",[5271,6219,5458],{},". Збалансовані дерева (AVL, Red-Black) розв'язують цю проблему через автоматичне перебалансування після кожної вставки\u002Fвидалення, гарантуючи висоту O(log n). Вони будуть темою окремих лекцій або статті 93 (STL-контейнери).",[5382,6222],{},[5385,6224,6226],{"id":6225},"проєктування-класу-bst-вузол-та-інтерфейс","Проєктування класу BST: вузол та інтерфейс",[5753,6228,6230],{"id":6229},"структура-вузла-treenode","Структура вузла TreeNode",[5390,6232,6233,6234,6237,6238,6241],{},"На відміну від однозв'язаного списку (один покажчик ",[5538,6235,6236],{},"next","), вузол дерева має ",[5271,6239,6240],{},"два"," покажчики: на ліву та праву дитину.",[5531,6243,6247],{"className":6244,"code":6245,"language":6246,"meta":5536,"style":5536},"language-cpp shiki shiki-themes light-plus dark-plus dark-plus","struct TreeNode\n{\n    int data;           \u002F\u002F Значення вузла\n    TreeNode* left;     \u002F\u002F Покажчик на ліве піддерево (менші значення)\n    TreeNode* right;    \u002F\u002F Покажчик на праве піддерево (більші значення)\n    \n    \u002F\u002F Конструктор для зручності\n    TreeNode(int value)\n        : data(value), left(nullptr), right(nullptr)\n    {\n    }\n};\n","cpp",[5538,6248,6249,6259,6265,6281,6297,6311,6316,6321,6338,6369,6374,6379],{"__ignoreMap":5536},[5541,6250,6251,6255],{"class":5543,"line":5544},[5541,6252,6254],{"class":6253},"su1O8","struct",[5541,6256,6258],{"class":6257},"sN1BT"," TreeNode\n",[5541,6260,6261],{"class":5543,"line":5550},[5541,6262,6264],{"class":6263},"sHH4Y","{\n",[5541,6266,6267,6270,6274,6277],{"class":5543,"line":5556},[5541,6268,6269],{"class":6253},"    int",[5541,6271,6273],{"class":6272},"siwwj"," data",[5541,6275,6276],{"class":6263},";",[5541,6278,6280],{"class":6279},"spJ8K","           \u002F\u002F Значення вузла\n",[5541,6282,6283,6286,6289,6292,6294],{"class":5543,"line":5562},[5541,6284,6285],{"class":6257},"    TreeNode",[5541,6287,6288],{"class":6253},"*",[5541,6290,6291],{"class":6272}," left",[5541,6293,6276],{"class":6263},[5541,6295,6296],{"class":6279},"     \u002F\u002F Покажчик на ліве піддерево (менші значення)\n",[5541,6298,6299,6301,6303,6306,6308],{"class":5543,"line":5569},[5541,6300,6285],{"class":6257},[5541,6302,6288],{"class":6253},[5541,6304,6305],{"class":6272}," right",[5541,6307,6276],{"class":6263},[5541,6309,6310],{"class":6279},"    \u002F\u002F Покажчик на праве піддерево (більші значення)\n",[5541,6312,6313],{"class":5543,"line":5575},[5541,6314,6315],{"class":6263},"    \n",[5541,6317,6318],{"class":5543,"line":5581},[5541,6319,6320],{"class":6279},"    \u002F\u002F Конструктор для зручності\n",[5541,6322,6323,6326,6329,6332,6335],{"class":5543,"line":5587},[5541,6324,6285],{"class":6325},"s8Opu",[5541,6327,6328],{"class":6263},"(",[5541,6330,6331],{"class":6253},"int",[5541,6333,6334],{"class":6272}," value",[5541,6336,6337],{"class":6263},")\n",[5541,6339,6340,6343,6346,6348,6350,6352,6354,6356,6359,6361,6363,6365,6367],{"class":5543,"line":5593},[5541,6341,6342],{"class":6263},"        : ",[5541,6344,6345],{"class":6325},"data",[5541,6347,6328],{"class":6263},[5541,6349,6028],{"class":6272},[5541,6351,5300],{"class":6263},[5541,6353,5495],{"class":6325},[5541,6355,6328],{"class":6263},[5541,6357,6358],{"class":6253},"nullptr",[5541,6360,5300],{"class":6263},[5541,6362,5499],{"class":6325},[5541,6364,6328],{"class":6263},[5541,6366,6358],{"class":6253},[5541,6368,6337],{"class":6263},[5541,6370,6371],{"class":5543,"line":5599},[5541,6372,6373],{"class":6263},"    {\n",[5541,6375,6376],{"class":5543,"line":5605},[5541,6377,6378],{"class":6263},"    }\n",[5541,6380,6381],{"class":5543,"line":5611},[5541,6382,6383],{"class":6263},"};\n",[5390,6385,6386,6389,6390,6393],{},[5271,6387,6388],{},"Інваріанти листкового вузла:"," Якщо ",[5538,6391,6392],{},"left == nullptr && right == nullptr",", вузол є листом.",[5390,6395,6396,6399],{},[5271,6397,6398],{},"Інваріанти внутрішнього вузла:"," Має принаймні одну ненульову дитину.",[5753,6401,6403],{"id":6402},"оголошення-класу-binarysearchtree","Оголошення класу BinarySearchTree",[5531,6405,6407],{"className":6244,"code":6406,"language":6246,"meta":5536,"style":5536},"\u002F\u002F BinarySearchTree.h\n#ifndef BINARY_SEARCH_TREE_H\n#define BINARY_SEARCH_TREE_H\n\n#include \u003Ciostream>\n\nstruct TreeNode\n{\n    int data;\n    TreeNode* left;\n    TreeNode* right;\n    \n    TreeNode(int value)\n        : data(value), left(nullptr), right(nullptr)\n    {\n    }\n};\n\nclass BinarySearchTree\n{\nprivate:\n    TreeNode* root;  \u002F\u002F Покажчик на корінь дерева\n    \n    \u002F\u002F Приватні рекурсивні допоміжні методи\n    TreeNode* insertRecursive(TreeNode* node, int value);\n    TreeNode* deleteRecursive(TreeNode* node, int value);\n    TreeNode* findMin(TreeNode* node) const;\n    bool searchRecursive(TreeNode* node, int value) const;\n    void inOrderRecursive(TreeNode* node) const;\n    void preOrderRecursive(TreeNode* node) const;\n    void postOrderRecursive(TreeNode* node) const;\n    void destroyTree(TreeNode* node);\n    int heightRecursive(TreeNode* node) const;\n\npublic:\n    \u002F\u002F Конструктор: створює порожнє дерево\n    BinarySearchTree();\n    \n    \u002F\u002F Деструктор: видаляє всі вузли (RAII)\n    ~BinarySearchTree();\n    \n    \u002F\u002F Заборона копіювання (для простоти)\n    BinarySearchTree(const BinarySearchTree&) = delete;\n    BinarySearchTree& operator=(const BinarySearchTree&) = delete;\n    \n    \u002F\u002F Вставити значення в дерево\n    void insert(int value);\n    \n    \u002F\u002F Видалити значення з дерева\n    void remove(int value);\n    \n    \u002F\u002F Пошук значення в дереві\n    bool search(int value) const;\n    \n    \u002F\u002F Перевірити, чи дерево порожнє\n    bool isEmpty() const;\n    \n    \u002F\u002F Отримати висоту дерева\n    int height() const;\n    \n    \u002F\u002F Обходи дерева\n    void inOrder() const;    \u002F\u002F Впорядкований: ліве → корінь → праве\n    void preOrder() const;   \u002F\u002F Префіксний: корінь → ліве → праве\n    void postOrder() const;  \u002F\u002F Постфіксний: ліве → праве → корінь\n};\n\n#endif\n",[5538,6408,6409,6414,6423,6430,6434,6443,6447,6453,6457,6466,6476,6486,6490,6502,6530,6534,6538,6542,6546,6554,6558,6563,6577,6581,6586,6614,6639,6664,6692,6714,6735,6756,6773,6794,6799,6805,6811,6820,6825,6831,6839,6844,6850,6872,6896,6901,6907,6923,6928,6934,6950,6955,6961,6981,6986,6992,7007,7012,7018,7032,7037,7043,7060,7077,7094,7099,7104],{"__ignoreMap":5536},[5541,6410,6411],{"class":5543,"line":5544},[5541,6412,6413],{"class":6279},"\u002F\u002F BinarySearchTree.h\n",[5541,6415,6416,6420],{"class":5543,"line":5550},[5541,6417,6419],{"class":6418},"s8xlr","#ifndef",[5541,6421,6422],{"class":6253}," BINARY_SEARCH_TREE_H\n",[5541,6424,6425,6428],{"class":5543,"line":5556},[5541,6426,6427],{"class":6418},"#define",[5541,6429,6422],{"class":6253},[5541,6431,6432],{"class":5543,"line":5562},[5541,6433,5566],{"emptyLinePlaceholder":5565},[5541,6435,6436,6439],{"class":5543,"line":5569},[5541,6437,6438],{"class":6418},"#include",[5541,6440,6442],{"class":6441},"sbdoH"," \u003Ciostream>\n",[5541,6444,6445],{"class":5543,"line":5575},[5541,6446,5566],{"emptyLinePlaceholder":5565},[5541,6448,6449,6451],{"class":5543,"line":5581},[5541,6450,6254],{"class":6253},[5541,6452,6258],{"class":6257},[5541,6454,6455],{"class":5543,"line":5587},[5541,6456,6264],{"class":6263},[5541,6458,6459,6461,6463],{"class":5543,"line":5593},[5541,6460,6269],{"class":6253},[5541,6462,6273],{"class":6272},[5541,6464,6465],{"class":6263},";\n",[5541,6467,6468,6470,6472,6474],{"class":5543,"line":5599},[5541,6469,6285],{"class":6257},[5541,6471,6288],{"class":6253},[5541,6473,6291],{"class":6272},[5541,6475,6465],{"class":6263},[5541,6477,6478,6480,6482,6484],{"class":5543,"line":5605},[5541,6479,6285],{"class":6257},[5541,6481,6288],{"class":6253},[5541,6483,6305],{"class":6272},[5541,6485,6465],{"class":6263},[5541,6487,6488],{"class":5543,"line":5611},[5541,6489,6315],{"class":6263},[5541,6491,6492,6494,6496,6498,6500],{"class":5543,"line":5617},[5541,6493,6285],{"class":6325},[5541,6495,6328],{"class":6263},[5541,6497,6331],{"class":6253},[5541,6499,6334],{"class":6272},[5541,6501,6337],{"class":6263},[5541,6503,6504,6506,6508,6510,6512,6514,6516,6518,6520,6522,6524,6526,6528],{"class":5543,"line":5623},[5541,6505,6342],{"class":6263},[5541,6507,6345],{"class":6325},[5541,6509,6328],{"class":6263},[5541,6511,6028],{"class":6272},[5541,6513,5300],{"class":6263},[5541,6515,5495],{"class":6325},[5541,6517,6328],{"class":6263},[5541,6519,6358],{"class":6253},[5541,6521,5300],{"class":6263},[5541,6523,5499],{"class":6325},[5541,6525,6328],{"class":6263},[5541,6527,6358],{"class":6253},[5541,6529,6337],{"class":6263},[5541,6531,6532],{"class":5543,"line":5628},[5541,6533,6373],{"class":6263},[5541,6535,6536],{"class":5543,"line":5634},[5541,6537,6378],{"class":6263},[5541,6539,6540],{"class":5543,"line":5640},[5541,6541,6383],{"class":6263},[5541,6543,6544],{"class":5543,"line":5646},[5541,6545,5566],{"emptyLinePlaceholder":5565},[5541,6547,6548,6551],{"class":5543,"line":5652},[5541,6549,6550],{"class":6253},"class",[5541,6552,6553],{"class":6257}," BinarySearchTree\n",[5541,6555,6556],{"class":5543,"line":5658},[5541,6557,6264],{"class":6263},[5541,6559,6560],{"class":5543,"line":5664},[5541,6561,6562],{"class":6253},"private:\n",[5541,6564,6565,6567,6569,6572,6574],{"class":5543,"line":5669},[5541,6566,6285],{"class":6257},[5541,6568,6288],{"class":6253},[5541,6570,6571],{"class":6272}," root",[5541,6573,6276],{"class":6263},[5541,6575,6576],{"class":6279},"  \u002F\u002F Покажчик на корінь дерева\n",[5541,6578,6579],{"class":5543,"line":5675},[5541,6580,6315],{"class":6263},[5541,6582,6583],{"class":5543,"line":5681},[5541,6584,6585],{"class":6279},"    \u002F\u002F Приватні рекурсивні допоміжні методи\n",[5541,6587,6588,6590,6592,6595,6597,6600,6602,6605,6607,6609,6611],{"class":5543,"line":5687},[5541,6589,6285],{"class":6257},[5541,6591,6288],{"class":6253},[5541,6593,6594],{"class":6325}," insertRecursive",[5541,6596,6328],{"class":6263},[5541,6598,6599],{"class":6257},"TreeNode",[5541,6601,6288],{"class":6253},[5541,6603,6604],{"class":6272}," node",[5541,6606,5742],{"class":6263},[5541,6608,6331],{"class":6253},[5541,6610,6334],{"class":6272},[5541,6612,6613],{"class":6263},");\n",[5541,6615,6616,6618,6620,6623,6625,6627,6629,6631,6633,6635,6637],{"class":5543,"line":5693},[5541,6617,6285],{"class":6257},[5541,6619,6288],{"class":6253},[5541,6621,6622],{"class":6325}," deleteRecursive",[5541,6624,6328],{"class":6263},[5541,6626,6599],{"class":6257},[5541,6628,6288],{"class":6253},[5541,6630,6604],{"class":6272},[5541,6632,5742],{"class":6263},[5541,6634,6331],{"class":6253},[5541,6636,6334],{"class":6272},[5541,6638,6613],{"class":6263},[5541,6640,6641,6643,6645,6648,6650,6652,6654,6656,6659,6662],{"class":5543,"line":5699},[5541,6642,6285],{"class":6257},[5541,6644,6288],{"class":6253},[5541,6646,6647],{"class":6325}," findMin",[5541,6649,6328],{"class":6263},[5541,6651,6599],{"class":6257},[5541,6653,6288],{"class":6253},[5541,6655,6604],{"class":6272},[5541,6657,6658],{"class":6263},") ",[5541,6660,6661],{"class":6253},"const",[5541,6663,6465],{"class":6263},[5541,6665,6666,6669,6672,6674,6676,6678,6680,6682,6684,6686,6688,6690],{"class":5543,"line":5704},[5541,6667,6668],{"class":6253},"    bool",[5541,6670,6671],{"class":6325}," searchRecursive",[5541,6673,6328],{"class":6263},[5541,6675,6599],{"class":6257},[5541,6677,6288],{"class":6253},[5541,6679,6604],{"class":6272},[5541,6681,5742],{"class":6263},[5541,6683,6331],{"class":6253},[5541,6685,6334],{"class":6272},[5541,6687,6658],{"class":6263},[5541,6689,6661],{"class":6253},[5541,6691,6465],{"class":6263},[5541,6693,6694,6697,6700,6702,6704,6706,6708,6710,6712],{"class":5543,"line":5710},[5541,6695,6696],{"class":6253},"    void",[5541,6698,6699],{"class":6325}," inOrderRecursive",[5541,6701,6328],{"class":6263},[5541,6703,6599],{"class":6257},[5541,6705,6288],{"class":6253},[5541,6707,6604],{"class":6272},[5541,6709,6658],{"class":6263},[5541,6711,6661],{"class":6253},[5541,6713,6465],{"class":6263},[5541,6715,6716,6718,6721,6723,6725,6727,6729,6731,6733],{"class":5543,"line":5716},[5541,6717,6696],{"class":6253},[5541,6719,6720],{"class":6325}," preOrderRecursive",[5541,6722,6328],{"class":6263},[5541,6724,6599],{"class":6257},[5541,6726,6288],{"class":6253},[5541,6728,6604],{"class":6272},[5541,6730,6658],{"class":6263},[5541,6732,6661],{"class":6253},[5541,6734,6465],{"class":6263},[5541,6736,6737,6739,6742,6744,6746,6748,6750,6752,6754],{"class":5543,"line":5722},[5541,6738,6696],{"class":6253},[5541,6740,6741],{"class":6325}," postOrderRecursive",[5541,6743,6328],{"class":6263},[5541,6745,6599],{"class":6257},[5541,6747,6288],{"class":6253},[5541,6749,6604],{"class":6272},[5541,6751,6658],{"class":6263},[5541,6753,6661],{"class":6253},[5541,6755,6465],{"class":6263},[5541,6757,6758,6760,6763,6765,6767,6769,6771],{"class":5543,"line":5727},[5541,6759,6696],{"class":6253},[5541,6761,6762],{"class":6325}," destroyTree",[5541,6764,6328],{"class":6263},[5541,6766,6599],{"class":6257},[5541,6768,6288],{"class":6253},[5541,6770,6604],{"class":6272},[5541,6772,6613],{"class":6263},[5541,6774,6775,6777,6780,6782,6784,6786,6788,6790,6792],{"class":5543,"line":5732},[5541,6776,6269],{"class":6253},[5541,6778,6779],{"class":6325}," heightRecursive",[5541,6781,6328],{"class":6263},[5541,6783,6599],{"class":6257},[5541,6785,6288],{"class":6253},[5541,6787,6604],{"class":6272},[5541,6789,6658],{"class":6263},[5541,6791,6661],{"class":6253},[5541,6793,6465],{"class":6263},[5541,6795,6797],{"class":5543,"line":6796},34,[5541,6798,5566],{"emptyLinePlaceholder":5565},[5541,6800,6802],{"class":5543,"line":6801},35,[5541,6803,6804],{"class":6253},"public:\n",[5541,6806,6808],{"class":5543,"line":6807},36,[5541,6809,6810],{"class":6279},"    \u002F\u002F Конструктор: створює порожнє дерево\n",[5541,6812,6814,6817],{"class":5543,"line":6813},37,[5541,6815,6816],{"class":6325},"    BinarySearchTree",[5541,6818,6819],{"class":6263},"();\n",[5541,6821,6823],{"class":5543,"line":6822},38,[5541,6824,6315],{"class":6263},[5541,6826,6828],{"class":5543,"line":6827},39,[5541,6829,6830],{"class":6279},"    \u002F\u002F Деструктор: видаляє всі вузли (RAII)\n",[5541,6832,6834,6837],{"class":5543,"line":6833},40,[5541,6835,6836],{"class":6325},"    ~BinarySearchTree",[5541,6838,6819],{"class":6263},[5541,6840,6842],{"class":5543,"line":6841},41,[5541,6843,6315],{"class":6263},[5541,6845,6847],{"class":5543,"line":6846},42,[5541,6848,6849],{"class":6279},"    \u002F\u002F Заборона копіювання (для простоти)\n",[5541,6851,6853,6855,6857,6859,6862,6865,6868,6870],{"class":5543,"line":6852},43,[5541,6854,6816],{"class":6325},[5541,6856,6328],{"class":6263},[5541,6858,6661],{"class":6253},[5541,6860,6861],{"class":6257}," BinarySearchTree",[5541,6863,6864],{"class":6253},"&",[5541,6866,6867],{"class":6263},") = ",[5541,6869,5312],{"class":6253},[5541,6871,6465],{"class":6263},[5541,6873,6875,6877,6879,6882,6884,6886,6888,6890,6892,6894],{"class":5543,"line":6874},44,[5541,6876,6816],{"class":6257},[5541,6878,6864],{"class":6253},[5541,6880,6881],{"class":6418}," operator=",[5541,6883,6328],{"class":6263},[5541,6885,6661],{"class":6253},[5541,6887,6861],{"class":6257},[5541,6889,6864],{"class":6253},[5541,6891,6867],{"class":6263},[5541,6893,5312],{"class":6253},[5541,6895,6465],{"class":6263},[5541,6897,6899],{"class":5543,"line":6898},45,[5541,6900,6315],{"class":6263},[5541,6902,6904],{"class":5543,"line":6903},46,[5541,6905,6906],{"class":6279},"    \u002F\u002F Вставити значення в дерево\n",[5541,6908,6910,6912,6915,6917,6919,6921],{"class":5543,"line":6909},47,[5541,6911,6696],{"class":6253},[5541,6913,6914],{"class":6325}," insert",[5541,6916,6328],{"class":6263},[5541,6918,6331],{"class":6253},[5541,6920,6334],{"class":6272},[5541,6922,6613],{"class":6263},[5541,6924,6926],{"class":5543,"line":6925},48,[5541,6927,6315],{"class":6263},[5541,6929,6931],{"class":5543,"line":6930},49,[5541,6932,6933],{"class":6279},"    \u002F\u002F Видалити значення з дерева\n",[5541,6935,6937,6939,6942,6944,6946,6948],{"class":5543,"line":6936},50,[5541,6938,6696],{"class":6253},[5541,6940,6941],{"class":6325}," remove",[5541,6943,6328],{"class":6263},[5541,6945,6331],{"class":6253},[5541,6947,6334],{"class":6272},[5541,6949,6613],{"class":6263},[5541,6951,6953],{"class":5543,"line":6952},51,[5541,6954,6315],{"class":6263},[5541,6956,6958],{"class":5543,"line":6957},52,[5541,6959,6960],{"class":6279},"    \u002F\u002F Пошук значення в дереві\n",[5541,6962,6964,6966,6969,6971,6973,6975,6977,6979],{"class":5543,"line":6963},53,[5541,6965,6668],{"class":6253},[5541,6967,6968],{"class":6325}," search",[5541,6970,6328],{"class":6263},[5541,6972,6331],{"class":6253},[5541,6974,6334],{"class":6272},[5541,6976,6658],{"class":6263},[5541,6978,6661],{"class":6253},[5541,6980,6465],{"class":6263},[5541,6982,6984],{"class":5543,"line":6983},54,[5541,6985,6315],{"class":6263},[5541,6987,6989],{"class":5543,"line":6988},55,[5541,6990,6991],{"class":6279},"    \u002F\u002F Перевірити, чи дерево порожнє\n",[5541,6993,6995,6997,7000,7003,7005],{"class":5543,"line":6994},56,[5541,6996,6668],{"class":6253},[5541,6998,6999],{"class":6325}," isEmpty",[5541,7001,7002],{"class":6263},"() ",[5541,7004,6661],{"class":6253},[5541,7006,6465],{"class":6263},[5541,7008,7010],{"class":5543,"line":7009},57,[5541,7011,6315],{"class":6263},[5541,7013,7015],{"class":5543,"line":7014},58,[5541,7016,7017],{"class":6279},"    \u002F\u002F Отримати висоту дерева\n",[5541,7019,7021,7023,7026,7028,7030],{"class":5543,"line":7020},59,[5541,7022,6269],{"class":6253},[5541,7024,7025],{"class":6325}," height",[5541,7027,7002],{"class":6263},[5541,7029,6661],{"class":6253},[5541,7031,6465],{"class":6263},[5541,7033,7035],{"class":5543,"line":7034},60,[5541,7036,6315],{"class":6263},[5541,7038,7040],{"class":5543,"line":7039},61,[5541,7041,7042],{"class":6279},"    \u002F\u002F Обходи дерева\n",[5541,7044,7046,7048,7051,7053,7055,7057],{"class":5543,"line":7045},62,[5541,7047,6696],{"class":6253},[5541,7049,7050],{"class":6325}," inOrder",[5541,7052,7002],{"class":6263},[5541,7054,6661],{"class":6253},[5541,7056,6276],{"class":6263},[5541,7058,7059],{"class":6279},"    \u002F\u002F Впорядкований: ліве → корінь → праве\n",[5541,7061,7063,7065,7068,7070,7072,7074],{"class":5543,"line":7062},63,[5541,7064,6696],{"class":6253},[5541,7066,7067],{"class":6325}," preOrder",[5541,7069,7002],{"class":6263},[5541,7071,6661],{"class":6253},[5541,7073,6276],{"class":6263},[5541,7075,7076],{"class":6279},"   \u002F\u002F Префіксний: корінь → ліве → праве\n",[5541,7078,7080,7082,7085,7087,7089,7091],{"class":5543,"line":7079},64,[5541,7081,6696],{"class":6253},[5541,7083,7084],{"class":6325}," postOrder",[5541,7086,7002],{"class":6263},[5541,7088,6661],{"class":6253},[5541,7090,6276],{"class":6263},[5541,7092,7093],{"class":6279},"  \u002F\u002F Постфіксний: ліве → праве → корінь\n",[5541,7095,7097],{"class":5543,"line":7096},65,[5541,7098,6383],{"class":6263},[5541,7100,7102],{"class":5543,"line":7101},66,[5541,7103,5566],{"emptyLinePlaceholder":5565},[5541,7105,7107],{"class":5543,"line":7106},67,[5541,7108,7109],{"class":6418},"#endif\n",[5390,7111,7112,7115,7116,7119,7120,5514],{},[5271,7113,7114],{},"Ключова особливість:"," Більшість операцій реалізовані як ",[5271,7117,7118],{},"рекурсивні"," приватні методи, що приймають вказівник на вузол. Публічні методи делегують роботу цим допоміжним функціям, передаючи ",[5538,7121,5351],{},[5461,7123,7125,7126,7129,7130,5285,7133,7136,7137,7140,7141,5514],{"title":7124},"Чому приватні рекурсивні помічники?","Публічний інтерфейс приховує деталі реалізації (користувач не має доступу до ",[5538,7127,7128],{},"TreeNode*","). Приватні методи дозволяють працювати безпосередньо з покажчиками для рекурсії. Це патерн ",[5271,7131,7132],{},"обгортки",[5287,7134,7135],{},"wrapper","): публічний метод ",[5538,7138,7139],{},"insert(value)"," викликає приватний ",[5538,7142,7143],{},"insertRecursive(root, value)",[5753,7145,7147],{"id":7146},"реалізація-конструктора-та-деструктора","Реалізація конструктора та деструктора",[5531,7149,7151],{"className":6244,"code":7150,"language":6246,"meta":5536,"style":5536},"\u002F\u002F BinarySearchTree.cpp\n#include \"BinarySearchTree.h\"\n\n\u002F\u002F Конструктор: ініціалізує порожнє дерево\nBinarySearchTree::BinarySearchTree()\n    : root(nullptr)\n{\n}\n\n\u002F\u002F Деструктор: видаляє всі вузли (post-order обхід)\nBinarySearchTree::~BinarySearchTree()\n{\n    destroyTree(root);\n}\n\n\u002F\u002F Рекурсивне видалення всього дерева\nvoid BinarySearchTree::destroyTree(TreeNode* node)\n{\n    if (node == nullptr)\n    {\n        return;  \u002F\u002F Базовий випадок: порожнє дерево\n    }\n    \n    \u002F\u002F Рекурсивно видаляємо ліве та праве піддерева\n    destroyTree(node->left);\n    destroyTree(node->right);\n    \n    \u002F\u002F Тепер можна видалити поточний вузол\n    delete node;\n}\n",[5538,7152,7153,7158,7165,7169,7174,7187,7200,7204,7208,7212,7217,7228,7232,7243,7247,7251,7256,7278,7282,7299,7303,7313,7317,7321,7326,7341,7355,7359,7364,7373],{"__ignoreMap":5536},[5541,7154,7155],{"class":5543,"line":5544},[5541,7156,7157],{"class":6279},"\u002F\u002F BinarySearchTree.cpp\n",[5541,7159,7160,7162],{"class":5543,"line":5550},[5541,7161,6438],{"class":6418},[5541,7163,7164],{"class":6441}," \"BinarySearchTree.h\"\n",[5541,7166,7167],{"class":5543,"line":5556},[5541,7168,5566],{"emptyLinePlaceholder":5565},[5541,7170,7171],{"class":5543,"line":5562},[5541,7172,7173],{"class":6279},"\u002F\u002F Конструктор: ініціалізує порожнє дерево\n",[5541,7175,7176,7179,7182,7184],{"class":5543,"line":5569},[5541,7177,7178],{"class":6257},"BinarySearchTree",[5541,7180,7181],{"class":6263},"::",[5541,7183,7178],{"class":6325},[5541,7185,7186],{"class":6263},"()\n",[5541,7188,7189,7192,7194,7196,7198],{"class":5543,"line":5575},[5541,7190,7191],{"class":6263},"    : ",[5541,7193,5351],{"class":6325},[5541,7195,6328],{"class":6263},[5541,7197,6358],{"class":6253},[5541,7199,6337],{"class":6263},[5541,7201,7202],{"class":5543,"line":5581},[5541,7203,6264],{"class":6263},[5541,7205,7206],{"class":5543,"line":5587},[5541,7207,5620],{"class":6263},[5541,7209,7210],{"class":5543,"line":5593},[5541,7211,5566],{"emptyLinePlaceholder":5565},[5541,7213,7214],{"class":5543,"line":5599},[5541,7215,7216],{"class":6279},"\u002F\u002F Деструктор: видаляє всі вузли (post-order обхід)\n",[5541,7218,7219,7221,7224,7226],{"class":5543,"line":5605},[5541,7220,7178],{"class":6257},[5541,7222,7223],{"class":6263},"::~",[5541,7225,7178],{"class":6325},[5541,7227,7186],{"class":6263},[5541,7229,7230],{"class":5543,"line":5611},[5541,7231,6264],{"class":6263},[5541,7233,7234,7237,7239,7241],{"class":5543,"line":5617},[5541,7235,7236],{"class":6325},"    destroyTree",[5541,7238,6328],{"class":6263},[5541,7240,5351],{"class":6272},[5541,7242,6613],{"class":6263},[5541,7244,7245],{"class":5543,"line":5623},[5541,7246,5620],{"class":6263},[5541,7248,7249],{"class":5543,"line":5628},[5541,7250,5566],{"emptyLinePlaceholder":5565},[5541,7252,7253],{"class":5543,"line":5634},[5541,7254,7255],{"class":6279},"\u002F\u002F Рекурсивне видалення всього дерева\n",[5541,7257,7258,7261,7263,7265,7268,7270,7272,7274,7276],{"class":5543,"line":5640},[5541,7259,7260],{"class":6253},"void",[5541,7262,6861],{"class":6257},[5541,7264,7181],{"class":6263},[5541,7266,7267],{"class":6325},"destroyTree",[5541,7269,6328],{"class":6263},[5541,7271,6599],{"class":6257},[5541,7273,6288],{"class":6253},[5541,7275,6604],{"class":6272},[5541,7277,6337],{"class":6263},[5541,7279,7280],{"class":5543,"line":5646},[5541,7281,6264],{"class":6263},[5541,7283,7284,7287,7289,7292,7295,7297],{"class":5543,"line":5652},[5541,7285,7286],{"class":6418},"    if",[5541,7288,5285],{"class":6263},[5541,7290,7291],{"class":6272},"node",[5541,7293,7294],{"class":6263}," == ",[5541,7296,6358],{"class":6253},[5541,7298,6337],{"class":6263},[5541,7300,7301],{"class":5543,"line":5658},[5541,7302,6373],{"class":6263},[5541,7304,7305,7308,7310],{"class":5543,"line":5664},[5541,7306,7307],{"class":6418},"        return",[5541,7309,6276],{"class":6263},[5541,7311,7312],{"class":6279},"  \u002F\u002F Базовий випадок: порожнє дерево\n",[5541,7314,7315],{"class":5543,"line":5669},[5541,7316,6378],{"class":6263},[5541,7318,7319],{"class":5543,"line":5675},[5541,7320,6315],{"class":6263},[5541,7322,7323],{"class":5543,"line":5681},[5541,7324,7325],{"class":6279},"    \u002F\u002F Рекурсивно видаляємо ліве та праве піддерева\n",[5541,7327,7328,7330,7332,7334,7337,7339],{"class":5543,"line":5687},[5541,7329,7236],{"class":6325},[5541,7331,6328],{"class":6263},[5541,7333,7291],{"class":6272},[5541,7335,7336],{"class":6263},"->",[5541,7338,5495],{"class":6272},[5541,7340,6613],{"class":6263},[5541,7342,7343,7345,7347,7349,7351,7353],{"class":5543,"line":5693},[5541,7344,7236],{"class":6325},[5541,7346,6328],{"class":6263},[5541,7348,7291],{"class":6272},[5541,7350,7336],{"class":6263},[5541,7352,5499],{"class":6272},[5541,7354,6613],{"class":6263},[5541,7356,7357],{"class":5543,"line":5699},[5541,7358,6315],{"class":6263},[5541,7360,7361],{"class":5543,"line":5704},[5541,7362,7363],{"class":6279},"    \u002F\u002F Тепер можна видалити поточний вузол\n",[5541,7365,7366,7369,7371],{"class":5543,"line":5710},[5541,7367,7368],{"class":6418},"    delete",[5541,7370,6604],{"class":6272},[5541,7372,6465],{"class":6263},[5541,7374,7375],{"class":5543,"line":5716},[5541,7376,5620],{"class":6263},[5390,7378,7379,7382,7383,7385,7386,7388],{},[5271,7380,7381],{},"Порядок видалення (post-order):"," Спершу видаляємо дітей, потім батька. Якщо видалити батька раніше, втратимо доступ до дітей (покажчики ",[5538,7384,5495],{}," та ",[5538,7387,5499],{}," зникнуть). Це відрізняється від однозв'язаного списку, де достатньо було ітеративного циклу.",[5382,7390],{},[5385,7392,7394],{"id":7393},"операція-вставки-рекурсивна-логіка","Операція вставки: рекурсивна логіка",[5390,7396,7397,7398,7401],{},"Вставка у BST — це ",[5271,7399,7400],{},"рекурсивний спуск"," від кореня до місця, де новий вузол має стати листом.",[5390,7403,7404],{},[5271,7405,7406],{},"Алгоритм:",[5405,7408,7409,7416,7451],{},[5267,7410,7411,7412,7415],{},"Якщо дерево порожнє (",[5538,7413,7414],{},"node == nullptr","), створити новий вузол — він стає коренем (або листом).",[5267,7417,7418,7419,7421,7422,7425,7426],{},"Інакше порівняти ",[5538,7420,6028],{}," з ",[5538,7423,7424],{},"node->data",":\n",[5264,7427,7428,7435,7441],{},[5267,7429,7430,7431,7434],{},"Якщо ",[5538,7432,7433],{},"value \u003C node->data"," — вставити у ліве піддерево (рекурсивно).",[5267,7436,7430,7437,7440],{},[5538,7438,7439],{},"value > node->data"," — вставити у праве піддерево (рекурсивно).",[5267,7442,7430,7443,7446,7447,7450],{},[5538,7444,7445],{},"value == node->data"," — дублікати зазвичай ",[5271,7448,7449],{},"не вставляються"," (або обробляються залежно від вимог).",[5267,7452,7453],{},"Повернути вказівник на (можливо оновлений) вузол.",[5531,7455,7457],{"className":6244,"code":7456,"language":6246,"meta":5536,"style":5536},"\u002F\u002F Публічний метод (обгортка)\nvoid BinarySearchTree::insert(int value)\n{\n    root = insertRecursive(root, value);\n}\n\n\u002F\u002F Приватний рекурсивний метод\nTreeNode* BinarySearchTree::insertRecursive(TreeNode* node, int value)\n{\n    \u002F\u002F Базовий випадок: дійшли до nullptr — створюємо новий вузол\n    if (node == nullptr)\n    {\n        return new TreeNode(value);\n    }\n    \n    \u002F\u002F Рекурсивний випадок: вибираємо напрямок\n    if (value \u003C node->data)\n    {\n        \u002F\u002F Значення менше — йдемо ліворуч\n        node->left = insertRecursive(node->left, value);\n    }\n    else if (value > node->data)\n    {\n        \u002F\u002F Значення більше — йдемо праворуч\n        node->right = insertRecursive(node->right, value);\n    }\n    else\n    {\n        \u002F\u002F value == node->data — дублікат, не вставляємо\n        std::cerr \u003C\u003C \"Значення \" \u003C\u003C value \u003C\u003C \" вже існує в дереві\\n\";\n    }\n    \n    \u002F\u002F Повертаємо вказівник на поточний вузол (незмінний для рекурсивного виклику)\n    return node;\n}\n",[5538,7458,7459,7464,7482,7486,7507,7511,7515,7520,7548,7552,7557,7571,7575,7591,7595,7599,7604,7623,7627,7632,7659,7663,7686,7690,7695,7721,7725,7730,7734,7739,7773,7777,7781,7786,7795],{"__ignoreMap":5536},[5541,7460,7461],{"class":5543,"line":5544},[5541,7462,7463],{"class":6279},"\u002F\u002F Публічний метод (обгортка)\n",[5541,7465,7466,7468,7470,7472,7474,7476,7478,7480],{"class":5543,"line":5550},[5541,7467,7260],{"class":6253},[5541,7469,6861],{"class":6257},[5541,7471,7181],{"class":6263},[5541,7473,5299],{"class":6325},[5541,7475,6328],{"class":6263},[5541,7477,6331],{"class":6253},[5541,7479,6334],{"class":6272},[5541,7481,6337],{"class":6263},[5541,7483,7484],{"class":5543,"line":5556},[5541,7485,6264],{"class":6263},[5541,7487,7488,7491,7494,7497,7499,7501,7503,7505],{"class":5543,"line":5562},[5541,7489,7490],{"class":6272},"    root",[5541,7492,7493],{"class":6263}," = ",[5541,7495,7496],{"class":6325},"insertRecursive",[5541,7498,6328],{"class":6263},[5541,7500,5351],{"class":6272},[5541,7502,5742],{"class":6263},[5541,7504,6028],{"class":6272},[5541,7506,6613],{"class":6263},[5541,7508,7509],{"class":5543,"line":5569},[5541,7510,5620],{"class":6263},[5541,7512,7513],{"class":5543,"line":5575},[5541,7514,5566],{"emptyLinePlaceholder":5565},[5541,7516,7517],{"class":5543,"line":5581},[5541,7518,7519],{"class":6279},"\u002F\u002F Приватний рекурсивний метод\n",[5541,7521,7522,7524,7526,7528,7530,7532,7534,7536,7538,7540,7542,7544,7546],{"class":5543,"line":5587},[5541,7523,6599],{"class":6257},[5541,7525,6288],{"class":6253},[5541,7527,6861],{"class":6257},[5541,7529,7181],{"class":6263},[5541,7531,7496],{"class":6325},[5541,7533,6328],{"class":6263},[5541,7535,6599],{"class":6257},[5541,7537,6288],{"class":6253},[5541,7539,6604],{"class":6272},[5541,7541,5742],{"class":6263},[5541,7543,6331],{"class":6253},[5541,7545,6334],{"class":6272},[5541,7547,6337],{"class":6263},[5541,7549,7550],{"class":5543,"line":5593},[5541,7551,6264],{"class":6263},[5541,7553,7554],{"class":5543,"line":5599},[5541,7555,7556],{"class":6279},"    \u002F\u002F Базовий випадок: дійшли до nullptr — створюємо новий вузол\n",[5541,7558,7559,7561,7563,7565,7567,7569],{"class":5543,"line":5605},[5541,7560,7286],{"class":6418},[5541,7562,5285],{"class":6263},[5541,7564,7291],{"class":6272},[5541,7566,7294],{"class":6263},[5541,7568,6358],{"class":6253},[5541,7570,6337],{"class":6263},[5541,7572,7573],{"class":5543,"line":5611},[5541,7574,6373],{"class":6263},[5541,7576,7577,7579,7582,7585,7587,7589],{"class":5543,"line":5617},[5541,7578,7307],{"class":6418},[5541,7580,7581],{"class":6418}," new",[5541,7583,7584],{"class":6325}," TreeNode",[5541,7586,6328],{"class":6263},[5541,7588,6028],{"class":6272},[5541,7590,6613],{"class":6263},[5541,7592,7593],{"class":5543,"line":5623},[5541,7594,6378],{"class":6263},[5541,7596,7597],{"class":5543,"line":5628},[5541,7598,6315],{"class":6263},[5541,7600,7601],{"class":5543,"line":5634},[5541,7602,7603],{"class":6279},"    \u002F\u002F Рекурсивний випадок: вибираємо напрямок\n",[5541,7605,7606,7608,7610,7612,7615,7617,7619,7621],{"class":5543,"line":5640},[5541,7607,7286],{"class":6418},[5541,7609,5285],{"class":6263},[5541,7611,6028],{"class":6272},[5541,7613,7614],{"class":6263}," \u003C ",[5541,7616,7291],{"class":6272},[5541,7618,7336],{"class":6263},[5541,7620,6345],{"class":6272},[5541,7622,6337],{"class":6263},[5541,7624,7625],{"class":5543,"line":5646},[5541,7626,6373],{"class":6263},[5541,7628,7629],{"class":5543,"line":5652},[5541,7630,7631],{"class":6279},"        \u002F\u002F Значення менше — йдемо ліворуч\n",[5541,7633,7634,7637,7639,7641,7643,7645,7647,7649,7651,7653,7655,7657],{"class":5543,"line":5658},[5541,7635,7636],{"class":6272},"        node",[5541,7638,7336],{"class":6263},[5541,7640,5495],{"class":6272},[5541,7642,7493],{"class":6263},[5541,7644,7496],{"class":6325},[5541,7646,6328],{"class":6263},[5541,7648,7291],{"class":6272},[5541,7650,7336],{"class":6263},[5541,7652,5495],{"class":6272},[5541,7654,5742],{"class":6263},[5541,7656,6028],{"class":6272},[5541,7658,6613],{"class":6263},[5541,7660,7661],{"class":5543,"line":5664},[5541,7662,6378],{"class":6263},[5541,7664,7665,7668,7671,7673,7675,7678,7680,7682,7684],{"class":5543,"line":5669},[5541,7666,7667],{"class":6418},"    else",[5541,7669,7670],{"class":6418}," if",[5541,7672,5285],{"class":6263},[5541,7674,6028],{"class":6272},[5541,7676,7677],{"class":6263}," > ",[5541,7679,7291],{"class":6272},[5541,7681,7336],{"class":6263},[5541,7683,6345],{"class":6272},[5541,7685,6337],{"class":6263},[5541,7687,7688],{"class":5543,"line":5675},[5541,7689,6373],{"class":6263},[5541,7691,7692],{"class":5543,"line":5681},[5541,7693,7694],{"class":6279},"        \u002F\u002F Значення більше — йдемо праворуч\n",[5541,7696,7697,7699,7701,7703,7705,7707,7709,7711,7713,7715,7717,7719],{"class":5543,"line":5687},[5541,7698,7636],{"class":6272},[5541,7700,7336],{"class":6263},[5541,7702,5499],{"class":6272},[5541,7704,7493],{"class":6263},[5541,7706,7496],{"class":6325},[5541,7708,6328],{"class":6263},[5541,7710,7291],{"class":6272},[5541,7712,7336],{"class":6263},[5541,7714,5499],{"class":6272},[5541,7716,5742],{"class":6263},[5541,7718,6028],{"class":6272},[5541,7720,6613],{"class":6263},[5541,7722,7723],{"class":5543,"line":5693},[5541,7724,6378],{"class":6263},[5541,7726,7727],{"class":5543,"line":5699},[5541,7728,7729],{"class":6418},"    else\n",[5541,7731,7732],{"class":5543,"line":5704},[5541,7733,6373],{"class":6263},[5541,7735,7736],{"class":5543,"line":5710},[5541,7737,7738],{"class":6279},"        \u002F\u002F value == node->data — дублікат, не вставляємо\n",[5541,7740,7741,7744,7746,7749,7752,7755,7757,7759,7761,7764,7768,7771],{"class":5543,"line":5716},[5541,7742,7743],{"class":6257},"        std",[5541,7745,7181],{"class":6263},[5541,7747,7748],{"class":6272},"cerr",[5541,7750,7751],{"class":6263}," \u003C\u003C ",[5541,7753,7754],{"class":6441},"\"Значення \"",[5541,7756,7751],{"class":6263},[5541,7758,6028],{"class":6272},[5541,7760,7751],{"class":6263},[5541,7762,7763],{"class":6441},"\" вже існує в дереві",[5541,7765,7767],{"class":7766},"sjcCO","\\n",[5541,7769,7770],{"class":6441},"\"",[5541,7772,6465],{"class":6263},[5541,7774,7775],{"class":5543,"line":5722},[5541,7776,6378],{"class":6263},[5541,7778,7779],{"class":5543,"line":5727},[5541,7780,6315],{"class":6263},[5541,7782,7783],{"class":5543,"line":5732},[5541,7784,7785],{"class":6279},"    \u002F\u002F Повертаємо вказівник на поточний вузол (незмінний для рекурсивного виклику)\n",[5541,7787,7788,7791,7793],{"class":5543,"line":6796},[5541,7789,7790],{"class":6418},"    return",[5541,7792,6604],{"class":6272},[5541,7794,6465],{"class":6263},[5541,7796,7797],{"class":5543,"line":6801},[5541,7798,5620],{"class":6263},[5390,7800,7801,7807,7808,7811,7812,7814,7815,7817,7818,7820,7821,7824],{},[5271,7802,7803,7804,7806],{},"Чому повертаємо ",[5538,7805,7128],{},"?"," Це дозволяє ",[5271,7809,7810],{},"реконструювати зв'язки"," під час розгортання рекурсії. Коли ми досягаємо базового випадку (",[5538,7813,6358],{},"), створюємо новий вузол та повертаємо його адресу. Батьківський рекурсивний виклик отримує цю адресу та присвоює її ",[5538,7816,5495],{}," або ",[5538,7819,5499],{},", тим самим ",[5271,7822,7823],{},"підключаючи"," новий вузол до дерева.",[5527,7826,7828],{"alt":7827},"Вставка 25 у дерево [50, 30, 70, 20, 40]",[5531,7829,7831],{"className":5533,"code":7830,"language":5535,"meta":5536,"style":5536},"@startuml\nskinparam style plain\nskinparam backgroundColor #FFFFFF\n\ntitle Вставка 25 у BST\n\nrectangle \"Крок 1: Порівняння з коренем\" as step1 #F1F5F9\ncircle \"50\" as root1 #DBEAFE\nnote right of root1 : 25 \u003C 50 → йдемо ліворуч\n\nrectangle \"Крок 2: Порівняння з 30\" as step2 #F1F5F9\ncircle \"30\" as node30 #DCFCE7\nnote right of node30 : 25 \u003C 30 → йдемо ліворуч\n\nrectangle \"Крок 3: Порівняння з 20\" as step3 #F1F5F9\ncircle \"20\" as node20 #E2E8F0\nnote right of node20 : 25 > 20 → йдемо праворуч\n\nrectangle \"Крок 4: Досягли nullptr\" as step4 #F1F5F9\ncircle \"nullptr\" as null #F8FAFC\nnote right of null : Створюємо новий вузол 25\n\nrectangle \"Результат\" as result #F1F5F9\ncircle \"50\" as rootR #DBEAFE\ncircle \"30\" as n30R #DCFCE7\ncircle \"70\" as n70R #DCFCE7\ncircle \"20\" as n20R #E2E8F0\ncircle \"25\" as n25R #FEF3C7\ncircle \"40\" as n40R #E2E8F0\n\nrootR -down-> n30R : left\nrootR -down-> n70R : right\nn30R -down-> n20R : left\nn30R -down-> n40R : right\nn20R -down-> n25R : right\n\nnote right of n25R #DCFCE7\n  Новий вузол\n  підключений до\n  правої гілки 20\nend note\n\nstep1 -[hidden]down-> root1\nstep2 -[hidden]down-> node30\nstep3 -[hidden]down-> node20\nstep4 -[hidden]down-> null\nresult -[hidden]down-> rootR\n\n@enduml\n",[5538,7832,7833,7837,7841,7845,7849,7854,7858,7863,7868,7873,7877,7882,7887,7892,7896,7901,7906,7911,7915,7920,7925,7930,7934,7939,7944,7949,7954,7959,7964,7969,7973,7978,7983,7988,7993,7998,8002,8007,8012,8017,8022,8026,8030,8035,8040,8045,8050,8055,8059],{"__ignoreMap":5536},[5541,7834,7835],{"class":5543,"line":5544},[5541,7836,5547],{},[5541,7838,7839],{"class":5543,"line":5550},[5541,7840,5553],{},[5541,7842,7843],{"class":5543,"line":5556},[5541,7844,5559],{},[5541,7846,7847],{"class":5543,"line":5562},[5541,7848,5566],{"emptyLinePlaceholder":5565},[5541,7850,7851],{"class":5543,"line":5569},[5541,7852,7853],{},"title Вставка 25 у BST\n",[5541,7855,7856],{"class":5543,"line":5575},[5541,7857,5566],{"emptyLinePlaceholder":5565},[5541,7859,7860],{"class":5543,"line":5581},[5541,7861,7862],{},"rectangle \"Крок 1: Порівняння з коренем\" as step1 #F1F5F9\n",[5541,7864,7865],{"class":5543,"line":5587},[5541,7866,7867],{},"circle \"50\" as root1 #DBEAFE\n",[5541,7869,7870],{"class":5543,"line":5593},[5541,7871,7872],{},"note right of root1 : 25 \u003C 50 → йдемо ліворуч\n",[5541,7874,7875],{"class":5543,"line":5599},[5541,7876,5566],{"emptyLinePlaceholder":5565},[5541,7878,7879],{"class":5543,"line":5605},[5541,7880,7881],{},"rectangle \"Крок 2: Порівняння з 30\" as step2 #F1F5F9\n",[5541,7883,7884],{"class":5543,"line":5611},[5541,7885,7886],{},"circle \"30\" as node30 #DCFCE7\n",[5541,7888,7889],{"class":5543,"line":5617},[5541,7890,7891],{},"note right of node30 : 25 \u003C 30 → йдемо ліворуч\n",[5541,7893,7894],{"class":5543,"line":5623},[5541,7895,5566],{"emptyLinePlaceholder":5565},[5541,7897,7898],{"class":5543,"line":5628},[5541,7899,7900],{},"rectangle \"Крок 3: Порівняння з 20\" as step3 #F1F5F9\n",[5541,7902,7903],{"class":5543,"line":5634},[5541,7904,7905],{},"circle \"20\" as node20 #E2E8F0\n",[5541,7907,7908],{"class":5543,"line":5640},[5541,7909,7910],{},"note right of node20 : 25 > 20 → йдемо праворуч\n",[5541,7912,7913],{"class":5543,"line":5646},[5541,7914,5566],{"emptyLinePlaceholder":5565},[5541,7916,7917],{"class":5543,"line":5652},[5541,7918,7919],{},"rectangle \"Крок 4: Досягли nullptr\" as step4 #F1F5F9\n",[5541,7921,7922],{"class":5543,"line":5658},[5541,7923,7924],{},"circle \"nullptr\" as null #F8FAFC\n",[5541,7926,7927],{"class":5543,"line":5664},[5541,7928,7929],{},"note right of null : Створюємо новий вузол 25\n",[5541,7931,7932],{"class":5543,"line":5669},[5541,7933,5566],{"emptyLinePlaceholder":5565},[5541,7935,7936],{"class":5543,"line":5675},[5541,7937,7938],{},"rectangle \"Результат\" as result #F1F5F9\n",[5541,7940,7941],{"class":5543,"line":5681},[5541,7942,7943],{},"circle \"50\" as rootR #DBEAFE\n",[5541,7945,7946],{"class":5543,"line":5687},[5541,7947,7948],{},"circle \"30\" as n30R #DCFCE7\n",[5541,7950,7951],{"class":5543,"line":5693},[5541,7952,7953],{},"circle \"70\" as n70R #DCFCE7\n",[5541,7955,7956],{"class":5543,"line":5699},[5541,7957,7958],{},"circle \"20\" as n20R #E2E8F0\n",[5541,7960,7961],{"class":5543,"line":5704},[5541,7962,7963],{},"circle \"25\" as n25R #FEF3C7\n",[5541,7965,7966],{"class":5543,"line":5710},[5541,7967,7968],{},"circle \"40\" as n40R #E2E8F0\n",[5541,7970,7971],{"class":5543,"line":5716},[5541,7972,5566],{"emptyLinePlaceholder":5565},[5541,7974,7975],{"class":5543,"line":5722},[5541,7976,7977],{},"rootR -down-> n30R : left\n",[5541,7979,7980],{"class":5543,"line":5727},[5541,7981,7982],{},"rootR -down-> n70R : right\n",[5541,7984,7985],{"class":5543,"line":5732},[5541,7986,7987],{},"n30R -down-> n20R : left\n",[5541,7989,7990],{"class":5543,"line":6796},[5541,7991,7992],{},"n30R -down-> n40R : right\n",[5541,7994,7995],{"class":5543,"line":6801},[5541,7996,7997],{},"n20R -down-> n25R : right\n",[5541,7999,8000],{"class":5543,"line":6807},[5541,8001,5566],{"emptyLinePlaceholder":5565},[5541,8003,8004],{"class":5543,"line":6813},[5541,8005,8006],{},"note right of n25R #DCFCE7\n",[5541,8008,8009],{"class":5543,"line":6822},[5541,8010,8011],{},"  Новий вузол\n",[5541,8013,8014],{"class":5543,"line":6827},[5541,8015,8016],{},"  підключений до\n",[5541,8018,8019],{"class":5543,"line":6833},[5541,8020,8021],{},"  правої гілки 20\n",[5541,8023,8024],{"class":5543,"line":6841},[5541,8025,5696],{},[5541,8027,8028],{"class":5543,"line":6846},[5541,8029,5566],{"emptyLinePlaceholder":5565},[5541,8031,8032],{"class":5543,"line":6852},[5541,8033,8034],{},"step1 -[hidden]down-> root1\n",[5541,8036,8037],{"class":5543,"line":6874},[5541,8038,8039],{},"step2 -[hidden]down-> node30\n",[5541,8041,8042],{"class":5543,"line":6898},[5541,8043,8044],{},"step3 -[hidden]down-> node20\n",[5541,8046,8047],{"class":5543,"line":6903},[5541,8048,8049],{},"step4 -[hidden]down-> null\n",[5541,8051,8052],{"class":5543,"line":6909},[5541,8053,8054],{},"result -[hidden]down-> rootR\n",[5541,8056,8057],{"class":5543,"line":6925},[5541,8058,5566],{"emptyLinePlaceholder":5565},[5541,8060,8061],{"class":5543,"line":6930},[5541,8062,5735],{},[5390,8064,8065,8067],{},[5271,8066,5423],{}," O(h), де h — висота дерева. Для збалансованого дерева h = O(log n), отже вставка — O(log n). Для виродженого дерева h = O(n), вставка — O(n).",[5382,8069],{},[5385,8071,8073],{"id":8072},"операція-пошуку-рекурсивний-та-ітеративний-варіанти","Операція пошуку: рекурсивний та ітеративний варіанти",[5390,8075,8076,8077,8079],{},"Пошук у BST — це ",[5271,8078,5399],{}," безпосередньо у структурі дерева.",[5753,8081,8083],{"id":8082},"рекурсивна-версія","Рекурсивна версія",[5531,8085,8087],{"className":6244,"code":8086,"language":6246,"meta":5536,"style":5536},"\u002F\u002F Публічний метод\nbool BinarySearchTree::search(int value) const\n{\n    return searchRecursive(root, value);\n}\n\n\u002F\u002F Приватний рекурсивний метод\nbool BinarySearchTree::searchRecursive(TreeNode* node, int value) const\n{\n    \u002F\u002F Базовий випадок 1: дійшли до nullptr — значення не знайдено\n    if (node == nullptr)\n    {\n        return false;\n    }\n    \n    \u002F\u002F Базовий випадок 2: знайшли значення\n    if (value == node->data)\n    {\n        return true;\n    }\n    \n    \u002F\u002F Рекурсивний випадок: вибираємо напрямок\n    if (value \u003C node->data)\n    {\n        return searchRecursive(node->left, value);   \u002F\u002F Шукаємо ліворуч\n    }\n    else\n    {\n        return searchRecursive(node->right, value);  \u002F\u002F Шукаємо праворуч\n    }\n}\n",[5538,8088,8089,8094,8116,8120,8136,8140,8144,8148,8177,8181,8186,8200,8204,8213,8217,8221,8226,8244,8248,8257,8261,8265,8269,8287,8291,8315,8319,8323,8327,8350,8354],{"__ignoreMap":5536},[5541,8090,8091],{"class":5543,"line":5544},[5541,8092,8093],{"class":6279},"\u002F\u002F Публічний метод\n",[5541,8095,8096,8099,8101,8103,8105,8107,8109,8111,8113],{"class":5543,"line":5550},[5541,8097,8098],{"class":6253},"bool",[5541,8100,6861],{"class":6257},[5541,8102,7181],{"class":6263},[5541,8104,5306],{"class":6325},[5541,8106,6328],{"class":6263},[5541,8108,6331],{"class":6253},[5541,8110,6334],{"class":6272},[5541,8112,6658],{"class":6263},[5541,8114,8115],{"class":6253},"const\n",[5541,8117,8118],{"class":5543,"line":5556},[5541,8119,6264],{"class":6263},[5541,8121,8122,8124,8126,8128,8130,8132,8134],{"class":5543,"line":5562},[5541,8123,7790],{"class":6418},[5541,8125,6671],{"class":6325},[5541,8127,6328],{"class":6263},[5541,8129,5351],{"class":6272},[5541,8131,5742],{"class":6263},[5541,8133,6028],{"class":6272},[5541,8135,6613],{"class":6263},[5541,8137,8138],{"class":5543,"line":5569},[5541,8139,5620],{"class":6263},[5541,8141,8142],{"class":5543,"line":5575},[5541,8143,5566],{"emptyLinePlaceholder":5565},[5541,8145,8146],{"class":5543,"line":5581},[5541,8147,7519],{"class":6279},[5541,8149,8150,8152,8154,8156,8159,8161,8163,8165,8167,8169,8171,8173,8175],{"class":5543,"line":5587},[5541,8151,8098],{"class":6253},[5541,8153,6861],{"class":6257},[5541,8155,7181],{"class":6263},[5541,8157,8158],{"class":6325},"searchRecursive",[5541,8160,6328],{"class":6263},[5541,8162,6599],{"class":6257},[5541,8164,6288],{"class":6253},[5541,8166,6604],{"class":6272},[5541,8168,5742],{"class":6263},[5541,8170,6331],{"class":6253},[5541,8172,6334],{"class":6272},[5541,8174,6658],{"class":6263},[5541,8176,8115],{"class":6253},[5541,8178,8179],{"class":5543,"line":5593},[5541,8180,6264],{"class":6263},[5541,8182,8183],{"class":5543,"line":5599},[5541,8184,8185],{"class":6279},"    \u002F\u002F Базовий випадок 1: дійшли до nullptr — значення не знайдено\n",[5541,8187,8188,8190,8192,8194,8196,8198],{"class":5543,"line":5605},[5541,8189,7286],{"class":6418},[5541,8191,5285],{"class":6263},[5541,8193,7291],{"class":6272},[5541,8195,7294],{"class":6263},[5541,8197,6358],{"class":6253},[5541,8199,6337],{"class":6263},[5541,8201,8202],{"class":5543,"line":5611},[5541,8203,6373],{"class":6263},[5541,8205,8206,8208,8211],{"class":5543,"line":5617},[5541,8207,7307],{"class":6418},[5541,8209,8210],{"class":6253}," false",[5541,8212,6465],{"class":6263},[5541,8214,8215],{"class":5543,"line":5623},[5541,8216,6378],{"class":6263},[5541,8218,8219],{"class":5543,"line":5628},[5541,8220,6315],{"class":6263},[5541,8222,8223],{"class":5543,"line":5634},[5541,8224,8225],{"class":6279},"    \u002F\u002F Базовий випадок 2: знайшли значення\n",[5541,8227,8228,8230,8232,8234,8236,8238,8240,8242],{"class":5543,"line":5640},[5541,8229,7286],{"class":6418},[5541,8231,5285],{"class":6263},[5541,8233,6028],{"class":6272},[5541,8235,7294],{"class":6263},[5541,8237,7291],{"class":6272},[5541,8239,7336],{"class":6263},[5541,8241,6345],{"class":6272},[5541,8243,6337],{"class":6263},[5541,8245,8246],{"class":5543,"line":5646},[5541,8247,6373],{"class":6263},[5541,8249,8250,8252,8255],{"class":5543,"line":5652},[5541,8251,7307],{"class":6418},[5541,8253,8254],{"class":6253}," true",[5541,8256,6465],{"class":6263},[5541,8258,8259],{"class":5543,"line":5658},[5541,8260,6378],{"class":6263},[5541,8262,8263],{"class":5543,"line":5664},[5541,8264,6315],{"class":6263},[5541,8266,8267],{"class":5543,"line":5669},[5541,8268,7603],{"class":6279},[5541,8270,8271,8273,8275,8277,8279,8281,8283,8285],{"class":5543,"line":5675},[5541,8272,7286],{"class":6418},[5541,8274,5285],{"class":6263},[5541,8276,6028],{"class":6272},[5541,8278,7614],{"class":6263},[5541,8280,7291],{"class":6272},[5541,8282,7336],{"class":6263},[5541,8284,6345],{"class":6272},[5541,8286,6337],{"class":6263},[5541,8288,8289],{"class":5543,"line":5681},[5541,8290,6373],{"class":6263},[5541,8292,8293,8295,8297,8299,8301,8303,8305,8307,8309,8312],{"class":5543,"line":5687},[5541,8294,7307],{"class":6418},[5541,8296,6671],{"class":6325},[5541,8298,6328],{"class":6263},[5541,8300,7291],{"class":6272},[5541,8302,7336],{"class":6263},[5541,8304,5495],{"class":6272},[5541,8306,5742],{"class":6263},[5541,8308,6028],{"class":6272},[5541,8310,8311],{"class":6263},");",[5541,8313,8314],{"class":6279},"   \u002F\u002F Шукаємо ліворуч\n",[5541,8316,8317],{"class":5543,"line":5693},[5541,8318,6378],{"class":6263},[5541,8320,8321],{"class":5543,"line":5699},[5541,8322,7729],{"class":6418},[5541,8324,8325],{"class":5543,"line":5704},[5541,8326,6373],{"class":6263},[5541,8328,8329,8331,8333,8335,8337,8339,8341,8343,8345,8347],{"class":5543,"line":5710},[5541,8330,7307],{"class":6418},[5541,8332,6671],{"class":6325},[5541,8334,6328],{"class":6263},[5541,8336,7291],{"class":6272},[5541,8338,7336],{"class":6263},[5541,8340,5499],{"class":6272},[5541,8342,5742],{"class":6263},[5541,8344,6028],{"class":6272},[5541,8346,8311],{"class":6263},[5541,8348,8349],{"class":6279},"  \u002F\u002F Шукаємо праворуч\n",[5541,8351,8352],{"class":5543,"line":5716},[5541,8353,6378],{"class":6263},[5541,8355,8356],{"class":5543,"line":5722},[5541,8357,5620],{"class":6263},[5753,8359,8361],{"id":8360},"ітеративна-версія-ефективніша-за-памяттю","Ітеративна версія (ефективніша за пам'яттю)",[5390,8363,8364],{},"Рекурсія використовує стек викликів — для глибоких дерев це може призвести до переповнення стека. Ітеративна версія використовує лише O(1) пам'яті.",[5531,8366,8368],{"className":6244,"code":8367,"language":6246,"meta":5536,"style":5536},"bool BinarySearchTree::search(int value) const\n{\n    TreeNode* current = root;\n    \n    while (current != nullptr)\n    {\n        if (value == current->data)\n        {\n            return true;  \u002F\u002F Знайдено\n        }\n        else if (value \u003C current->data)\n        {\n            current = current->left;   \u002F\u002F Йдемо ліворуч\n        }\n        else\n        {\n            current = current->right;  \u002F\u002F Йдемо праворуч\n        }\n    }\n    \n    return false;  \u002F\u002F Дійшли до nullptr — не знайдено\n}\n",[5538,8369,8370,8390,8394,8409,8413,8430,8434,8453,8458,8470,8475,8496,8500,8518,8522,8527,8531,8548,8552,8556,8560,8571],{"__ignoreMap":5536},[5541,8371,8372,8374,8376,8378,8380,8382,8384,8386,8388],{"class":5543,"line":5544},[5541,8373,8098],{"class":6253},[5541,8375,6861],{"class":6257},[5541,8377,7181],{"class":6263},[5541,8379,5306],{"class":6325},[5541,8381,6328],{"class":6263},[5541,8383,6331],{"class":6253},[5541,8385,6334],{"class":6272},[5541,8387,6658],{"class":6263},[5541,8389,8115],{"class":6253},[5541,8391,8392],{"class":5543,"line":5550},[5541,8393,6264],{"class":6263},[5541,8395,8396,8398,8400,8403,8405,8407],{"class":5543,"line":5556},[5541,8397,6285],{"class":6257},[5541,8399,6288],{"class":6253},[5541,8401,8402],{"class":6272}," current",[5541,8404,7493],{"class":6263},[5541,8406,5351],{"class":6272},[5541,8408,6465],{"class":6263},[5541,8410,8411],{"class":5543,"line":5562},[5541,8412,6315],{"class":6263},[5541,8414,8415,8418,8420,8423,8426,8428],{"class":5543,"line":5569},[5541,8416,8417],{"class":6418},"    while",[5541,8419,5285],{"class":6263},[5541,8421,8422],{"class":6272},"current",[5541,8424,8425],{"class":6263}," != ",[5541,8427,6358],{"class":6253},[5541,8429,6337],{"class":6263},[5541,8431,8432],{"class":5543,"line":5575},[5541,8433,6373],{"class":6263},[5541,8435,8436,8439,8441,8443,8445,8447,8449,8451],{"class":5543,"line":5581},[5541,8437,8438],{"class":6418},"        if",[5541,8440,5285],{"class":6263},[5541,8442,6028],{"class":6272},[5541,8444,7294],{"class":6263},[5541,8446,8422],{"class":6272},[5541,8448,7336],{"class":6263},[5541,8450,6345],{"class":6272},[5541,8452,6337],{"class":6263},[5541,8454,8455],{"class":5543,"line":5587},[5541,8456,8457],{"class":6263},"        {\n",[5541,8459,8460,8463,8465,8467],{"class":5543,"line":5593},[5541,8461,8462],{"class":6418},"            return",[5541,8464,8254],{"class":6253},[5541,8466,6276],{"class":6263},[5541,8468,8469],{"class":6279},"  \u002F\u002F Знайдено\n",[5541,8471,8472],{"class":5543,"line":5599},[5541,8473,8474],{"class":6263},"        }\n",[5541,8476,8477,8480,8482,8484,8486,8488,8490,8492,8494],{"class":5543,"line":5605},[5541,8478,8479],{"class":6418},"        else",[5541,8481,7670],{"class":6418},[5541,8483,5285],{"class":6263},[5541,8485,6028],{"class":6272},[5541,8487,7614],{"class":6263},[5541,8489,8422],{"class":6272},[5541,8491,7336],{"class":6263},[5541,8493,6345],{"class":6272},[5541,8495,6337],{"class":6263},[5541,8497,8498],{"class":5543,"line":5611},[5541,8499,8457],{"class":6263},[5541,8501,8502,8505,8507,8509,8511,8513,8515],{"class":5543,"line":5617},[5541,8503,8504],{"class":6272},"            current",[5541,8506,7493],{"class":6263},[5541,8508,8422],{"class":6272},[5541,8510,7336],{"class":6263},[5541,8512,5495],{"class":6272},[5541,8514,6276],{"class":6263},[5541,8516,8517],{"class":6279},"   \u002F\u002F Йдемо ліворуч\n",[5541,8519,8520],{"class":5543,"line":5623},[5541,8521,8474],{"class":6263},[5541,8523,8524],{"class":5543,"line":5628},[5541,8525,8526],{"class":6418},"        else\n",[5541,8528,8529],{"class":5543,"line":5634},[5541,8530,8457],{"class":6263},[5541,8532,8533,8535,8537,8539,8541,8543,8545],{"class":5543,"line":5640},[5541,8534,8504],{"class":6272},[5541,8536,7493],{"class":6263},[5541,8538,8422],{"class":6272},[5541,8540,7336],{"class":6263},[5541,8542,5499],{"class":6272},[5541,8544,6276],{"class":6263},[5541,8546,8547],{"class":6279},"  \u002F\u002F Йдемо праворуч\n",[5541,8549,8550],{"class":5543,"line":5646},[5541,8551,8474],{"class":6263},[5541,8553,8554],{"class":5543,"line":5652},[5541,8555,6378],{"class":6263},[5541,8557,8558],{"class":5543,"line":5658},[5541,8559,6315],{"class":6263},[5541,8561,8562,8564,8566,8568],{"class":5543,"line":5664},[5541,8563,7790],{"class":6418},[5541,8565,8210],{"class":6253},[5541,8567,6276],{"class":6263},[5541,8569,8570],{"class":6279},"  \u002F\u002F Дійшли до nullptr — не знайдено\n",[5541,8572,8573],{"class":5543,"line":5669},[5541,8574,5620],{"class":6263},[5390,8576,8577,8579],{},[5271,8578,5423],{}," O(h) = O(log n) для збалансованого дерева. На кожному кроці ми відкидаємо половину дерева (або ліве піддерево, або праве).",[5961,8581,8583],{"title":8582},"Коли використовувати рекурсію vs ітерацію?",[5264,8584,8585,8591],{},[5267,8586,8587,8590],{},[5271,8588,8589],{},"Рекурсія:"," Природна для дерев, код чистіший та коротший. Підходить для вставки, видалення, обходів.",[5267,8592,8593,8596],{},[5271,8594,8595],{},"Ітерація:"," Ефективніша за пам'яттю для пошуку (найпростіша операція). Для складних операцій (видалення, балансування) рекурсія зазвичай зручніша.",[5382,8598],{},[5385,8600,8602],{"id":8601},"операція-видалення-найскладніший-випадок","Операція видалення: найскладніший випадок",[5390,8604,8605,8606,8609,8610,6012],{},"Видалення з BST — найскладніша операція, оскільки потрібно ",[5271,8607,8608],{},"зберегти BST-інваріант"," після видалення вузла. Існує ",[5271,8611,8612],{},"три випадки",[5753,8614,8616],{"id":8615},"випадок-1-вузол-лист-без-дітей","Випадок 1: Вузол-лист (без дітей)",[5390,8618,8619,8620,5514],{},"Просто видаляємо вузол — батьківський покажчик стає ",[5538,8621,6358],{},[5531,8623,8626],{"className":8624,"code":8625,"language":6061},[6059],"Видалити 20:\n       50\n      \u002F  \\\n    30    70\n   \u002F  \\\n  20  40   →  Просто delete 20, встановити left = nullptr\n",[5538,8627,8625],{"__ignoreMap":5536},[5753,8629,8631],{"id":8630},"випадок-2-вузол-з-однією-дитиною","Випадок 2: Вузол з однією дитиною",[5390,8633,8634],{},"Замінюємо вузол його єдиною дитиною — «перемикаємо» покажчик батька на дитину видаляємого вузла.",[5531,8636,8639],{"className":8637,"code":8638,"language":6061},[6059],"Видалити 30 (має лише праву дитину 40):\n       50                    50\n      \u002F  \\                  \u002F  \\\n    30    70    →         40    70\n      \\\n      40\n",[5538,8640,8638],{"__ignoreMap":5536},[5753,8642,8644],{"id":8643},"випадок-3-вузол-з-двома-дітьми-найскладніший","Випадок 3: Вузол з двома дітьми (найскладніший)",[5390,8646,8647,8648],{},"Не можна просто видалити вузол — втратимо обидва піддерева. ",[5271,8649,7406],{},[5405,8651,8652,8662,8665],{},[5267,8653,8654,8655,5285,8658,8661],{},"Знайти ",[5271,8656,8657],{},"in-order наступника",[5287,8659,8660],{},"inorder successor",") — найменший вузол у правому піддереві (найлівіший вузол правої гілки).",[5267,8663,8664],{},"Скопіювати значення наступника у видаляємий вузол.",[5267,8666,8667],{},"Рекурсивно видалити наступника (який тепер стає дублікатом).",[5390,8669,8670,8673,8674,7385,8677,8680],{},[5271,8671,8672],{},"Чому це працює?"," In-order наступник — це найменше значення, що більше за видаляємий вузол. Він гарантовано ",[5271,8675,8676],{},"більший за все ліве піддерево",[5271,8678,8679],{},"менший за решту правого піддерева",", тому зберігає BST-інваріант.",[5531,8682,8685],{"className":8683,"code":8684,"language":6061},[6059],"Видалити 50 (має двох дітей):\n       50                    60  ← Копіюємо 60 сюди\n      \u002F  \\                  \u002F  \\\n    30    70    →         30    70\n         \u002F \\                     \\\n        60  80                   80\n        \nПотім рекурсивно видаляємо 60 з правого піддерева (випадок 2 або 1)\n",[5538,8686,8684],{"__ignoreMap":5536},[5753,8688,8690],{"id":8689},"реалізація-видалення","Реалізація видалення",[5531,8692,8694],{"className":6244,"code":8693,"language":6246,"meta":5536,"style":5536},"\u002F\u002F Публічний метод\nvoid BinarySearchTree::remove(int value)\n{\n    root = deleteRecursive(root, value);\n}\n\n\u002F\u002F Приватний рекурсивний метод\nTreeNode* BinarySearchTree::deleteRecursive(TreeNode* node, int value)\n{\n    \u002F\u002F Базовий випадок: дійшли до nullptr — значення не знайдено\n    if (node == nullptr)\n    {\n        return nullptr;\n    }\n    \n    \u002F\u002F Рекурсивний пошук вузла для видалення\n    if (value \u003C node->data)\n    {\n        node->left = deleteRecursive(node->left, value);\n    }\n    else if (value > node->data)\n    {\n        node->right = deleteRecursive(node->right, value);\n    }\n    else\n    {\n        \u002F\u002F Знайшли вузол для видалення\n        \n        \u002F\u002F Випадок 1: Вузол-лист (без дітей)\n        if (node->left == nullptr && node->right == nullptr)\n        {\n            delete node;\n            return nullptr;\n        }\n        \n        \u002F\u002F Випадок 2a: Вузол має лише праву дитину\n        if (node->left == nullptr)\n        {\n            TreeNode* temp = node->right;\n            delete node;\n            return temp;\n        }\n        \n        \u002F\u002F Випадок 2b: Вузол має лише ліву дитину\n        if (node->right == nullptr)\n        {\n            TreeNode* temp = node->left;\n            delete node;\n            return temp;\n        }\n        \n        \u002F\u002F Випадок 3: Вузол має двох дітей\n        \u002F\u002F Знаходимо in-order наступника (мінімум у правому піддереві)\n        TreeNode* successor = findMin(node->right);\n        \n        \u002F\u002F Копіюємо значення наступника у поточний вузол\n        node->data = successor->data;\n        \n        \u002F\u002F Рекурсивно видаляємо наступника з правого піддерева\n        node->right = deleteRecursive(node->right, successor->data);\n    }\n    \n    return node;\n}\n\n\u002F\u002F Допоміжний метод: знайти мінімальний вузол у піддереві\nTreeNode* BinarySearchTree::findMin(TreeNode* node) const\n{\n    while (node->left != nullptr)\n    {\n        node = node->left;  \u002F\u002F Йдемо максимально ліворуч\n    }\n    return node;\n}\n",[5538,8695,8696,8700,8719,8723,8742,8746,8750,8754,8782,8786,8791,8805,8809,8818,8822,8826,8831,8849,8853,8879,8883,8903,8907,8933,8937,8941,8945,8950,8955,8960,8991,8995,9004,9012,9016,9020,9025,9043,9047,9067,9075,9083,9087,9091,9096,9114,9118,9136,9144,9152,9156,9160,9165,9170,9195,9199,9204,9223,9227,9232,9262,9266,9270,9278,9282,9286,9291,9315,9320,9339,9344,9362,9367,9376],{"__ignoreMap":5536},[5541,8697,8698],{"class":5543,"line":5544},[5541,8699,8093],{"class":6279},[5541,8701,8702,8704,8706,8708,8711,8713,8715,8717],{"class":5543,"line":5550},[5541,8703,7260],{"class":6253},[5541,8705,6861],{"class":6257},[5541,8707,7181],{"class":6263},[5541,8709,8710],{"class":6325},"remove",[5541,8712,6328],{"class":6263},[5541,8714,6331],{"class":6253},[5541,8716,6334],{"class":6272},[5541,8718,6337],{"class":6263},[5541,8720,8721],{"class":5543,"line":5556},[5541,8722,6264],{"class":6263},[5541,8724,8725,8727,8729,8732,8734,8736,8738,8740],{"class":5543,"line":5562},[5541,8726,7490],{"class":6272},[5541,8728,7493],{"class":6263},[5541,8730,8731],{"class":6325},"deleteRecursive",[5541,8733,6328],{"class":6263},[5541,8735,5351],{"class":6272},[5541,8737,5742],{"class":6263},[5541,8739,6028],{"class":6272},[5541,8741,6613],{"class":6263},[5541,8743,8744],{"class":5543,"line":5569},[5541,8745,5620],{"class":6263},[5541,8747,8748],{"class":5543,"line":5575},[5541,8749,5566],{"emptyLinePlaceholder":5565},[5541,8751,8752],{"class":5543,"line":5581},[5541,8753,7519],{"class":6279},[5541,8755,8756,8758,8760,8762,8764,8766,8768,8770,8772,8774,8776,8778,8780],{"class":5543,"line":5587},[5541,8757,6599],{"class":6257},[5541,8759,6288],{"class":6253},[5541,8761,6861],{"class":6257},[5541,8763,7181],{"class":6263},[5541,8765,8731],{"class":6325},[5541,8767,6328],{"class":6263},[5541,8769,6599],{"class":6257},[5541,8771,6288],{"class":6253},[5541,8773,6604],{"class":6272},[5541,8775,5742],{"class":6263},[5541,8777,6331],{"class":6253},[5541,8779,6334],{"class":6272},[5541,8781,6337],{"class":6263},[5541,8783,8784],{"class":5543,"line":5593},[5541,8785,6264],{"class":6263},[5541,8787,8788],{"class":5543,"line":5599},[5541,8789,8790],{"class":6279},"    \u002F\u002F Базовий випадок: дійшли до nullptr — значення не знайдено\n",[5541,8792,8793,8795,8797,8799,8801,8803],{"class":5543,"line":5605},[5541,8794,7286],{"class":6418},[5541,8796,5285],{"class":6263},[5541,8798,7291],{"class":6272},[5541,8800,7294],{"class":6263},[5541,8802,6358],{"class":6253},[5541,8804,6337],{"class":6263},[5541,8806,8807],{"class":5543,"line":5611},[5541,8808,6373],{"class":6263},[5541,8810,8811,8813,8816],{"class":5543,"line":5617},[5541,8812,7307],{"class":6418},[5541,8814,8815],{"class":6253}," nullptr",[5541,8817,6465],{"class":6263},[5541,8819,8820],{"class":5543,"line":5623},[5541,8821,6378],{"class":6263},[5541,8823,8824],{"class":5543,"line":5628},[5541,8825,6315],{"class":6263},[5541,8827,8828],{"class":5543,"line":5634},[5541,8829,8830],{"class":6279},"    \u002F\u002F Рекурсивний пошук вузла для видалення\n",[5541,8832,8833,8835,8837,8839,8841,8843,8845,8847],{"class":5543,"line":5640},[5541,8834,7286],{"class":6418},[5541,8836,5285],{"class":6263},[5541,8838,6028],{"class":6272},[5541,8840,7614],{"class":6263},[5541,8842,7291],{"class":6272},[5541,8844,7336],{"class":6263},[5541,8846,6345],{"class":6272},[5541,8848,6337],{"class":6263},[5541,8850,8851],{"class":5543,"line":5646},[5541,8852,6373],{"class":6263},[5541,8854,8855,8857,8859,8861,8863,8865,8867,8869,8871,8873,8875,8877],{"class":5543,"line":5652},[5541,8856,7636],{"class":6272},[5541,8858,7336],{"class":6263},[5541,8860,5495],{"class":6272},[5541,8862,7493],{"class":6263},[5541,8864,8731],{"class":6325},[5541,8866,6328],{"class":6263},[5541,8868,7291],{"class":6272},[5541,8870,7336],{"class":6263},[5541,8872,5495],{"class":6272},[5541,8874,5742],{"class":6263},[5541,8876,6028],{"class":6272},[5541,8878,6613],{"class":6263},[5541,8880,8881],{"class":5543,"line":5658},[5541,8882,6378],{"class":6263},[5541,8884,8885,8887,8889,8891,8893,8895,8897,8899,8901],{"class":5543,"line":5664},[5541,8886,7667],{"class":6418},[5541,8888,7670],{"class":6418},[5541,8890,5285],{"class":6263},[5541,8892,6028],{"class":6272},[5541,8894,7677],{"class":6263},[5541,8896,7291],{"class":6272},[5541,8898,7336],{"class":6263},[5541,8900,6345],{"class":6272},[5541,8902,6337],{"class":6263},[5541,8904,8905],{"class":5543,"line":5669},[5541,8906,6373],{"class":6263},[5541,8908,8909,8911,8913,8915,8917,8919,8921,8923,8925,8927,8929,8931],{"class":5543,"line":5675},[5541,8910,7636],{"class":6272},[5541,8912,7336],{"class":6263},[5541,8914,5499],{"class":6272},[5541,8916,7493],{"class":6263},[5541,8918,8731],{"class":6325},[5541,8920,6328],{"class":6263},[5541,8922,7291],{"class":6272},[5541,8924,7336],{"class":6263},[5541,8926,5499],{"class":6272},[5541,8928,5742],{"class":6263},[5541,8930,6028],{"class":6272},[5541,8932,6613],{"class":6263},[5541,8934,8935],{"class":5543,"line":5681},[5541,8936,6378],{"class":6263},[5541,8938,8939],{"class":5543,"line":5687},[5541,8940,7729],{"class":6418},[5541,8942,8943],{"class":5543,"line":5693},[5541,8944,6373],{"class":6263},[5541,8946,8947],{"class":5543,"line":5699},[5541,8948,8949],{"class":6279},"        \u002F\u002F Знайшли вузол для видалення\n",[5541,8951,8952],{"class":5543,"line":5704},[5541,8953,8954],{"class":6263},"        \n",[5541,8956,8957],{"class":5543,"line":5710},[5541,8958,8959],{"class":6279},"        \u002F\u002F Випадок 1: Вузол-лист (без дітей)\n",[5541,8961,8962,8964,8966,8968,8970,8972,8974,8976,8979,8981,8983,8985,8987,8989],{"class":5543,"line":5716},[5541,8963,8438],{"class":6418},[5541,8965,5285],{"class":6263},[5541,8967,7291],{"class":6272},[5541,8969,7336],{"class":6263},[5541,8971,5495],{"class":6272},[5541,8973,7294],{"class":6263},[5541,8975,6358],{"class":6253},[5541,8977,8978],{"class":6263}," && ",[5541,8980,7291],{"class":6272},[5541,8982,7336],{"class":6263},[5541,8984,5499],{"class":6272},[5541,8986,7294],{"class":6263},[5541,8988,6358],{"class":6253},[5541,8990,6337],{"class":6263},[5541,8992,8993],{"class":5543,"line":5722},[5541,8994,8457],{"class":6263},[5541,8996,8997,9000,9002],{"class":5543,"line":5727},[5541,8998,8999],{"class":6418},"            delete",[5541,9001,6604],{"class":6272},[5541,9003,6465],{"class":6263},[5541,9005,9006,9008,9010],{"class":5543,"line":5732},[5541,9007,8462],{"class":6418},[5541,9009,8815],{"class":6253},[5541,9011,6465],{"class":6263},[5541,9013,9014],{"class":5543,"line":6796},[5541,9015,8474],{"class":6263},[5541,9017,9018],{"class":5543,"line":6801},[5541,9019,8954],{"class":6263},[5541,9021,9022],{"class":5543,"line":6807},[5541,9023,9024],{"class":6279},"        \u002F\u002F Випадок 2a: Вузол має лише праву дитину\n",[5541,9026,9027,9029,9031,9033,9035,9037,9039,9041],{"class":5543,"line":6813},[5541,9028,8438],{"class":6418},[5541,9030,5285],{"class":6263},[5541,9032,7291],{"class":6272},[5541,9034,7336],{"class":6263},[5541,9036,5495],{"class":6272},[5541,9038,7294],{"class":6263},[5541,9040,6358],{"class":6253},[5541,9042,6337],{"class":6263},[5541,9044,9045],{"class":5543,"line":6822},[5541,9046,8457],{"class":6263},[5541,9048,9049,9052,9054,9057,9059,9061,9063,9065],{"class":5543,"line":6827},[5541,9050,9051],{"class":6257},"            TreeNode",[5541,9053,6288],{"class":6253},[5541,9055,9056],{"class":6272}," temp",[5541,9058,7493],{"class":6263},[5541,9060,7291],{"class":6272},[5541,9062,7336],{"class":6263},[5541,9064,5499],{"class":6272},[5541,9066,6465],{"class":6263},[5541,9068,9069,9071,9073],{"class":5543,"line":6833},[5541,9070,8999],{"class":6418},[5541,9072,6604],{"class":6272},[5541,9074,6465],{"class":6263},[5541,9076,9077,9079,9081],{"class":5543,"line":6841},[5541,9078,8462],{"class":6418},[5541,9080,9056],{"class":6272},[5541,9082,6465],{"class":6263},[5541,9084,9085],{"class":5543,"line":6846},[5541,9086,8474],{"class":6263},[5541,9088,9089],{"class":5543,"line":6852},[5541,9090,8954],{"class":6263},[5541,9092,9093],{"class":5543,"line":6874},[5541,9094,9095],{"class":6279},"        \u002F\u002F Випадок 2b: Вузол має лише ліву дитину\n",[5541,9097,9098,9100,9102,9104,9106,9108,9110,9112],{"class":5543,"line":6898},[5541,9099,8438],{"class":6418},[5541,9101,5285],{"class":6263},[5541,9103,7291],{"class":6272},[5541,9105,7336],{"class":6263},[5541,9107,5499],{"class":6272},[5541,9109,7294],{"class":6263},[5541,9111,6358],{"class":6253},[5541,9113,6337],{"class":6263},[5541,9115,9116],{"class":5543,"line":6903},[5541,9117,8457],{"class":6263},[5541,9119,9120,9122,9124,9126,9128,9130,9132,9134],{"class":5543,"line":6909},[5541,9121,9051],{"class":6257},[5541,9123,6288],{"class":6253},[5541,9125,9056],{"class":6272},[5541,9127,7493],{"class":6263},[5541,9129,7291],{"class":6272},[5541,9131,7336],{"class":6263},[5541,9133,5495],{"class":6272},[5541,9135,6465],{"class":6263},[5541,9137,9138,9140,9142],{"class":5543,"line":6925},[5541,9139,8999],{"class":6418},[5541,9141,6604],{"class":6272},[5541,9143,6465],{"class":6263},[5541,9145,9146,9148,9150],{"class":5543,"line":6930},[5541,9147,8462],{"class":6418},[5541,9149,9056],{"class":6272},[5541,9151,6465],{"class":6263},[5541,9153,9154],{"class":5543,"line":6936},[5541,9155,8474],{"class":6263},[5541,9157,9158],{"class":5543,"line":6952},[5541,9159,8954],{"class":6263},[5541,9161,9162],{"class":5543,"line":6957},[5541,9163,9164],{"class":6279},"        \u002F\u002F Випадок 3: Вузол має двох дітей\n",[5541,9166,9167],{"class":5543,"line":6963},[5541,9168,9169],{"class":6279},"        \u002F\u002F Знаходимо in-order наступника (мінімум у правому піддереві)\n",[5541,9171,9172,9175,9177,9180,9182,9185,9187,9189,9191,9193],{"class":5543,"line":6983},[5541,9173,9174],{"class":6257},"        TreeNode",[5541,9176,6288],{"class":6253},[5541,9178,9179],{"class":6272}," successor",[5541,9181,7493],{"class":6263},[5541,9183,9184],{"class":6325},"findMin",[5541,9186,6328],{"class":6263},[5541,9188,7291],{"class":6272},[5541,9190,7336],{"class":6263},[5541,9192,5499],{"class":6272},[5541,9194,6613],{"class":6263},[5541,9196,9197],{"class":5543,"line":6988},[5541,9198,8954],{"class":6263},[5541,9200,9201],{"class":5543,"line":6994},[5541,9202,9203],{"class":6279},"        \u002F\u002F Копіюємо значення наступника у поточний вузол\n",[5541,9205,9206,9208,9210,9212,9214,9217,9219,9221],{"class":5543,"line":7009},[5541,9207,7636],{"class":6272},[5541,9209,7336],{"class":6263},[5541,9211,6345],{"class":6272},[5541,9213,7493],{"class":6263},[5541,9215,9216],{"class":6272},"successor",[5541,9218,7336],{"class":6263},[5541,9220,6345],{"class":6272},[5541,9222,6465],{"class":6263},[5541,9224,9225],{"class":5543,"line":7014},[5541,9226,8954],{"class":6263},[5541,9228,9229],{"class":5543,"line":7020},[5541,9230,9231],{"class":6279},"        \u002F\u002F Рекурсивно видаляємо наступника з правого піддерева\n",[5541,9233,9234,9236,9238,9240,9242,9244,9246,9248,9250,9252,9254,9256,9258,9260],{"class":5543,"line":7034},[5541,9235,7636],{"class":6272},[5541,9237,7336],{"class":6263},[5541,9239,5499],{"class":6272},[5541,9241,7493],{"class":6263},[5541,9243,8731],{"class":6325},[5541,9245,6328],{"class":6263},[5541,9247,7291],{"class":6272},[5541,9249,7336],{"class":6263},[5541,9251,5499],{"class":6272},[5541,9253,5742],{"class":6263},[5541,9255,9216],{"class":6272},[5541,9257,7336],{"class":6263},[5541,9259,6345],{"class":6272},[5541,9261,6613],{"class":6263},[5541,9263,9264],{"class":5543,"line":7039},[5541,9265,6378],{"class":6263},[5541,9267,9268],{"class":5543,"line":7045},[5541,9269,6315],{"class":6263},[5541,9271,9272,9274,9276],{"class":5543,"line":7062},[5541,9273,7790],{"class":6418},[5541,9275,6604],{"class":6272},[5541,9277,6465],{"class":6263},[5541,9279,9280],{"class":5543,"line":7079},[5541,9281,5620],{"class":6263},[5541,9283,9284],{"class":5543,"line":7096},[5541,9285,5566],{"emptyLinePlaceholder":5565},[5541,9287,9288],{"class":5543,"line":7101},[5541,9289,9290],{"class":6279},"\u002F\u002F Допоміжний метод: знайти мінімальний вузол у піддереві\n",[5541,9292,9293,9295,9297,9299,9301,9303,9305,9307,9309,9311,9313],{"class":5543,"line":7106},[5541,9294,6599],{"class":6257},[5541,9296,6288],{"class":6253},[5541,9298,6861],{"class":6257},[5541,9300,7181],{"class":6263},[5541,9302,9184],{"class":6325},[5541,9304,6328],{"class":6263},[5541,9306,6599],{"class":6257},[5541,9308,6288],{"class":6253},[5541,9310,6604],{"class":6272},[5541,9312,6658],{"class":6263},[5541,9314,8115],{"class":6253},[5541,9316,9318],{"class":5543,"line":9317},68,[5541,9319,6264],{"class":6263},[5541,9321,9323,9325,9327,9329,9331,9333,9335,9337],{"class":5543,"line":9322},69,[5541,9324,8417],{"class":6418},[5541,9326,5285],{"class":6263},[5541,9328,7291],{"class":6272},[5541,9330,7336],{"class":6263},[5541,9332,5495],{"class":6272},[5541,9334,8425],{"class":6263},[5541,9336,6358],{"class":6253},[5541,9338,6337],{"class":6263},[5541,9340,9342],{"class":5543,"line":9341},70,[5541,9343,6373],{"class":6263},[5541,9345,9347,9349,9351,9353,9355,9357,9359],{"class":5543,"line":9346},71,[5541,9348,7636],{"class":6272},[5541,9350,7493],{"class":6263},[5541,9352,7291],{"class":6272},[5541,9354,7336],{"class":6263},[5541,9356,5495],{"class":6272},[5541,9358,6276],{"class":6263},[5541,9360,9361],{"class":6279},"  \u002F\u002F Йдемо максимально ліворуч\n",[5541,9363,9365],{"class":5543,"line":9364},72,[5541,9366,6378],{"class":6263},[5541,9368,9370,9372,9374],{"class":5543,"line":9369},73,[5541,9371,7790],{"class":6418},[5541,9373,6604],{"class":6272},[5541,9375,6465],{"class":6263},[5541,9377,9379],{"class":5543,"line":9378},74,[5541,9380,5620],{"class":6263},[5461,9382,9384,9385,5285,9388,9391],{"title":9383},"Альтернатива: in-order попередник","Замість наступника можна використати ",[5271,9386,9387],{},"in-order попередника",[5287,9389,9390],{},"inorder predecessor",") — найбільший вузол у лівому піддереві (найправіший вузол лівої гілки). Це теж зберігає BST-інваріант. Вибір між наступником та попередником довільний, деякі реалізації чергують їх для кращого балансування.",[5390,9393,9394,9396],{},[5271,9395,5423],{}," O(h) = O(log n) для збалансованого дерева. У випадку 3 потрібно знайти мінімум (O(h)) та виконати рекурсивне видалення (ще O(h)), але це все ще O(h).",[5382,9398],{},[5385,9400,9402],{"id":9401},"обходи-дерева-in-order-pre-order-post-order","Обходи дерева: in-order, pre-order, post-order",[5390,9404,9405,5285,9408,9411],{},[5271,9406,9407],{},"Обхід дерева",[5287,9409,9410],{},"tree traversal",") — це процес відвідування всіх вузлів дерева у певному порядку. Існує три основні стратегії для бінарних дерев:",[5753,9413,9415],{"id":9414},"_1-in-order-впорядкований-обхід-ліве-корінь-праве","1. In-Order (впорядкований обхід): ліве → корінь → праве",[5390,9417,9418,9421,9422,9425],{},[5271,9419,9420],{},"Властивість:"," Для BST in-order обхід ",[5271,9423,9424],{},"виводить елементи у відсортованому порядку"," (зростання).",[5531,9427,9429],{"className":6244,"code":9428,"language":6246,"meta":5536,"style":5536},"void BinarySearchTree::inOrder() const\n{\n    inOrderRecursive(root);\n    std::cout \u003C\u003C '\\n';\n}\n\nvoid BinarySearchTree::inOrderRecursive(TreeNode* node) const\n{\n    if (node == nullptr)\n    {\n        return;  \u002F\u002F Базовий випадок\n    }\n    \n    inOrderRecursive(node->left);        \u002F\u002F 1. Обійти ліве піддерево\n    std::cout \u003C\u003C node->data \u003C\u003C \" \";      \u002F\u002F 2. Відвідати корінь\n    inOrderRecursive(node->right);       \u002F\u002F 3. Обійти праве піддерево\n}\n",[5538,9430,9431,9446,9450,9461,9482,9486,9490,9513,9517,9531,9535,9544,9548,9552,9569,9595,9612],{"__ignoreMap":5536},[5541,9432,9433,9435,9437,9439,9442,9444],{"class":5543,"line":5544},[5541,9434,7260],{"class":6253},[5541,9436,6861],{"class":6257},[5541,9438,7181],{"class":6263},[5541,9440,9441],{"class":6325},"inOrder",[5541,9443,7002],{"class":6263},[5541,9445,8115],{"class":6253},[5541,9447,9448],{"class":5543,"line":5550},[5541,9449,6264],{"class":6263},[5541,9451,9452,9455,9457,9459],{"class":5543,"line":5556},[5541,9453,9454],{"class":6325},"    inOrderRecursive",[5541,9456,6328],{"class":6263},[5541,9458,5351],{"class":6272},[5541,9460,6613],{"class":6263},[5541,9462,9463,9466,9468,9471,9473,9476,9478,9480],{"class":5543,"line":5562},[5541,9464,9465],{"class":6257},"    std",[5541,9467,7181],{"class":6263},[5541,9469,9470],{"class":6272},"cout",[5541,9472,7751],{"class":6263},[5541,9474,9475],{"class":6441},"'",[5541,9477,7767],{"class":7766},[5541,9479,9475],{"class":6441},[5541,9481,6465],{"class":6263},[5541,9483,9484],{"class":5543,"line":5569},[5541,9485,5620],{"class":6263},[5541,9487,9488],{"class":5543,"line":5575},[5541,9489,5566],{"emptyLinePlaceholder":5565},[5541,9491,9492,9494,9496,9498,9501,9503,9505,9507,9509,9511],{"class":5543,"line":5581},[5541,9493,7260],{"class":6253},[5541,9495,6861],{"class":6257},[5541,9497,7181],{"class":6263},[5541,9499,9500],{"class":6325},"inOrderRecursive",[5541,9502,6328],{"class":6263},[5541,9504,6599],{"class":6257},[5541,9506,6288],{"class":6253},[5541,9508,6604],{"class":6272},[5541,9510,6658],{"class":6263},[5541,9512,8115],{"class":6253},[5541,9514,9515],{"class":5543,"line":5587},[5541,9516,6264],{"class":6263},[5541,9518,9519,9521,9523,9525,9527,9529],{"class":5543,"line":5593},[5541,9520,7286],{"class":6418},[5541,9522,5285],{"class":6263},[5541,9524,7291],{"class":6272},[5541,9526,7294],{"class":6263},[5541,9528,6358],{"class":6253},[5541,9530,6337],{"class":6263},[5541,9532,9533],{"class":5543,"line":5599},[5541,9534,6373],{"class":6263},[5541,9536,9537,9539,9541],{"class":5543,"line":5605},[5541,9538,7307],{"class":6418},[5541,9540,6276],{"class":6263},[5541,9542,9543],{"class":6279},"  \u002F\u002F Базовий випадок\n",[5541,9545,9546],{"class":5543,"line":5611},[5541,9547,6378],{"class":6263},[5541,9549,9550],{"class":5543,"line":5617},[5541,9551,6315],{"class":6263},[5541,9553,9554,9556,9558,9560,9562,9564,9566],{"class":5543,"line":5623},[5541,9555,9454],{"class":6325},[5541,9557,6328],{"class":6263},[5541,9559,7291],{"class":6272},[5541,9561,7336],{"class":6263},[5541,9563,5495],{"class":6272},[5541,9565,8311],{"class":6263},[5541,9567,9568],{"class":6279},"        \u002F\u002F 1. Обійти ліве піддерево\n",[5541,9570,9571,9573,9575,9577,9579,9581,9583,9585,9587,9590,9592],{"class":5543,"line":5628},[5541,9572,9465],{"class":6257},[5541,9574,7181],{"class":6263},[5541,9576,9470],{"class":6272},[5541,9578,7751],{"class":6263},[5541,9580,7291],{"class":6272},[5541,9582,7336],{"class":6263},[5541,9584,6345],{"class":6272},[5541,9586,7751],{"class":6263},[5541,9588,9589],{"class":6441},"\" \"",[5541,9591,6276],{"class":6263},[5541,9593,9594],{"class":6279},"      \u002F\u002F 2. Відвідати корінь\n",[5541,9596,9597,9599,9601,9603,9605,9607,9609],{"class":5543,"line":5634},[5541,9598,9454],{"class":6325},[5541,9600,6328],{"class":6263},[5541,9602,7291],{"class":6272},[5541,9604,7336],{"class":6263},[5541,9606,5499],{"class":6272},[5541,9608,8311],{"class":6263},[5541,9610,9611],{"class":6279},"       \u002F\u002F 3. Обійти праве піддерево\n",[5541,9613,9614],{"class":5543,"line":5640},[5541,9615,5620],{"class":6263},[5390,9617,9618],{},[5271,9619,9620,9621,6012],{},"Для дерева ",[5538,9622,9623],{},"[50, 30, 70, 20, 40, 60, 80]",[5531,9625,9628],{"className":9626,"code":9627,"language":6061},[6059],"In-Order: 20 30 40 50 60 70 80  ← Відсортовано!\n",[5538,9629,9627],{"__ignoreMap":5536},[5753,9631,9633],{"id":9632},"_2-pre-order-префіксний-обхід-корінь-ліве-праве","2. Pre-Order (префіксний обхід): корінь → ліве → праве",[5390,9635,9636,9639],{},[5271,9637,9638],{},"Використання:"," Копіювання дерева, серіалізація структури.",[5531,9641,9643],{"className":6244,"code":9642,"language":6246,"meta":5536,"style":5536},"void BinarySearchTree::preOrder() const\n{\n    preOrderRecursive(root);\n    std::cout \u003C\u003C '\\n';\n}\n\nvoid BinarySearchTree::preOrderRecursive(TreeNode* node) const\n{\n    if (node == nullptr)\n    {\n        return;\n    }\n    \n    std::cout \u003C\u003C node->data \u003C\u003C \" \";      \u002F\u002F 1. Відвідати корінь\n    preOrderRecursive(node->left);       \u002F\u002F 2. Обійти ліве піддерево\n    preOrderRecursive(node->right);      \u002F\u002F 3. Обійти праве піддерево\n}\n",[5538,9644,9645,9660,9664,9675,9693,9697,9701,9724,9728,9742,9746,9752,9756,9760,9785,9802,9819],{"__ignoreMap":5536},[5541,9646,9647,9649,9651,9653,9656,9658],{"class":5543,"line":5544},[5541,9648,7260],{"class":6253},[5541,9650,6861],{"class":6257},[5541,9652,7181],{"class":6263},[5541,9654,9655],{"class":6325},"preOrder",[5541,9657,7002],{"class":6263},[5541,9659,8115],{"class":6253},[5541,9661,9662],{"class":5543,"line":5550},[5541,9663,6264],{"class":6263},[5541,9665,9666,9669,9671,9673],{"class":5543,"line":5556},[5541,9667,9668],{"class":6325},"    preOrderRecursive",[5541,9670,6328],{"class":6263},[5541,9672,5351],{"class":6272},[5541,9674,6613],{"class":6263},[5541,9676,9677,9679,9681,9683,9685,9687,9689,9691],{"class":5543,"line":5562},[5541,9678,9465],{"class":6257},[5541,9680,7181],{"class":6263},[5541,9682,9470],{"class":6272},[5541,9684,7751],{"class":6263},[5541,9686,9475],{"class":6441},[5541,9688,7767],{"class":7766},[5541,9690,9475],{"class":6441},[5541,9692,6465],{"class":6263},[5541,9694,9695],{"class":5543,"line":5569},[5541,9696,5620],{"class":6263},[5541,9698,9699],{"class":5543,"line":5575},[5541,9700,5566],{"emptyLinePlaceholder":5565},[5541,9702,9703,9705,9707,9709,9712,9714,9716,9718,9720,9722],{"class":5543,"line":5581},[5541,9704,7260],{"class":6253},[5541,9706,6861],{"class":6257},[5541,9708,7181],{"class":6263},[5541,9710,9711],{"class":6325},"preOrderRecursive",[5541,9713,6328],{"class":6263},[5541,9715,6599],{"class":6257},[5541,9717,6288],{"class":6253},[5541,9719,6604],{"class":6272},[5541,9721,6658],{"class":6263},[5541,9723,8115],{"class":6253},[5541,9725,9726],{"class":5543,"line":5587},[5541,9727,6264],{"class":6263},[5541,9729,9730,9732,9734,9736,9738,9740],{"class":5543,"line":5593},[5541,9731,7286],{"class":6418},[5541,9733,5285],{"class":6263},[5541,9735,7291],{"class":6272},[5541,9737,7294],{"class":6263},[5541,9739,6358],{"class":6253},[5541,9741,6337],{"class":6263},[5541,9743,9744],{"class":5543,"line":5599},[5541,9745,6373],{"class":6263},[5541,9747,9748,9750],{"class":5543,"line":5605},[5541,9749,7307],{"class":6418},[5541,9751,6465],{"class":6263},[5541,9753,9754],{"class":5543,"line":5611},[5541,9755,6378],{"class":6263},[5541,9757,9758],{"class":5543,"line":5617},[5541,9759,6315],{"class":6263},[5541,9761,9762,9764,9766,9768,9770,9772,9774,9776,9778,9780,9782],{"class":5543,"line":5623},[5541,9763,9465],{"class":6257},[5541,9765,7181],{"class":6263},[5541,9767,9470],{"class":6272},[5541,9769,7751],{"class":6263},[5541,9771,7291],{"class":6272},[5541,9773,7336],{"class":6263},[5541,9775,6345],{"class":6272},[5541,9777,7751],{"class":6263},[5541,9779,9589],{"class":6441},[5541,9781,6276],{"class":6263},[5541,9783,9784],{"class":6279},"      \u002F\u002F 1. Відвідати корінь\n",[5541,9786,9787,9789,9791,9793,9795,9797,9799],{"class":5543,"line":5628},[5541,9788,9668],{"class":6325},[5541,9790,6328],{"class":6263},[5541,9792,7291],{"class":6272},[5541,9794,7336],{"class":6263},[5541,9796,5495],{"class":6272},[5541,9798,8311],{"class":6263},[5541,9800,9801],{"class":6279},"       \u002F\u002F 2. Обійти ліве піддерево\n",[5541,9803,9804,9806,9808,9810,9812,9814,9816],{"class":5543,"line":5634},[5541,9805,9668],{"class":6325},[5541,9807,6328],{"class":6263},[5541,9809,7291],{"class":6272},[5541,9811,7336],{"class":6263},[5541,9813,5499],{"class":6272},[5541,9815,8311],{"class":6263},[5541,9817,9818],{"class":6279},"      \u002F\u002F 3. Обійти праве піддерево\n",[5541,9820,9821],{"class":5543,"line":5640},[5541,9822,5620],{"class":6263},[5390,9824,9825],{},[5271,9826,9827],{},"Для того ж дерева:",[5531,9829,9832],{"className":9830,"code":9831,"language":6061},[6059],"Pre-Order: 50 30 20 40 70 60 80\n",[5538,9833,9831],{"__ignoreMap":5536},[5753,9835,9837],{"id":9836},"_3-post-order-постфіксний-обхід-ліве-праве-корінь","3. Post-Order (постфіксний обхід): ліве → праве → корінь",[5390,9839,9840,9842],{},[5271,9841,9638],{}," Видалення дерева (як у деструкторі), обчислення виразів у синтаксичних деревах.",[5531,9844,9846],{"className":6244,"code":9845,"language":6246,"meta":5536,"style":5536},"void BinarySearchTree::postOrder() const\n{\n    postOrderRecursive(root);\n    std::cout \u003C\u003C '\\n';\n}\n\nvoid BinarySearchTree::postOrderRecursive(TreeNode* node) const\n{\n    if (node == nullptr)\n    {\n        return;\n    }\n    \n    postOrderRecursive(node->left);       \u002F\u002F 1. Обійти ліве піддерево\n    postOrderRecursive(node->right);      \u002F\u002F 2. Обійти праве піддерево\n    std::cout \u003C\u003C node->data \u003C\u003C \" \";       \u002F\u002F 3. Відвідати корінь\n}\n",[5538,9847,9848,9863,9867,9878,9896,9900,9904,9927,9931,9945,9949,9955,9959,9963,9980,9997,10022],{"__ignoreMap":5536},[5541,9849,9850,9852,9854,9856,9859,9861],{"class":5543,"line":5544},[5541,9851,7260],{"class":6253},[5541,9853,6861],{"class":6257},[5541,9855,7181],{"class":6263},[5541,9857,9858],{"class":6325},"postOrder",[5541,9860,7002],{"class":6263},[5541,9862,8115],{"class":6253},[5541,9864,9865],{"class":5543,"line":5550},[5541,9866,6264],{"class":6263},[5541,9868,9869,9872,9874,9876],{"class":5543,"line":5556},[5541,9870,9871],{"class":6325},"    postOrderRecursive",[5541,9873,6328],{"class":6263},[5541,9875,5351],{"class":6272},[5541,9877,6613],{"class":6263},[5541,9879,9880,9882,9884,9886,9888,9890,9892,9894],{"class":5543,"line":5562},[5541,9881,9465],{"class":6257},[5541,9883,7181],{"class":6263},[5541,9885,9470],{"class":6272},[5541,9887,7751],{"class":6263},[5541,9889,9475],{"class":6441},[5541,9891,7767],{"class":7766},[5541,9893,9475],{"class":6441},[5541,9895,6465],{"class":6263},[5541,9897,9898],{"class":5543,"line":5569},[5541,9899,5620],{"class":6263},[5541,9901,9902],{"class":5543,"line":5575},[5541,9903,5566],{"emptyLinePlaceholder":5565},[5541,9905,9906,9908,9910,9912,9915,9917,9919,9921,9923,9925],{"class":5543,"line":5581},[5541,9907,7260],{"class":6253},[5541,9909,6861],{"class":6257},[5541,9911,7181],{"class":6263},[5541,9913,9914],{"class":6325},"postOrderRecursive",[5541,9916,6328],{"class":6263},[5541,9918,6599],{"class":6257},[5541,9920,6288],{"class":6253},[5541,9922,6604],{"class":6272},[5541,9924,6658],{"class":6263},[5541,9926,8115],{"class":6253},[5541,9928,9929],{"class":5543,"line":5587},[5541,9930,6264],{"class":6263},[5541,9932,9933,9935,9937,9939,9941,9943],{"class":5543,"line":5593},[5541,9934,7286],{"class":6418},[5541,9936,5285],{"class":6263},[5541,9938,7291],{"class":6272},[5541,9940,7294],{"class":6263},[5541,9942,6358],{"class":6253},[5541,9944,6337],{"class":6263},[5541,9946,9947],{"class":5543,"line":5599},[5541,9948,6373],{"class":6263},[5541,9950,9951,9953],{"class":5543,"line":5605},[5541,9952,7307],{"class":6418},[5541,9954,6465],{"class":6263},[5541,9956,9957],{"class":5543,"line":5611},[5541,9958,6378],{"class":6263},[5541,9960,9961],{"class":5543,"line":5617},[5541,9962,6315],{"class":6263},[5541,9964,9965,9967,9969,9971,9973,9975,9977],{"class":5543,"line":5623},[5541,9966,9871],{"class":6325},[5541,9968,6328],{"class":6263},[5541,9970,7291],{"class":6272},[5541,9972,7336],{"class":6263},[5541,9974,5495],{"class":6272},[5541,9976,8311],{"class":6263},[5541,9978,9979],{"class":6279},"       \u002F\u002F 1. Обійти ліве піддерево\n",[5541,9981,9982,9984,9986,9988,9990,9992,9994],{"class":5543,"line":5628},[5541,9983,9871],{"class":6325},[5541,9985,6328],{"class":6263},[5541,9987,7291],{"class":6272},[5541,9989,7336],{"class":6263},[5541,9991,5499],{"class":6272},[5541,9993,8311],{"class":6263},[5541,9995,9996],{"class":6279},"      \u002F\u002F 2. Обійти праве піддерево\n",[5541,9998,9999,10001,10003,10005,10007,10009,10011,10013,10015,10017,10019],{"class":5543,"line":5634},[5541,10000,9465],{"class":6257},[5541,10002,7181],{"class":6263},[5541,10004,9470],{"class":6272},[5541,10006,7751],{"class":6263},[5541,10008,7291],{"class":6272},[5541,10010,7336],{"class":6263},[5541,10012,6345],{"class":6272},[5541,10014,7751],{"class":6263},[5541,10016,9589],{"class":6441},[5541,10018,6276],{"class":6263},[5541,10020,10021],{"class":6279},"       \u002F\u002F 3. Відвідати корінь\n",[5541,10023,10024],{"class":5543,"line":5640},[5541,10025,5620],{"class":6263},[5390,10027,10028],{},[5271,10029,9827],{},[5531,10031,10034],{"className":10032,"code":10033,"language":6061},[6059],"Post-Order: 20 40 30 60 80 70 50\n",[5538,10035,10033],{"__ignoreMap":5536},[5527,10037,10039],{"alt":10038},"Порядок обходів дерева",[5531,10040,10042],{"className":5533,"code":10041,"language":5535,"meta":5536,"style":5536},"@startuml\nskinparam style plain\nskinparam backgroundColor #FFFFFF\n\ntitle Візуалізація трьох обходів\n\npackage \"Дерево\" #F1F5F9 {\n    circle \"50\" as root\n    circle \"30\" as left\n    circle \"70\" as right\n    circle \"20\" as ll\n    circle \"40\" as lr\n    circle \"60\" as rl\n    circle \"80\" as rr\n}\n\nroot -down-> left\nroot -down-> right\nleft -down-> ll\nleft -down-> lr\nright -down-> rl\nright -down-> rr\n\nnote right of root #DBEAFE\n  **In-Order** (ліве → корінь → праве):\n  20, 30, 40, **50**, 60, 70, 80\n  \n  **Pre-Order** (корінь → ліве → праве):\n  **50**, 30, 20, 40, 70, 60, 80\n  \n  **Post-Order** (ліве → праве → корінь):\n  20, 40, 30, 60, 80, 70, **50**\nend note\n\n@enduml\n",[5538,10043,10044,10048,10052,10056,10060,10065,10069,10074,10079,10084,10089,10094,10099,10104,10109,10113,10117,10122,10127,10132,10137,10142,10147,10151,10156,10161,10166,10171,10176,10181,10185,10190,10195,10199,10203],{"__ignoreMap":5536},[5541,10045,10046],{"class":5543,"line":5544},[5541,10047,5547],{},[5541,10049,10050],{"class":5543,"line":5550},[5541,10051,5553],{},[5541,10053,10054],{"class":5543,"line":5556},[5541,10055,5559],{},[5541,10057,10058],{"class":5543,"line":5562},[5541,10059,5566],{"emptyLinePlaceholder":5565},[5541,10061,10062],{"class":5543,"line":5569},[5541,10063,10064],{},"title Візуалізація трьох обходів\n",[5541,10066,10067],{"class":5543,"line":5575},[5541,10068,5566],{"emptyLinePlaceholder":5565},[5541,10070,10071],{"class":5543,"line":5581},[5541,10072,10073],{},"package \"Дерево\" #F1F5F9 {\n",[5541,10075,10076],{"class":5543,"line":5587},[5541,10077,10078],{},"    circle \"50\" as root\n",[5541,10080,10081],{"class":5543,"line":5593},[5541,10082,10083],{},"    circle \"30\" as left\n",[5541,10085,10086],{"class":5543,"line":5599},[5541,10087,10088],{},"    circle \"70\" as right\n",[5541,10090,10091],{"class":5543,"line":5605},[5541,10092,10093],{},"    circle \"20\" as ll\n",[5541,10095,10096],{"class":5543,"line":5611},[5541,10097,10098],{},"    circle \"40\" as lr\n",[5541,10100,10101],{"class":5543,"line":5617},[5541,10102,10103],{},"    circle \"60\" as rl\n",[5541,10105,10106],{"class":5543,"line":5623},[5541,10107,10108],{},"    circle \"80\" as rr\n",[5541,10110,10111],{"class":5543,"line":5628},[5541,10112,5620],{},[5541,10114,10115],{"class":5543,"line":5634},[5541,10116,5566],{"emptyLinePlaceholder":5565},[5541,10118,10119],{"class":5543,"line":5640},[5541,10120,10121],{},"root -down-> left\n",[5541,10123,10124],{"class":5543,"line":5646},[5541,10125,10126],{},"root -down-> right\n",[5541,10128,10129],{"class":5543,"line":5652},[5541,10130,10131],{},"left -down-> ll\n",[5541,10133,10134],{"class":5543,"line":5658},[5541,10135,10136],{},"left -down-> lr\n",[5541,10138,10139],{"class":5543,"line":5664},[5541,10140,10141],{},"right -down-> rl\n",[5541,10143,10144],{"class":5543,"line":5669},[5541,10145,10146],{},"right -down-> rr\n",[5541,10148,10149],{"class":5543,"line":5675},[5541,10150,5566],{"emptyLinePlaceholder":5565},[5541,10152,10153],{"class":5543,"line":5681},[5541,10154,10155],{},"note right of root #DBEAFE\n",[5541,10157,10158],{"class":5543,"line":5687},[5541,10159,10160],{},"  **In-Order** (ліве → корінь → праве):\n",[5541,10162,10163],{"class":5543,"line":5693},[5541,10164,10165],{},"  20, 30, 40, **50**, 60, 70, 80\n",[5541,10167,10168],{"class":5543,"line":5699},[5541,10169,10170],{},"  \n",[5541,10172,10173],{"class":5543,"line":5704},[5541,10174,10175],{},"  **Pre-Order** (корінь → ліве → праве):\n",[5541,10177,10178],{"class":5543,"line":5710},[5541,10179,10180],{},"  **50**, 30, 20, 40, 70, 60, 80\n",[5541,10182,10183],{"class":5543,"line":5716},[5541,10184,10170],{},[5541,10186,10187],{"class":5543,"line":5722},[5541,10188,10189],{},"  **Post-Order** (ліве → праве → корінь):\n",[5541,10191,10192],{"class":5543,"line":5727},[5541,10193,10194],{},"  20, 40, 30, 60, 80, 70, **50**\n",[5541,10196,10197],{"class":5543,"line":5732},[5541,10198,5696],{},[5541,10200,10201],{"class":5543,"line":6796},[5541,10202,5566],{"emptyLinePlaceholder":5565},[5541,10204,10205],{"class":5543,"line":6801},[5541,10206,5735],{},[5390,10208,10209,10211],{},[5271,10210,5423],{}," Всі обходи — O(n), оскільки відвідуємо кожен вузол рівно один раз.",[5382,10213],{},[5385,10215,10217],{"id":10216},"обчислення-висоти-дерева","Обчислення висоти дерева",[5390,10219,10220,5285,10223,10226],{},[5271,10221,10222],{},"Висота дерева",[5287,10224,10225],{},"height",") — найбільша відстань від кореня до листа. Порожнє дерево має висоту -1, дерево з одним вузлом — висоту 0.",[5531,10228,10230],{"className":6244,"code":10229,"language":6246,"meta":5536,"style":5536},"\u002F\u002F Публічний метод\nint BinarySearchTree::height() const\n{\n    return heightRecursive(root);\n}\n\n\u002F\u002F Приватний рекурсивний метод\nint BinarySearchTree::heightRecursive(TreeNode* node) const\n{\n    \u002F\u002F Базовий випадок: порожнє дерево\n    if (node == nullptr)\n    {\n        return -1;\n    }\n    \n    \u002F\u002F Рекурсивно обчислюємо висоту лівого та правого піддерев\n    int leftHeight = heightRecursive(node->left);\n    int rightHeight = heightRecursive(node->right);\n    \n    \u002F\u002F Висота поточного вузла = максимум висот дітей + 1\n    return std::max(leftHeight, rightHeight) + 1;\n}\n",[5538,10231,10232,10236,10250,10254,10266,10270,10274,10278,10301,10305,10310,10324,10328,10341,10345,10349,10354,10375,10396,10400,10405,10434],{"__ignoreMap":5536},[5541,10233,10234],{"class":5543,"line":5544},[5541,10235,8093],{"class":6279},[5541,10237,10238,10240,10242,10244,10246,10248],{"class":5543,"line":5550},[5541,10239,6331],{"class":6253},[5541,10241,6861],{"class":6257},[5541,10243,7181],{"class":6263},[5541,10245,10225],{"class":6325},[5541,10247,7002],{"class":6263},[5541,10249,8115],{"class":6253},[5541,10251,10252],{"class":5543,"line":5556},[5541,10253,6264],{"class":6263},[5541,10255,10256,10258,10260,10262,10264],{"class":5543,"line":5562},[5541,10257,7790],{"class":6418},[5541,10259,6779],{"class":6325},[5541,10261,6328],{"class":6263},[5541,10263,5351],{"class":6272},[5541,10265,6613],{"class":6263},[5541,10267,10268],{"class":5543,"line":5569},[5541,10269,5620],{"class":6263},[5541,10271,10272],{"class":5543,"line":5575},[5541,10273,5566],{"emptyLinePlaceholder":5565},[5541,10275,10276],{"class":5543,"line":5581},[5541,10277,7519],{"class":6279},[5541,10279,10280,10282,10284,10286,10289,10291,10293,10295,10297,10299],{"class":5543,"line":5587},[5541,10281,6331],{"class":6253},[5541,10283,6861],{"class":6257},[5541,10285,7181],{"class":6263},[5541,10287,10288],{"class":6325},"heightRecursive",[5541,10290,6328],{"class":6263},[5541,10292,6599],{"class":6257},[5541,10294,6288],{"class":6253},[5541,10296,6604],{"class":6272},[5541,10298,6658],{"class":6263},[5541,10300,8115],{"class":6253},[5541,10302,10303],{"class":5543,"line":5593},[5541,10304,6264],{"class":6263},[5541,10306,10307],{"class":5543,"line":5599},[5541,10308,10309],{"class":6279},"    \u002F\u002F Базовий випадок: порожнє дерево\n",[5541,10311,10312,10314,10316,10318,10320,10322],{"class":5543,"line":5605},[5541,10313,7286],{"class":6418},[5541,10315,5285],{"class":6263},[5541,10317,7291],{"class":6272},[5541,10319,7294],{"class":6263},[5541,10321,6358],{"class":6253},[5541,10323,6337],{"class":6263},[5541,10325,10326],{"class":5543,"line":5611},[5541,10327,6373],{"class":6263},[5541,10329,10330,10332,10335,10339],{"class":5543,"line":5617},[5541,10331,7307],{"class":6418},[5541,10333,10334],{"class":6263}," -",[5541,10336,10338],{"class":10337},"sJj4R","1",[5541,10340,6465],{"class":6263},[5541,10342,10343],{"class":5543,"line":5623},[5541,10344,6378],{"class":6263},[5541,10346,10347],{"class":5543,"line":5628},[5541,10348,6315],{"class":6263},[5541,10350,10351],{"class":5543,"line":5634},[5541,10352,10353],{"class":6279},"    \u002F\u002F Рекурсивно обчислюємо висоту лівого та правого піддерев\n",[5541,10355,10356,10358,10361,10363,10365,10367,10369,10371,10373],{"class":5543,"line":5640},[5541,10357,6269],{"class":6253},[5541,10359,10360],{"class":6272}," leftHeight",[5541,10362,7493],{"class":6263},[5541,10364,10288],{"class":6325},[5541,10366,6328],{"class":6263},[5541,10368,7291],{"class":6272},[5541,10370,7336],{"class":6263},[5541,10372,5495],{"class":6272},[5541,10374,6613],{"class":6263},[5541,10376,10377,10379,10382,10384,10386,10388,10390,10392,10394],{"class":5543,"line":5646},[5541,10378,6269],{"class":6253},[5541,10380,10381],{"class":6272}," rightHeight",[5541,10383,7493],{"class":6263},[5541,10385,10288],{"class":6325},[5541,10387,6328],{"class":6263},[5541,10389,7291],{"class":6272},[5541,10391,7336],{"class":6263},[5541,10393,5499],{"class":6272},[5541,10395,6613],{"class":6263},[5541,10397,10398],{"class":5543,"line":5652},[5541,10399,6315],{"class":6263},[5541,10401,10402],{"class":5543,"line":5658},[5541,10403,10404],{"class":6279},"    \u002F\u002F Висота поточного вузла = максимум висот дітей + 1\n",[5541,10406,10407,10409,10412,10414,10417,10419,10422,10424,10427,10430,10432],{"class":5543,"line":5664},[5541,10408,7790],{"class":6418},[5541,10410,10411],{"class":6257}," std",[5541,10413,7181],{"class":6263},[5541,10415,10416],{"class":6325},"max",[5541,10418,6328],{"class":6263},[5541,10420,10421],{"class":6272},"leftHeight",[5541,10423,5742],{"class":6263},[5541,10425,10426],{"class":6272},"rightHeight",[5541,10428,10429],{"class":6263},") + ",[5541,10431,10338],{"class":10337},[5541,10433,6465],{"class":6263},[5541,10435,10436],{"class":5543,"line":5669},[5541,10437,5620],{"class":6263},[5390,10439,10440,10444],{},[5271,10441,9620,10442,6012],{},[5538,10443,9623],{}," Висота = 2 (рівні: 0, 1, 2).",[5390,10446,10447,10449],{},[5271,10448,5423],{}," O(n) — потрібно відвідати всі вузли для обчислення максимальної глибини.",[5382,10451],{},[5385,10453,10455],{"id":10454},"практичне-використання-приклад-програми","Практичне використання: приклад програми",[5531,10457,10459],{"className":6244,"code":10458,"language":6246,"meta":5536,"style":5536},"#include \"BinarySearchTree.h\"\n#include \u003Ciostream>\n\nint main()\n{\n    BinarySearchTree bst;\n    \n    std::cout \u003C\u003C \"=== Демонстрація бінарного дерева пошуку ===\\n\\n\";\n    \n    \u002F\u002F Вставка елементів\n    std::cout \u003C\u003C \"Вставка елементів: 50, 30, 70, 20, 40, 60, 80\\n\";\n    bst.insert(50);\n    bst.insert(30);\n    bst.insert(70);\n    bst.insert(20);\n    bst.insert(40);\n    bst.insert(60);\n    bst.insert(80);\n    \n    \u002F\u002F Обходи дерева\n    std::cout \u003C\u003C \"\\nОбходи дерева:\\n\";\n    std::cout \u003C\u003C \"In-Order (відсортовано):   \";\n    bst.inOrder();   \u002F\u002F 20 30 40 50 60 70 80\n    \n    std::cout \u003C\u003C \"Pre-Order (корінь спершу): \";\n    bst.preOrder();  \u002F\u002F 50 30 20 40 70 60 80\n    \n    std::cout \u003C\u003C \"Post-Order (корінь останнім): \";\n    bst.postOrder(); \u002F\u002F 20 40 30 60 80 70 50\n    \n    \u002F\u002F Висота дерева\n    std::cout \u003C\u003C \"\\nВисота дерева: \" \u003C\u003C bst.height() \u003C\u003C '\\n';\n    \n    \u002F\u002F Пошук елементів\n    std::cout \u003C\u003C \"\\nПошук елемента 40: \" \n              \u003C\u003C (bst.search(40) ? \"знайдено ✓\" : \"не знайдено ✗\") \u003C\u003C '\\n';\n    std::cout \u003C\u003C \"Пошук елемента 99: \" \n              \u003C\u003C (bst.search(99) ? \"знайдено ✓\" : \"не знайдено ✗\") \u003C\u003C '\\n';\n    \n    \u002F\u002F Видалення елементів\n    std::cout \u003C\u003C \"\\nВидалення елемента 20 (лист)\\n\";\n    bst.remove(20);\n    std::cout \u003C\u003C \"In-Order після видалення: \";\n    bst.inOrder();   \u002F\u002F 30 40 50 60 70 80\n    \n    std::cout \u003C\u003C \"\\nВидалення елемента 30 (одна дитина)\\n\";\n    bst.remove(30);\n    std::cout \u003C\u003C \"In-Order після видалення: \";\n    bst.inOrder();   \u002F\u002F 40 50 60 70 80\n    \n    std::cout \u003C\u003C \"\\nВидалення елемента 50 (дві дитини, корінь)\\n\";\n    bst.remove(50);\n    std::cout \u003C\u003C \"In-Order після видалення: \";\n    bst.inOrder();   \u002F\u002F 40 60 70 80\n    \n    return 0;\n}\n",[5538,10460,10461,10467,10473,10477,10486,10490,10499,10503,10523,10527,10532,10551,10566,10580,10594,10608,10622,10636,10650,10654,10658,10681,10696,10710,10714,10729,10742,10746,10761,10774,10778,10783,10820,10824,10829,10849,10887,10902,10935,10939,10944,10967,10981,10996,11009,11013,11036,11050,11064,11077,11081,11104,11118,11132,11145,11149,11158],{"__ignoreMap":5536},[5541,10462,10463,10465],{"class":5543,"line":5544},[5541,10464,6438],{"class":6418},[5541,10466,7164],{"class":6441},[5541,10468,10469,10471],{"class":5543,"line":5550},[5541,10470,6438],{"class":6418},[5541,10472,6442],{"class":6441},[5541,10474,10475],{"class":5543,"line":5556},[5541,10476,5566],{"emptyLinePlaceholder":5565},[5541,10478,10479,10481,10484],{"class":5543,"line":5562},[5541,10480,6331],{"class":6253},[5541,10482,10483],{"class":6325}," main",[5541,10485,7186],{"class":6263},[5541,10487,10488],{"class":5543,"line":5569},[5541,10489,6264],{"class":6263},[5541,10491,10492,10494,10497],{"class":5543,"line":5575},[5541,10493,6816],{"class":6257},[5541,10495,10496],{"class":6272}," bst",[5541,10498,6465],{"class":6263},[5541,10500,10501],{"class":5543,"line":5581},[5541,10502,6315],{"class":6263},[5541,10504,10505,10507,10509,10511,10513,10516,10519,10521],{"class":5543,"line":5587},[5541,10506,9465],{"class":6257},[5541,10508,7181],{"class":6263},[5541,10510,9470],{"class":6272},[5541,10512,7751],{"class":6263},[5541,10514,10515],{"class":6441},"\"=== Демонстрація бінарного дерева пошуку ===",[5541,10517,10518],{"class":7766},"\\n\\n",[5541,10520,7770],{"class":6441},[5541,10522,6465],{"class":6263},[5541,10524,10525],{"class":5543,"line":5593},[5541,10526,6315],{"class":6263},[5541,10528,10529],{"class":5543,"line":5599},[5541,10530,10531],{"class":6279},"    \u002F\u002F Вставка елементів\n",[5541,10533,10534,10536,10538,10540,10542,10545,10547,10549],{"class":5543,"line":5605},[5541,10535,9465],{"class":6257},[5541,10537,7181],{"class":6263},[5541,10539,9470],{"class":6272},[5541,10541,7751],{"class":6263},[5541,10543,10544],{"class":6441},"\"Вставка елементів: 50, 30, 70, 20, 40, 60, 80",[5541,10546,7767],{"class":7766},[5541,10548,7770],{"class":6441},[5541,10550,6465],{"class":6263},[5541,10552,10553,10556,10558,10560,10562,10564],{"class":5543,"line":5611},[5541,10554,10555],{"class":6272},"    bst",[5541,10557,5514],{"class":6263},[5541,10559,5299],{"class":6325},[5541,10561,6328],{"class":6263},[5541,10563,5816],{"class":10337},[5541,10565,6613],{"class":6263},[5541,10567,10568,10570,10572,10574,10576,10578],{"class":5543,"line":5617},[5541,10569,10555],{"class":6272},[5541,10571,5514],{"class":6263},[5541,10573,5299],{"class":6325},[5541,10575,6328],{"class":6263},[5541,10577,5845],{"class":10337},[5541,10579,6613],{"class":6263},[5541,10581,10582,10584,10586,10588,10590,10592],{"class":5543,"line":5623},[5541,10583,10555],{"class":6272},[5541,10585,5514],{"class":6263},[5541,10587,5299],{"class":6325},[5541,10589,6328],{"class":6263},[5541,10591,5849],{"class":10337},[5541,10593,6613],{"class":6263},[5541,10595,10596,10598,10600,10602,10604,10606],{"class":5543,"line":5628},[5541,10597,10555],{"class":6272},[5541,10599,5514],{"class":6263},[5541,10601,5299],{"class":6325},[5541,10603,6328],{"class":6263},[5541,10605,5886],{"class":10337},[5541,10607,6613],{"class":6263},[5541,10609,10610,10612,10614,10616,10618,10620],{"class":5543,"line":5634},[5541,10611,10555],{"class":6272},[5541,10613,5514],{"class":6263},[5541,10615,5299],{"class":6325},[5541,10617,6328],{"class":6263},[5541,10619,5889],{"class":10337},[5541,10621,6613],{"class":6263},[5541,10623,10624,10626,10628,10630,10632,10634],{"class":5543,"line":5640},[5541,10625,10555],{"class":6272},[5541,10627,5514],{"class":6263},[5541,10629,5299],{"class":6325},[5541,10631,6328],{"class":6263},[5541,10633,5892],{"class":10337},[5541,10635,6613],{"class":6263},[5541,10637,10638,10640,10642,10644,10646,10648],{"class":5543,"line":5646},[5541,10639,10555],{"class":6272},[5541,10641,5514],{"class":6263},[5541,10643,5299],{"class":6325},[5541,10645,6328],{"class":6263},[5541,10647,5895],{"class":10337},[5541,10649,6613],{"class":6263},[5541,10651,10652],{"class":5543,"line":5652},[5541,10653,6315],{"class":6263},[5541,10655,10656],{"class":5543,"line":5658},[5541,10657,7042],{"class":6279},[5541,10659,10660,10662,10664,10666,10668,10670,10672,10675,10677,10679],{"class":5543,"line":5664},[5541,10661,9465],{"class":6257},[5541,10663,7181],{"class":6263},[5541,10665,9470],{"class":6272},[5541,10667,7751],{"class":6263},[5541,10669,7770],{"class":6441},[5541,10671,7767],{"class":7766},[5541,10673,10674],{"class":6441},"Обходи дерева:",[5541,10676,7767],{"class":7766},[5541,10678,7770],{"class":6441},[5541,10680,6465],{"class":6263},[5541,10682,10683,10685,10687,10689,10691,10694],{"class":5543,"line":5669},[5541,10684,9465],{"class":6257},[5541,10686,7181],{"class":6263},[5541,10688,9470],{"class":6272},[5541,10690,7751],{"class":6263},[5541,10692,10693],{"class":6441},"\"In-Order (відсортовано):   \"",[5541,10695,6465],{"class":6263},[5541,10697,10698,10700,10702,10704,10707],{"class":5543,"line":5675},[5541,10699,10555],{"class":6272},[5541,10701,5514],{"class":6263},[5541,10703,9441],{"class":6325},[5541,10705,10706],{"class":6263},"();",[5541,10708,10709],{"class":6279},"   \u002F\u002F 20 30 40 50 60 70 80\n",[5541,10711,10712],{"class":5543,"line":5681},[5541,10713,6315],{"class":6263},[5541,10715,10716,10718,10720,10722,10724,10727],{"class":5543,"line":5687},[5541,10717,9465],{"class":6257},[5541,10719,7181],{"class":6263},[5541,10721,9470],{"class":6272},[5541,10723,7751],{"class":6263},[5541,10725,10726],{"class":6441},"\"Pre-Order (корінь спершу): \"",[5541,10728,6465],{"class":6263},[5541,10730,10731,10733,10735,10737,10739],{"class":5543,"line":5693},[5541,10732,10555],{"class":6272},[5541,10734,5514],{"class":6263},[5541,10736,9655],{"class":6325},[5541,10738,10706],{"class":6263},[5541,10740,10741],{"class":6279},"  \u002F\u002F 50 30 20 40 70 60 80\n",[5541,10743,10744],{"class":5543,"line":5699},[5541,10745,6315],{"class":6263},[5541,10747,10748,10750,10752,10754,10756,10759],{"class":5543,"line":5704},[5541,10749,9465],{"class":6257},[5541,10751,7181],{"class":6263},[5541,10753,9470],{"class":6272},[5541,10755,7751],{"class":6263},[5541,10757,10758],{"class":6441},"\"Post-Order (корінь останнім): \"",[5541,10760,6465],{"class":6263},[5541,10762,10763,10765,10767,10769,10771],{"class":5543,"line":5710},[5541,10764,10555],{"class":6272},[5541,10766,5514],{"class":6263},[5541,10768,9858],{"class":6325},[5541,10770,10706],{"class":6263},[5541,10772,10773],{"class":6279}," \u002F\u002F 20 40 30 60 80 70 50\n",[5541,10775,10776],{"class":5543,"line":5716},[5541,10777,6315],{"class":6263},[5541,10779,10780],{"class":5543,"line":5722},[5541,10781,10782],{"class":6279},"    \u002F\u002F Висота дерева\n",[5541,10784,10785,10787,10789,10791,10793,10795,10797,10800,10802,10805,10807,10809,10812,10814,10816,10818],{"class":5543,"line":5727},[5541,10786,9465],{"class":6257},[5541,10788,7181],{"class":6263},[5541,10790,9470],{"class":6272},[5541,10792,7751],{"class":6263},[5541,10794,7770],{"class":6441},[5541,10796,7767],{"class":7766},[5541,10798,10799],{"class":6441},"Висота дерева: \"",[5541,10801,7751],{"class":6263},[5541,10803,10804],{"class":6272},"bst",[5541,10806,5514],{"class":6263},[5541,10808,10225],{"class":6325},[5541,10810,10811],{"class":6263},"() \u003C\u003C ",[5541,10813,9475],{"class":6441},[5541,10815,7767],{"class":7766},[5541,10817,9475],{"class":6441},[5541,10819,6465],{"class":6263},[5541,10821,10822],{"class":5543,"line":5732},[5541,10823,6315],{"class":6263},[5541,10825,10826],{"class":5543,"line":6796},[5541,10827,10828],{"class":6279},"    \u002F\u002F Пошук елементів\n",[5541,10830,10831,10833,10835,10837,10839,10841,10843,10846],{"class":5543,"line":6801},[5541,10832,9465],{"class":6257},[5541,10834,7181],{"class":6263},[5541,10836,9470],{"class":6272},[5541,10838,7751],{"class":6263},[5541,10840,7770],{"class":6441},[5541,10842,7767],{"class":7766},[5541,10844,10845],{"class":6441},"Пошук елемента 40: \"",[5541,10847,10848],{"class":6263}," \n",[5541,10850,10851,10854,10856,10858,10860,10862,10864,10867,10870,10873,10876,10879,10881,10883,10885],{"class":5543,"line":6807},[5541,10852,10853],{"class":6263},"              \u003C\u003C (",[5541,10855,10804],{"class":6272},[5541,10857,5514],{"class":6263},[5541,10859,5306],{"class":6325},[5541,10861,6328],{"class":6263},[5541,10863,5889],{"class":10337},[5541,10865,10866],{"class":6263},") ? ",[5541,10868,10869],{"class":6441},"\"знайдено ✓\"",[5541,10871,10872],{"class":6263}," : ",[5541,10874,10875],{"class":6441},"\"не знайдено ✗\"",[5541,10877,10878],{"class":6263},") \u003C\u003C ",[5541,10880,9475],{"class":6441},[5541,10882,7767],{"class":7766},[5541,10884,9475],{"class":6441},[5541,10886,6465],{"class":6263},[5541,10888,10889,10891,10893,10895,10897,10900],{"class":5543,"line":6813},[5541,10890,9465],{"class":6257},[5541,10892,7181],{"class":6263},[5541,10894,9470],{"class":6272},[5541,10896,7751],{"class":6263},[5541,10898,10899],{"class":6441},"\"Пошук елемента 99: \"",[5541,10901,10848],{"class":6263},[5541,10903,10904,10906,10908,10910,10912,10914,10917,10919,10921,10923,10925,10927,10929,10931,10933],{"class":5543,"line":6822},[5541,10905,10853],{"class":6263},[5541,10907,10804],{"class":6272},[5541,10909,5514],{"class":6263},[5541,10911,5306],{"class":6325},[5541,10913,6328],{"class":6263},[5541,10915,10916],{"class":10337},"99",[5541,10918,10866],{"class":6263},[5541,10920,10869],{"class":6441},[5541,10922,10872],{"class":6263},[5541,10924,10875],{"class":6441},[5541,10926,10878],{"class":6263},[5541,10928,9475],{"class":6441},[5541,10930,7767],{"class":7766},[5541,10932,9475],{"class":6441},[5541,10934,6465],{"class":6263},[5541,10936,10937],{"class":5543,"line":6827},[5541,10938,6315],{"class":6263},[5541,10940,10941],{"class":5543,"line":6833},[5541,10942,10943],{"class":6279},"    \u002F\u002F Видалення елементів\n",[5541,10945,10946,10948,10950,10952,10954,10956,10958,10961,10963,10965],{"class":5543,"line":6841},[5541,10947,9465],{"class":6257},[5541,10949,7181],{"class":6263},[5541,10951,9470],{"class":6272},[5541,10953,7751],{"class":6263},[5541,10955,7770],{"class":6441},[5541,10957,7767],{"class":7766},[5541,10959,10960],{"class":6441},"Видалення елемента 20 (лист)",[5541,10962,7767],{"class":7766},[5541,10964,7770],{"class":6441},[5541,10966,6465],{"class":6263},[5541,10968,10969,10971,10973,10975,10977,10979],{"class":5543,"line":6846},[5541,10970,10555],{"class":6272},[5541,10972,5514],{"class":6263},[5541,10974,8710],{"class":6325},[5541,10976,6328],{"class":6263},[5541,10978,5886],{"class":10337},[5541,10980,6613],{"class":6263},[5541,10982,10983,10985,10987,10989,10991,10994],{"class":5543,"line":6852},[5541,10984,9465],{"class":6257},[5541,10986,7181],{"class":6263},[5541,10988,9470],{"class":6272},[5541,10990,7751],{"class":6263},[5541,10992,10993],{"class":6441},"\"In-Order після видалення: \"",[5541,10995,6465],{"class":6263},[5541,10997,10998,11000,11002,11004,11006],{"class":5543,"line":6874},[5541,10999,10555],{"class":6272},[5541,11001,5514],{"class":6263},[5541,11003,9441],{"class":6325},[5541,11005,10706],{"class":6263},[5541,11007,11008],{"class":6279},"   \u002F\u002F 30 40 50 60 70 80\n",[5541,11010,11011],{"class":5543,"line":6898},[5541,11012,6315],{"class":6263},[5541,11014,11015,11017,11019,11021,11023,11025,11027,11030,11032,11034],{"class":5543,"line":6903},[5541,11016,9465],{"class":6257},[5541,11018,7181],{"class":6263},[5541,11020,9470],{"class":6272},[5541,11022,7751],{"class":6263},[5541,11024,7770],{"class":6441},[5541,11026,7767],{"class":7766},[5541,11028,11029],{"class":6441},"Видалення елемента 30 (одна дитина)",[5541,11031,7767],{"class":7766},[5541,11033,7770],{"class":6441},[5541,11035,6465],{"class":6263},[5541,11037,11038,11040,11042,11044,11046,11048],{"class":5543,"line":6909},[5541,11039,10555],{"class":6272},[5541,11041,5514],{"class":6263},[5541,11043,8710],{"class":6325},[5541,11045,6328],{"class":6263},[5541,11047,5845],{"class":10337},[5541,11049,6613],{"class":6263},[5541,11051,11052,11054,11056,11058,11060,11062],{"class":5543,"line":6925},[5541,11053,9465],{"class":6257},[5541,11055,7181],{"class":6263},[5541,11057,9470],{"class":6272},[5541,11059,7751],{"class":6263},[5541,11061,10993],{"class":6441},[5541,11063,6465],{"class":6263},[5541,11065,11066,11068,11070,11072,11074],{"class":5543,"line":6930},[5541,11067,10555],{"class":6272},[5541,11069,5514],{"class":6263},[5541,11071,9441],{"class":6325},[5541,11073,10706],{"class":6263},[5541,11075,11076],{"class":6279},"   \u002F\u002F 40 50 60 70 80\n",[5541,11078,11079],{"class":5543,"line":6936},[5541,11080,6315],{"class":6263},[5541,11082,11083,11085,11087,11089,11091,11093,11095,11098,11100,11102],{"class":5543,"line":6952},[5541,11084,9465],{"class":6257},[5541,11086,7181],{"class":6263},[5541,11088,9470],{"class":6272},[5541,11090,7751],{"class":6263},[5541,11092,7770],{"class":6441},[5541,11094,7767],{"class":7766},[5541,11096,11097],{"class":6441},"Видалення елемента 50 (дві дитини, корінь)",[5541,11099,7767],{"class":7766},[5541,11101,7770],{"class":6441},[5541,11103,6465],{"class":6263},[5541,11105,11106,11108,11110,11112,11114,11116],{"class":5543,"line":6957},[5541,11107,10555],{"class":6272},[5541,11109,5514],{"class":6263},[5541,11111,8710],{"class":6325},[5541,11113,6328],{"class":6263},[5541,11115,5816],{"class":10337},[5541,11117,6613],{"class":6263},[5541,11119,11120,11122,11124,11126,11128,11130],{"class":5543,"line":6963},[5541,11121,9465],{"class":6257},[5541,11123,7181],{"class":6263},[5541,11125,9470],{"class":6272},[5541,11127,7751],{"class":6263},[5541,11129,10993],{"class":6441},[5541,11131,6465],{"class":6263},[5541,11133,11134,11136,11138,11140,11142],{"class":5543,"line":6983},[5541,11135,10555],{"class":6272},[5541,11137,5514],{"class":6263},[5541,11139,9441],{"class":6325},[5541,11141,10706],{"class":6263},[5541,11143,11144],{"class":6279},"   \u002F\u002F 40 60 70 80\n",[5541,11146,11147],{"class":5543,"line":6988},[5541,11148,6315],{"class":6263},[5541,11150,11151,11153,11156],{"class":5543,"line":6994},[5541,11152,7790],{"class":6418},[5541,11154,11155],{"class":10337}," 0",[5541,11157,6465],{"class":6263},[5541,11159,11160],{"class":5543,"line":7009},[5541,11161,5620],{"class":6263},[11163,11164,11166,11180,11188,11191,11195,11198,11201,11210,11218,11227,11230,11238,11241,11249,11258,11261,11264,11272,11275,11278,11285,11288,11291],"terminal-preview",{"title":11165},"g++ -std=c++17 main.cpp BinarySearchTree.cpp -o bst && .\u002Fbst",[11167,11168,11170,6036,11175],"div",{"className":11169},[5543],[5541,11171,11174],{"className":11172},[11173],"opacity-40","$",[5271,11176,11179],{"className":11177},[11178],"font-bold",".\u002Fbst",[11167,11181,11183],{"className":11182},[5543],[5541,11184,11187],{"className":11185},[11186,11178],"text-blue-400","=== Демонстрація бінарного дерева пошуку ===",[11167,11189],{"className":11190},[5543],[11167,11192,11194],{"className":11193},[5543],"Вставка елементів: 50, 30, 70, 20, 40, 60, 80",[11167,11196],{"className":11197},[5543],[11167,11199,10674],{"className":11200},[5543],[11167,11202,11204,11205],{"className":11203},[5543],"In-Order (відсортовано):   ",[5541,11206,11209],{"className":11207},[11208],"text-green-400","20 30 40 50 60 70 80",[11167,11211,11213,11214],{"className":11212},[5543],"Pre-Order (корінь спершу): ",[5541,11215,11217],{"className":11216},[11186],"50 30 20 40 70 60 80",[11167,11219,11221,11222],{"className":11220},[5543],"Post-Order (корінь останнім): ",[5541,11223,11226],{"className":11224},[11225],"text-yellow-400","20 40 30 60 80 70 50",[11167,11228],{"className":11229},[5543],[11167,11231,11233,11234],{"className":11232},[5543],"Висота дерева: ",[5541,11235,11237],{"className":11236},[11186,11178],"2",[11167,11239],{"className":11240},[5543],[11167,11242,11244,11245],{"className":11243},[5543],"Пошук елемента 40: ",[5541,11246,11248],{"className":11247},[11208,11178],"знайдено ✓",[11167,11250,11252,11253],{"className":11251},[5543],"Пошук елемента 99: ",[5541,11254,11257],{"className":11255},[11256,11178],"text-rose-400","не знайдено ✗",[11167,11259],{"className":11260},[5543],[11167,11262,10960],{"className":11263},[5543],[11167,11265,11267,11268],{"className":11266},[5543],"In-Order після видалення: ",[5541,11269,11271],{"className":11270},[11208],"30 40 50 60 70 80",[11167,11273],{"className":11274},[5543],[11167,11276,11029],{"className":11277},[5543],[11167,11279,11267,11281],{"className":11280},[5543],[5541,11282,11284],{"className":11283},[11208],"40 50 60 70 80",[11167,11286],{"className":11287},[5543],[11167,11289,11097],{"className":11290},[5543],[11167,11292,11267,11294],{"className":11293},[5543],[5541,11295,11297],{"className":11296},[11208],"40 60 70 80",[5382,11299],{},[5385,11301,11303],{"id":11302},"проблема-виродження-та-шляхи-балансування","Проблема виродження та шляхи балансування",[5753,11305,11307],{"id":11306},"сценарій-виродження-відсортоване-вставлення","Сценарій виродження: відсортоване вставлення",[5390,11309,6202,11310,6206,11312,6012],{},[5271,11311,6205],{},[5271,11313,11314],{},"лінійний ланцюжок",[5531,11316,11318],{"className":6244,"code":11317,"language":6246,"meta":5536,"style":5536},"BinarySearchTree bst;\nbst.insert(10);\nbst.insert(20);\nbst.insert(30);\nbst.insert(40);\nbst.insert(50);\n",[5538,11319,11320,11328,11343,11357,11371,11385],{"__ignoreMap":5536},[5541,11321,11322,11324,11326],{"class":5543,"line":5544},[5541,11323,7178],{"class":6272},[5541,11325,10496],{"class":6272},[5541,11327,6465],{"class":6263},[5541,11329,11330,11332,11334,11336,11338,11341],{"class":5543,"line":5550},[5541,11331,10804],{"class":6272},[5541,11333,5514],{"class":6263},[5541,11335,5299],{"class":6325},[5541,11337,6328],{"class":6263},[5541,11339,11340],{"class":10337},"10",[5541,11342,6613],{"class":6263},[5541,11344,11345,11347,11349,11351,11353,11355],{"class":5543,"line":5556},[5541,11346,10804],{"class":6272},[5541,11348,5514],{"class":6263},[5541,11350,5299],{"class":6325},[5541,11352,6328],{"class":6263},[5541,11354,5886],{"class":10337},[5541,11356,6613],{"class":6263},[5541,11358,11359,11361,11363,11365,11367,11369],{"class":5543,"line":5562},[5541,11360,10804],{"class":6272},[5541,11362,5514],{"class":6263},[5541,11364,5299],{"class":6325},[5541,11366,6328],{"class":6263},[5541,11368,5845],{"class":10337},[5541,11370,6613],{"class":6263},[5541,11372,11373,11375,11377,11379,11381,11383],{"class":5543,"line":5569},[5541,11374,10804],{"class":6272},[5541,11376,5514],{"class":6263},[5541,11378,5299],{"class":6325},[5541,11380,6328],{"class":6263},[5541,11382,5889],{"class":10337},[5541,11384,6613],{"class":6263},[5541,11386,11387,11389,11391,11393,11395,11397],{"class":5543,"line":5575},[5541,11388,10804],{"class":6272},[5541,11390,5514],{"class":6263},[5541,11392,5299],{"class":6325},[5541,11394,6328],{"class":6263},[5541,11396,5816],{"class":10337},[5541,11398,6613],{"class":6263},[5390,11400,11401],{},[5271,11402,11403],{},"Результуюча структура:",[5531,11405,11407],{"className":11406,"code":6212,"language":6061},[6059],[5538,11408,6212],{"__ignoreMap":5536},[5390,11410,11411,11414],{},[5271,11412,11413],{},"Наслідки:"," Висота дерева = n - 1 = 4. Пошук елемента 50 потребує 5 кроків (O(n)), замість очікуваних ~log₂(5) ≈ 2 кроків.",[6124,11416,11418,11421,11439],{"title":11417},"Гірший випадок BST дорівнює однозв'язаному списку",[5390,11419,11420],{},"У виродженому дереві:",[5264,11422,11423,11429,11434],{},[5267,11424,11425,11428],{},[5271,11426,11427],{},"Пошук:"," O(n) замість O(log n)",[5267,11430,11431,11428],{},[5271,11432,11433],{},"Вставка:",[5267,11435,11436,11428],{},[5271,11437,11438],{},"Видалення:",[5390,11440,11441],{},"Всі переваги дерева зникають. Це критична вада базового BST.",[5753,11443,11445],{"id":11444},"рішення-самобалансувальні-дерева","Рішення: самобалансувальні дерева",[5390,11447,11448,11449,5742,11451,11453,11454,11457],{},"Промислові реалізації (",[5538,11450,5741],{},[5538,11452,5745],{},") використовують ",[5271,11455,11456],{},"самобалансувальні дерева",", що гарантують висоту O(log n) через автоматичне перебалансування після кожної вставки\u002Fвидалення.",[5390,11459,11460],{},[5271,11461,11462],{},"Основні типи:",[5405,11464,11465,11478,11488],{},[5267,11466,11467,11470,11471,5285,11474,11477],{},[5271,11468,11469],{},"AVL-дерево:"," Жорстко збалансоване — різниця висот лівого та правого піддерев не перевищує 1. Після кожної операції виконуються ",[5271,11472,11473],{},"ротації",[5287,11475,11476],{},"rotations",") для відновлення балансу.",[5267,11479,11480,11483,11484,5742,11486,5514],{},[5271,11481,11482],{},"Red-Black дерево:"," М'якше збалансоване — гарантує висоту ≤ 2·log₂(n). Кожен вузол має колір (червоний\u002Fчорний), балансування через зміну кольорів та ротації. Використовується у ",[5538,11485,5745],{},[5538,11487,5741],{},[5267,11489,11490,11493],{},[5271,11491,11492],{},"B-дерево:"," Узагальнення бінарного дерева — кожен вузол може мати багато дітей (не лише 2). Використовується у базах даних та файлових системах.",[5961,11495,11497,11500],{"title":11496},"Чому не реалізовувати балансування у цій лекції?",[5390,11498,11499],{},"AVL та Red-Black дерева — складні алгоритми, що потребують окремої лекції. Базове BST демонструє фундаментальні концепції дерев та рекурсії. Розуміння BST — передумова для вивчення збалансованих варіантів.",[5390,11501,11502,11503,11511],{},"У промисловому коді ",[5271,11504,11505,11506,11508,11509],{},"завжди використовуйте ",[5538,11507,5741],{}," \u002F ",[5538,11510,5745],{}," (стаття 93), які реалізують Red-Black дерева. Власне BST корисне лише для освітніх цілей або дуже специфічних сценаріїв з гарантовано випадковим порядком вставки.",[5382,11513],{},[5385,11515,11517],{"id":11516},"порівняння-bst-з-іншими-структурами","Порівняння BST з іншими структурами",[5256,11519,11520,11550,11578],{},[5259,11521,11524,11529,11537,11542],{"icon":11522,"title":11523},"i-lucide-grid-3x3","Масив (Array)",[5390,11525,11526],{},[5271,11527,11528],{},"Переваги:",[5264,11530,11531,11534],{},[5267,11532,11533],{},"Довільний доступ O(1)",[5267,11535,11536],{},"Локальність кешу",[5390,11538,11539],{},[5271,11540,11541],{},"Недоліки:",[5264,11543,11544,11547],{},[5267,11545,11546],{},"Вставка\u002Fвидалення O(n)",[5267,11548,11549],{},"Фіксована\u002Fреалокована ємність",[5259,11551,11554,11558,11566,11570],{"icon":11552,"title":11553},"i-lucide-arrow-right-circle","Однозв'язаний список (Linked List)",[5390,11555,11556],{},[5271,11557,11528],{},[5264,11559,11560,11563],{},[5267,11561,11562],{},"Вставка на початок O(1)",[5267,11564,11565],{},"Динамічний розмір",[5390,11567,11568],{},[5271,11569,11541],{},[5264,11571,11572,11575],{},[5267,11573,11574],{},"Пошук O(n)",[5267,11576,11577],{},"Немає довільного доступу",[5259,11579,11581,11585,11606,11610],{"icon":4606,"title":11580},"Бінарне дерево пошуку (BST)",[5390,11582,11583],{},[5271,11584,11528],{},[5264,11586,11587,11593,11598,11603],{},[5267,11588,11589,11590,11592],{},"Пошук ",[5271,11591,5316],{}," (збалансоване)",[5267,11594,11595,11596,11592],{},"Вставка ",[5271,11597,5316],{},[5267,11599,11600,11601,11592],{},"Видалення ",[5271,11602,5316],{},[5267,11604,11605],{},"In-order обхід дає відсортовану послідовність",[5390,11607,11608],{},[5271,11609,11541],{},[5264,11611,11612,11614,11617,11620],{},[5267,11613,11577],{},[5267,11615,11616],{},"Може вироджуватися до O(n) (без балансування)",[5267,11618,11619],{},"Більший overhead пам'яті (два покажчики на вузол)",[5267,11621,11622],{},"Складніше у реалізації",[5390,11624,11625,11628,11629,11632,11633,11636],{},[5271,11626,11627],{},"Висновок:"," BST оптимальне для ",[5271,11630,11631],{},"динамічних множин",", де переважають операції ",[5271,11634,11635],{},"пошуку, вставки, видалення"," над довільним доступом. Для статичних відсортованих даних краще масив + бінарний пошук. Для частих вставок на початок — список.",[5382,11638],{},[5385,11640,11642],{"id":11641},"резюме-від-лінійності-до-ієрархії","Резюме: від лінійності до ієрархії",[5390,11644,11645,11646,11648,11649,11651],{},"У цій лекції ми зробили фундаментальний стрибок від ",[5271,11647,5273],{}," (масиви, списки, стеки, черги) до ",[5271,11650,5277],{}," (дерева). Бінарне дерево пошуку демонструє потужність рекурсії та логарифмічну ефективність для упорядкованих даних.",[5390,11653,11654],{},[5271,11655,11656],{},"Ключові концепції:",[5264,11658,11659,11664,11670,11676,11682],{},[5267,11660,11661,11663],{},[5271,11662,6020],{}," Ліве піддерево \u003C корінь \u003C праве піддерево (рекурсивно).",[5267,11665,11666,11669],{},[5271,11667,11668],{},"Рекурсивна природа дерев:"," Більшість операцій природно виражаються через рекурсію.",[5267,11671,11672,11675],{},[5271,11673,11674],{},"Обходи:"," In-order (відсортовано), pre-order (корінь спершу), post-order (корінь останнім).",[5267,11677,11678,11681],{},[5271,11679,11680],{},"Логарифмічна складність:"," O(log n) для збалансованих дерев, O(n) для вироджених.",[5267,11683,11684,11687],{},[5271,11685,11686],{},"Видалення з двома дітьми:"," Найскладніший випадок — заміна на in-order наступника.",[5256,11689,11690,11711],{},[5259,11691,11694],{"icon":11692,"title":11693},"i-lucide-graduation-cap","🎓 Що ми опанували",[5264,11695,11696,11699,11702,11705,11708],{},[5267,11697,11698],{},"Спроєктували ієрархічну структуру даних з рекурсивними операціями.",[5267,11700,11701],{},"Реалізували BST з вставкою, пошуком, видаленням за O(log n).",[5267,11703,11704],{},"Вивчили три типи обходів дерева та їхнє застосування.",[5267,11706,11707],{},"Зрозуміли проблему виродження та необхідність балансування.",[5267,11709,11710],{},"Порівняли компроміси між масивами, списками та деревами.",[5259,11712,11714,11724,11730],{"icon":4765,"title":11713},"🚀 Наступні кроки",[5390,11715,11716,11719,11720,11723],{},[5271,11717,11718],{},"Стаття 92 — Хеш-таблиця:","\nВивчимо структуру даних з ",[5271,11721,11722],{},"O(1) пошуком"," у середньому — хеш-функції, колізії, метод ланцюжків.",[5390,11725,11726,11729],{},[5271,11727,11728],{},"Стаття 93 — Контейнери STL (std::vector, std::list, std::set, std::map):","\nПрофесійні реалізації всіх вивчених структур у стандартній бібліотеці C++.",[5390,11731,11732,11735,11736,5514],{},[5271,11733,11734],{},"Стаття 94 — Ітератори STL:","\nУніверсальний механізм обходу контейнерів, алгоритми ",[5538,11737,11738],{},"\u003Calgorithm>",[5382,11740],{},[5385,11742,11744],{"id":11743},"практичні-завдання","Практичні завдання",[11746,11747,11748,11789,12236,12280,12954,12997],"accordion",{},[11749,11750,11753,11763,11778,11783],"accordion-item",{"icon":11751,"label":11752},"i-lucide-clipboard-list","📋 Завдання 1: Валідація BST",[5390,11754,11755,11758,11759,11762],{},[5271,11756,11757],{},"Завдання:"," Напишіть метод ",[5538,11760,11761],{},"bool isValidBST()",", який перевіряє, чи дійсно дерево задовольняє BST-інваріант (не лише локально, а глобально).",[5390,11764,11765,11768,11769,7385,11772,11774,11775,5514],{},[5271,11766,11767],{},"Підказка:"," Використовуйте рекурсивний допоміжний метод з параметрами ",[5538,11770,11771],{},"min",[5538,11773,10416],{}," — кожен вузол має знаходитися у діапазоні ",[5538,11776,11777],{},"(min, max)",[5390,11779,11780],{},[5271,11781,11782],{},"Приклад невалідного дерева:",[5531,11784,11787],{"className":11785,"code":11786,"language":6061},[6059],"    50\n   \u002F  \\\n  30   70\n \u002F\n60  ← Помилка: 60 > 50, але знаходиться в лівому піддереві\n",[5538,11788,11786],{"__ignoreMap":5536},[11749,11790,11793,12069,12074],{"icon":11791,"label":11792},"i-lucide-check-circle","✅ Розв'язок завдання 1",[5531,11794,11796],{"className":6244,"code":11795,"language":6246,"meta":5536,"style":5536},"class BinarySearchTree\n{\nprivate:\n    bool isValidBSTRecursive(TreeNode* node, int min, int max) const\n    {\n        \u002F\u002F Базовий випадок: порожнє дерево валідне\n        if (node == nullptr)\n        {\n            return true;\n        }\n        \n        \u002F\u002F Перевірка поточного вузла: має бути у діапазоні (min, max)\n        if (node->data \u003C= min || node->data >= max)\n        {\n            return false;\n        }\n        \n        \u002F\u002F Рекурсивна перевірка піддерев з оновленими межами\n        return isValidBSTRecursive(node->left, min, node->data) &&\n               isValidBSTRecursive(node->right, node->data, max);\n    }\n\npublic:\n    bool isValidBST() const\n    {\n        \u002F\u002F Початкові межі: (-∞, +∞)\n        return isValidBSTRecursive(root, INT_MIN, INT_MAX);\n    }\n};\n",[5538,11797,11798,11804,11808,11812,11845,11849,11854,11868,11872,11880,11884,11888,11893,11926,11930,11938,11942,11946,11951,11980,12007,12011,12015,12019,12030,12034,12039,12061,12065],{"__ignoreMap":5536},[5541,11799,11800,11802],{"class":5543,"line":5544},[5541,11801,6550],{"class":6253},[5541,11803,6553],{"class":6257},[5541,11805,11806],{"class":5543,"line":5550},[5541,11807,6264],{"class":6263},[5541,11809,11810],{"class":5543,"line":5556},[5541,11811,6562],{"class":6253},[5541,11813,11814,11816,11819,11821,11823,11825,11827,11829,11831,11834,11836,11838,11841,11843],{"class":5543,"line":5562},[5541,11815,6668],{"class":6253},[5541,11817,11818],{"class":6325}," isValidBSTRecursive",[5541,11820,6328],{"class":6263},[5541,11822,6599],{"class":6257},[5541,11824,6288],{"class":6253},[5541,11826,6604],{"class":6272},[5541,11828,5742],{"class":6263},[5541,11830,6331],{"class":6253},[5541,11832,11833],{"class":6272}," min",[5541,11835,5742],{"class":6263},[5541,11837,6331],{"class":6253},[5541,11839,11840],{"class":6272}," max",[5541,11842,6658],{"class":6263},[5541,11844,8115],{"class":6253},[5541,11846,11847],{"class":5543,"line":5569},[5541,11848,6373],{"class":6263},[5541,11850,11851],{"class":5543,"line":5575},[5541,11852,11853],{"class":6279},"        \u002F\u002F Базовий випадок: порожнє дерево валідне\n",[5541,11855,11856,11858,11860,11862,11864,11866],{"class":5543,"line":5581},[5541,11857,8438],{"class":6418},[5541,11859,5285],{"class":6263},[5541,11861,7291],{"class":6272},[5541,11863,7294],{"class":6263},[5541,11865,6358],{"class":6253},[5541,11867,6337],{"class":6263},[5541,11869,11870],{"class":5543,"line":5587},[5541,11871,8457],{"class":6263},[5541,11873,11874,11876,11878],{"class":5543,"line":5593},[5541,11875,8462],{"class":6418},[5541,11877,8254],{"class":6253},[5541,11879,6465],{"class":6263},[5541,11881,11882],{"class":5543,"line":5599},[5541,11883,8474],{"class":6263},[5541,11885,11886],{"class":5543,"line":5605},[5541,11887,8954],{"class":6263},[5541,11889,11890],{"class":5543,"line":5611},[5541,11891,11892],{"class":6279},"        \u002F\u002F Перевірка поточного вузла: має бути у діапазоні (min, max)\n",[5541,11894,11895,11897,11899,11901,11903,11905,11908,11910,11913,11915,11917,11919,11922,11924],{"class":5543,"line":5617},[5541,11896,8438],{"class":6418},[5541,11898,5285],{"class":6263},[5541,11900,7291],{"class":6272},[5541,11902,7336],{"class":6263},[5541,11904,6345],{"class":6272},[5541,11906,11907],{"class":6263}," \u003C= ",[5541,11909,11771],{"class":6272},[5541,11911,11912],{"class":6263}," || ",[5541,11914,7291],{"class":6272},[5541,11916,7336],{"class":6263},[5541,11918,6345],{"class":6272},[5541,11920,11921],{"class":6263}," >= ",[5541,11923,10416],{"class":6272},[5541,11925,6337],{"class":6263},[5541,11927,11928],{"class":5543,"line":5623},[5541,11929,8457],{"class":6263},[5541,11931,11932,11934,11936],{"class":5543,"line":5628},[5541,11933,8462],{"class":6418},[5541,11935,8210],{"class":6253},[5541,11937,6465],{"class":6263},[5541,11939,11940],{"class":5543,"line":5634},[5541,11941,8474],{"class":6263},[5541,11943,11944],{"class":5543,"line":5640},[5541,11945,8954],{"class":6263},[5541,11947,11948],{"class":5543,"line":5646},[5541,11949,11950],{"class":6279},"        \u002F\u002F Рекурсивна перевірка піддерев з оновленими межами\n",[5541,11952,11953,11955,11957,11959,11961,11963,11965,11967,11969,11971,11973,11975,11977],{"class":5543,"line":5652},[5541,11954,7307],{"class":6418},[5541,11956,11818],{"class":6325},[5541,11958,6328],{"class":6263},[5541,11960,7291],{"class":6272},[5541,11962,7336],{"class":6263},[5541,11964,5495],{"class":6272},[5541,11966,5742],{"class":6263},[5541,11968,11771],{"class":6272},[5541,11970,5742],{"class":6263},[5541,11972,7291],{"class":6272},[5541,11974,7336],{"class":6263},[5541,11976,6345],{"class":6272},[5541,11978,11979],{"class":6263},") &&\n",[5541,11981,11982,11985,11987,11989,11991,11993,11995,11997,11999,12001,12003,12005],{"class":5543,"line":5658},[5541,11983,11984],{"class":6325},"               isValidBSTRecursive",[5541,11986,6328],{"class":6263},[5541,11988,7291],{"class":6272},[5541,11990,7336],{"class":6263},[5541,11992,5499],{"class":6272},[5541,11994,5742],{"class":6263},[5541,11996,7291],{"class":6272},[5541,11998,7336],{"class":6263},[5541,12000,6345],{"class":6272},[5541,12002,5742],{"class":6263},[5541,12004,10416],{"class":6272},[5541,12006,6613],{"class":6263},[5541,12008,12009],{"class":5543,"line":5664},[5541,12010,6378],{"class":6263},[5541,12012,12013],{"class":5543,"line":5669},[5541,12014,5566],{"emptyLinePlaceholder":5565},[5541,12016,12017],{"class":5543,"line":5675},[5541,12018,6804],{"class":6253},[5541,12020,12021,12023,12026,12028],{"class":5543,"line":5681},[5541,12022,6668],{"class":6253},[5541,12024,12025],{"class":6325}," isValidBST",[5541,12027,7002],{"class":6263},[5541,12029,8115],{"class":6253},[5541,12031,12032],{"class":5543,"line":5687},[5541,12033,6373],{"class":6263},[5541,12035,12036],{"class":5543,"line":5693},[5541,12037,12038],{"class":6279},"        \u002F\u002F Початкові межі: (-∞, +∞)\n",[5541,12040,12041,12043,12045,12047,12049,12051,12054,12056,12059],{"class":5543,"line":5699},[5541,12042,7307],{"class":6418},[5541,12044,11818],{"class":6325},[5541,12046,6328],{"class":6263},[5541,12048,5351],{"class":6272},[5541,12050,5742],{"class":6263},[5541,12052,12053],{"class":6272},"INT_MIN",[5541,12055,5742],{"class":6263},[5541,12057,12058],{"class":6272},"INT_MAX",[5541,12060,6613],{"class":6263},[5541,12062,12063],{"class":5543,"line":5704},[5541,12064,6378],{"class":6263},[5541,12066,12067],{"class":5543,"line":5710},[5541,12068,6383],{"class":6263},[5390,12070,12071],{},[5271,12072,12073],{},"Тестування:",[5531,12075,12077],{"className":6244,"code":12076,"language":6246,"meta":5536,"style":5536},"int main()\n{\n    BinarySearchTree bst;\n    bst.insert(50);\n    bst.insert(30);\n    bst.insert(70);\n    bst.insert(20);\n    bst.insert(40);\n    \n    std::cout \u003C\u003C \"Дерево валідне: \" \u003C\u003C std::boolalpha \u003C\u003C bst.isValidBST() \u003C\u003C '\\n';\n    \u002F\u002F Виведе: true\n    \n    return 0;\n}\n",[5538,12078,12079,12087,12091,12099,12113,12127,12141,12155,12169,12173,12215,12220,12224,12232],{"__ignoreMap":5536},[5541,12080,12081,12083,12085],{"class":5543,"line":5544},[5541,12082,6331],{"class":6253},[5541,12084,10483],{"class":6325},[5541,12086,7186],{"class":6263},[5541,12088,12089],{"class":5543,"line":5550},[5541,12090,6264],{"class":6263},[5541,12092,12093,12095,12097],{"class":5543,"line":5556},[5541,12094,6816],{"class":6257},[5541,12096,10496],{"class":6272},[5541,12098,6465],{"class":6263},[5541,12100,12101,12103,12105,12107,12109,12111],{"class":5543,"line":5562},[5541,12102,10555],{"class":6272},[5541,12104,5514],{"class":6263},[5541,12106,5299],{"class":6325},[5541,12108,6328],{"class":6263},[5541,12110,5816],{"class":10337},[5541,12112,6613],{"class":6263},[5541,12114,12115,12117,12119,12121,12123,12125],{"class":5543,"line":5569},[5541,12116,10555],{"class":6272},[5541,12118,5514],{"class":6263},[5541,12120,5299],{"class":6325},[5541,12122,6328],{"class":6263},[5541,12124,5845],{"class":10337},[5541,12126,6613],{"class":6263},[5541,12128,12129,12131,12133,12135,12137,12139],{"class":5543,"line":5575},[5541,12130,10555],{"class":6272},[5541,12132,5514],{"class":6263},[5541,12134,5299],{"class":6325},[5541,12136,6328],{"class":6263},[5541,12138,5849],{"class":10337},[5541,12140,6613],{"class":6263},[5541,12142,12143,12145,12147,12149,12151,12153],{"class":5543,"line":5581},[5541,12144,10555],{"class":6272},[5541,12146,5514],{"class":6263},[5541,12148,5299],{"class":6325},[5541,12150,6328],{"class":6263},[5541,12152,5886],{"class":10337},[5541,12154,6613],{"class":6263},[5541,12156,12157,12159,12161,12163,12165,12167],{"class":5543,"line":5587},[5541,12158,10555],{"class":6272},[5541,12160,5514],{"class":6263},[5541,12162,5299],{"class":6325},[5541,12164,6328],{"class":6263},[5541,12166,5889],{"class":10337},[5541,12168,6613],{"class":6263},[5541,12170,12171],{"class":5543,"line":5593},[5541,12172,6315],{"class":6263},[5541,12174,12175,12177,12179,12181,12183,12186,12188,12191,12193,12196,12198,12200,12202,12205,12207,12209,12211,12213],{"class":5543,"line":5599},[5541,12176,9465],{"class":6257},[5541,12178,7181],{"class":6263},[5541,12180,9470],{"class":6272},[5541,12182,7751],{"class":6263},[5541,12184,12185],{"class":6441},"\"Дерево валідне: \"",[5541,12187,7751],{"class":6263},[5541,12189,12190],{"class":6257},"std",[5541,12192,7181],{"class":6263},[5541,12194,12195],{"class":6272},"boolalpha",[5541,12197,7751],{"class":6263},[5541,12199,10804],{"class":6272},[5541,12201,5514],{"class":6263},[5541,12203,12204],{"class":6325},"isValidBST",[5541,12206,10811],{"class":6263},[5541,12208,9475],{"class":6441},[5541,12210,7767],{"class":7766},[5541,12212,9475],{"class":6441},[5541,12214,6465],{"class":6263},[5541,12216,12217],{"class":5543,"line":5605},[5541,12218,12219],{"class":6279},"    \u002F\u002F Виведе: true\n",[5541,12221,12222],{"class":5543,"line":5611},[5541,12223,6315],{"class":6263},[5541,12225,12226,12228,12230],{"class":5543,"line":5617},[5541,12227,7790],{"class":6418},[5541,12229,11155],{"class":10337},[5541,12231,6465],{"class":6263},[5541,12233,12234],{"class":5543,"line":5623},[5541,12235,5620],{"class":6263},[11749,12237,12239,12247,12252,12260],{"icon":11751,"label":12238},"📋 Завдання 2: Знаходження k-го найменшого елемента",[5390,12240,12241,11758,12243,12246],{},[5271,12242,11757],{},[5538,12244,12245],{},"int kthSmallest(int k)",", який повертає k-й найменший елемент у BST (1-indexed: k=1 — найменший).",[5390,12248,12249,12251],{},[5271,12250,11767],{}," In-order обхід дає елементи у відсортованому порядку. Використовуйте лічильник та зупиняйтесь на k-му елементі.",[5390,12253,12254,12257,12258,6012],{},[5271,12255,12256],{},"Приклад:"," Для дерева ",[5538,12259,9623],{},[5264,12261,12262,12268,12274],{},[5267,12263,12264,12267],{},[5538,12265,12266],{},"kthSmallest(1)"," → 20",[5267,12269,12270,12273],{},[5538,12271,12272],{},"kthSmallest(4)"," → 50",[5267,12275,12276,12279],{},[5538,12277,12278],{},"kthSmallest(7)"," → 80",[11749,12281,12283,12666,12670,12930],{"icon":11791,"label":12282},"✅ Розв'язок завдання 2",[5531,12284,12286],{"className":6244,"code":12285,"language":6246,"meta":5536,"style":5536},"class BinarySearchTree\n{\nprivate:\n    void kthSmallestRecursive(TreeNode* node, int k, int& count, int& result) const\n    {\n        if (node == nullptr || count >= k)\n        {\n            return;  \u002F\u002F Базовий випадок або вже знайшли\n        }\n        \n        \u002F\u002F In-order обхід: ліве → корінь → праве\n        kthSmallestRecursive(node->left, k, count, result);\n        \n        \u002F\u002F Відвідуємо поточний вузол\n        ++count;\n        if (count == k)\n        {\n            result = node->data;\n            return;  \u002F\u002F Знайшли k-й елемент\n        }\n        \n        kthSmallestRecursive(node->right, k, count, result);\n    }\n\npublic:\n    int kthSmallest(int k) const\n    {\n        int count = 0;\n        int result = -1;\n        kthSmallestRecursive(root, k, count, result);\n        \n        if (count \u003C k)\n        {\n            throw std::out_of_range(\"k перевищує кількість елементів у дереві\");\n        }\n        \n        return result;\n    }\n};\n",[5538,12287,12288,12294,12298,12302,12343,12347,12371,12375,12384,12388,12392,12397,12425,12429,12434,12443,12457,12461,12476,12485,12489,12493,12519,12523,12527,12531,12548,12552,12566,12579,12601,12605,12619,12623,12642,12646,12650,12658,12662],{"__ignoreMap":5536},[5541,12289,12290,12292],{"class":5543,"line":5544},[5541,12291,6550],{"class":6253},[5541,12293,6553],{"class":6257},[5541,12295,12296],{"class":5543,"line":5550},[5541,12297,6264],{"class":6263},[5541,12299,12300],{"class":5543,"line":5556},[5541,12301,6562],{"class":6253},[5541,12303,12304,12306,12309,12311,12313,12315,12317,12319,12321,12324,12326,12329,12332,12334,12336,12339,12341],{"class":5543,"line":5562},[5541,12305,6696],{"class":6253},[5541,12307,12308],{"class":6325}," kthSmallestRecursive",[5541,12310,6328],{"class":6263},[5541,12312,6599],{"class":6257},[5541,12314,6288],{"class":6253},[5541,12316,6604],{"class":6272},[5541,12318,5742],{"class":6263},[5541,12320,6331],{"class":6253},[5541,12322,12323],{"class":6272}," k",[5541,12325,5742],{"class":6263},[5541,12327,12328],{"class":6253},"int&",[5541,12330,12331],{"class":6272}," count",[5541,12333,5742],{"class":6263},[5541,12335,12328],{"class":6253},[5541,12337,12338],{"class":6272}," result",[5541,12340,6658],{"class":6263},[5541,12342,8115],{"class":6253},[5541,12344,12345],{"class":5543,"line":5569},[5541,12346,6373],{"class":6263},[5541,12348,12349,12351,12353,12355,12357,12359,12361,12364,12366,12369],{"class":5543,"line":5575},[5541,12350,8438],{"class":6418},[5541,12352,5285],{"class":6263},[5541,12354,7291],{"class":6272},[5541,12356,7294],{"class":6263},[5541,12358,6358],{"class":6253},[5541,12360,11912],{"class":6263},[5541,12362,12363],{"class":6272},"count",[5541,12365,11921],{"class":6263},[5541,12367,12368],{"class":6272},"k",[5541,12370,6337],{"class":6263},[5541,12372,12373],{"class":5543,"line":5581},[5541,12374,8457],{"class":6263},[5541,12376,12377,12379,12381],{"class":5543,"line":5587},[5541,12378,8462],{"class":6418},[5541,12380,6276],{"class":6263},[5541,12382,12383],{"class":6279},"  \u002F\u002F Базовий випадок або вже знайшли\n",[5541,12385,12386],{"class":5543,"line":5593},[5541,12387,8474],{"class":6263},[5541,12389,12390],{"class":5543,"line":5599},[5541,12391,8954],{"class":6263},[5541,12393,12394],{"class":5543,"line":5605},[5541,12395,12396],{"class":6279},"        \u002F\u002F In-order обхід: ліве → корінь → праве\n",[5541,12398,12399,12402,12404,12406,12408,12410,12412,12414,12416,12418,12420,12423],{"class":5543,"line":5611},[5541,12400,12401],{"class":6325},"        kthSmallestRecursive",[5541,12403,6328],{"class":6263},[5541,12405,7291],{"class":6272},[5541,12407,7336],{"class":6263},[5541,12409,5495],{"class":6272},[5541,12411,5742],{"class":6263},[5541,12413,12368],{"class":6272},[5541,12415,5742],{"class":6263},[5541,12417,12363],{"class":6272},[5541,12419,5742],{"class":6263},[5541,12421,12422],{"class":6272},"result",[5541,12424,6613],{"class":6263},[5541,12426,12427],{"class":5543,"line":5617},[5541,12428,8954],{"class":6263},[5541,12430,12431],{"class":5543,"line":5623},[5541,12432,12433],{"class":6279},"        \u002F\u002F Відвідуємо поточний вузол\n",[5541,12435,12436,12439,12441],{"class":5543,"line":5628},[5541,12437,12438],{"class":6263},"        ++",[5541,12440,12363],{"class":6272},[5541,12442,6465],{"class":6263},[5541,12444,12445,12447,12449,12451,12453,12455],{"class":5543,"line":5634},[5541,12446,8438],{"class":6418},[5541,12448,5285],{"class":6263},[5541,12450,12363],{"class":6272},[5541,12452,7294],{"class":6263},[5541,12454,12368],{"class":6272},[5541,12456,6337],{"class":6263},[5541,12458,12459],{"class":5543,"line":5640},[5541,12460,8457],{"class":6263},[5541,12462,12463,12466,12468,12470,12472,12474],{"class":5543,"line":5646},[5541,12464,12465],{"class":6272},"            result",[5541,12467,7493],{"class":6263},[5541,12469,7291],{"class":6272},[5541,12471,7336],{"class":6263},[5541,12473,6345],{"class":6272},[5541,12475,6465],{"class":6263},[5541,12477,12478,12480,12482],{"class":5543,"line":5652},[5541,12479,8462],{"class":6418},[5541,12481,6276],{"class":6263},[5541,12483,12484],{"class":6279},"  \u002F\u002F Знайшли k-й елемент\n",[5541,12486,12487],{"class":5543,"line":5658},[5541,12488,8474],{"class":6263},[5541,12490,12491],{"class":5543,"line":5664},[5541,12492,8954],{"class":6263},[5541,12494,12495,12497,12499,12501,12503,12505,12507,12509,12511,12513,12515,12517],{"class":5543,"line":5669},[5541,12496,12401],{"class":6325},[5541,12498,6328],{"class":6263},[5541,12500,7291],{"class":6272},[5541,12502,7336],{"class":6263},[5541,12504,5499],{"class":6272},[5541,12506,5742],{"class":6263},[5541,12508,12368],{"class":6272},[5541,12510,5742],{"class":6263},[5541,12512,12363],{"class":6272},[5541,12514,5742],{"class":6263},[5541,12516,12422],{"class":6272},[5541,12518,6613],{"class":6263},[5541,12520,12521],{"class":5543,"line":5675},[5541,12522,6378],{"class":6263},[5541,12524,12525],{"class":5543,"line":5681},[5541,12526,5566],{"emptyLinePlaceholder":5565},[5541,12528,12529],{"class":5543,"line":5687},[5541,12530,6804],{"class":6253},[5541,12532,12533,12535,12538,12540,12542,12544,12546],{"class":5543,"line":5693},[5541,12534,6269],{"class":6253},[5541,12536,12537],{"class":6325}," kthSmallest",[5541,12539,6328],{"class":6263},[5541,12541,6331],{"class":6253},[5541,12543,12323],{"class":6272},[5541,12545,6658],{"class":6263},[5541,12547,8115],{"class":6253},[5541,12549,12550],{"class":5543,"line":5699},[5541,12551,6373],{"class":6263},[5541,12553,12554,12557,12559,12561,12564],{"class":5543,"line":5704},[5541,12555,12556],{"class":6253},"        int",[5541,12558,12331],{"class":6272},[5541,12560,7493],{"class":6263},[5541,12562,12563],{"class":10337},"0",[5541,12565,6465],{"class":6263},[5541,12567,12568,12570,12572,12575,12577],{"class":5543,"line":5710},[5541,12569,12556],{"class":6253},[5541,12571,12338],{"class":6272},[5541,12573,12574],{"class":6263}," = -",[5541,12576,10338],{"class":10337},[5541,12578,6465],{"class":6263},[5541,12580,12581,12583,12585,12587,12589,12591,12593,12595,12597,12599],{"class":5543,"line":5716},[5541,12582,12401],{"class":6325},[5541,12584,6328],{"class":6263},[5541,12586,5351],{"class":6272},[5541,12588,5742],{"class":6263},[5541,12590,12368],{"class":6272},[5541,12592,5742],{"class":6263},[5541,12594,12363],{"class":6272},[5541,12596,5742],{"class":6263},[5541,12598,12422],{"class":6272},[5541,12600,6613],{"class":6263},[5541,12602,12603],{"class":5543,"line":5722},[5541,12604,8954],{"class":6263},[5541,12606,12607,12609,12611,12613,12615,12617],{"class":5543,"line":5727},[5541,12608,8438],{"class":6418},[5541,12610,5285],{"class":6263},[5541,12612,12363],{"class":6272},[5541,12614,7614],{"class":6263},[5541,12616,12368],{"class":6272},[5541,12618,6337],{"class":6263},[5541,12620,12621],{"class":5543,"line":5732},[5541,12622,8457],{"class":6263},[5541,12624,12625,12628,12630,12632,12635,12637,12640],{"class":5543,"line":6796},[5541,12626,12627],{"class":6418},"            throw",[5541,12629,10411],{"class":6257},[5541,12631,7181],{"class":6263},[5541,12633,12634],{"class":6325},"out_of_range",[5541,12636,6328],{"class":6263},[5541,12638,12639],{"class":6441},"\"k перевищує кількість елементів у дереві\"",[5541,12641,6613],{"class":6263},[5541,12643,12644],{"class":5543,"line":6801},[5541,12645,8474],{"class":6263},[5541,12647,12648],{"class":5543,"line":6807},[5541,12649,8954],{"class":6263},[5541,12651,12652,12654,12656],{"class":5543,"line":6813},[5541,12653,7307],{"class":6418},[5541,12655,12338],{"class":6272},[5541,12657,6465],{"class":6263},[5541,12659,12660],{"class":5543,"line":6822},[5541,12661,6378],{"class":6263},[5541,12663,12664],{"class":5543,"line":6827},[5541,12665,6383],{"class":6263},[5390,12667,12668],{},[5271,12669,12073],{},[5531,12671,12673],{"className":6244,"code":12672,"language":6246,"meta":5536,"style":5536},"int main()\n{\n    BinarySearchTree bst;\n    bst.insert(50);\n    bst.insert(30);\n    bst.insert(70);\n    bst.insert(20);\n    bst.insert(40);\n    bst.insert(60);\n    bst.insert(80);\n    \n    std::cout \u003C\u003C \"1-й найменший: \" \u003C\u003C bst.kthSmallest(1) \u003C\u003C '\\n';  \u002F\u002F 20\n    std::cout \u003C\u003C \"4-й найменший: \" \u003C\u003C bst.kthSmallest(4) \u003C\u003C '\\n';  \u002F\u002F 50\n    std::cout \u003C\u003C \"7-й найменший: \" \u003C\u003C bst.kthSmallest(7) \u003C\u003C '\\n';  \u002F\u002F 80\n    \n    return 0;\n}\n",[5538,12674,12675,12683,12687,12695,12709,12723,12737,12751,12765,12779,12793,12797,12836,12875,12914,12918,12926],{"__ignoreMap":5536},[5541,12676,12677,12679,12681],{"class":5543,"line":5544},[5541,12678,6331],{"class":6253},[5541,12680,10483],{"class":6325},[5541,12682,7186],{"class":6263},[5541,12684,12685],{"class":5543,"line":5550},[5541,12686,6264],{"class":6263},[5541,12688,12689,12691,12693],{"class":5543,"line":5556},[5541,12690,6816],{"class":6257},[5541,12692,10496],{"class":6272},[5541,12694,6465],{"class":6263},[5541,12696,12697,12699,12701,12703,12705,12707],{"class":5543,"line":5562},[5541,12698,10555],{"class":6272},[5541,12700,5514],{"class":6263},[5541,12702,5299],{"class":6325},[5541,12704,6328],{"class":6263},[5541,12706,5816],{"class":10337},[5541,12708,6613],{"class":6263},[5541,12710,12711,12713,12715,12717,12719,12721],{"class":5543,"line":5569},[5541,12712,10555],{"class":6272},[5541,12714,5514],{"class":6263},[5541,12716,5299],{"class":6325},[5541,12718,6328],{"class":6263},[5541,12720,5845],{"class":10337},[5541,12722,6613],{"class":6263},[5541,12724,12725,12727,12729,12731,12733,12735],{"class":5543,"line":5575},[5541,12726,10555],{"class":6272},[5541,12728,5514],{"class":6263},[5541,12730,5299],{"class":6325},[5541,12732,6328],{"class":6263},[5541,12734,5849],{"class":10337},[5541,12736,6613],{"class":6263},[5541,12738,12739,12741,12743,12745,12747,12749],{"class":5543,"line":5581},[5541,12740,10555],{"class":6272},[5541,12742,5514],{"class":6263},[5541,12744,5299],{"class":6325},[5541,12746,6328],{"class":6263},[5541,12748,5886],{"class":10337},[5541,12750,6613],{"class":6263},[5541,12752,12753,12755,12757,12759,12761,12763],{"class":5543,"line":5587},[5541,12754,10555],{"class":6272},[5541,12756,5514],{"class":6263},[5541,12758,5299],{"class":6325},[5541,12760,6328],{"class":6263},[5541,12762,5889],{"class":10337},[5541,12764,6613],{"class":6263},[5541,12766,12767,12769,12771,12773,12775,12777],{"class":5543,"line":5593},[5541,12768,10555],{"class":6272},[5541,12770,5514],{"class":6263},[5541,12772,5299],{"class":6325},[5541,12774,6328],{"class":6263},[5541,12776,5892],{"class":10337},[5541,12778,6613],{"class":6263},[5541,12780,12781,12783,12785,12787,12789,12791],{"class":5543,"line":5599},[5541,12782,10555],{"class":6272},[5541,12784,5514],{"class":6263},[5541,12786,5299],{"class":6325},[5541,12788,6328],{"class":6263},[5541,12790,5895],{"class":10337},[5541,12792,6613],{"class":6263},[5541,12794,12795],{"class":5543,"line":5605},[5541,12796,6315],{"class":6263},[5541,12798,12799,12801,12803,12805,12807,12810,12812,12814,12816,12819,12821,12823,12825,12827,12829,12831,12833],{"class":5543,"line":5611},[5541,12800,9465],{"class":6257},[5541,12802,7181],{"class":6263},[5541,12804,9470],{"class":6272},[5541,12806,7751],{"class":6263},[5541,12808,12809],{"class":6441},"\"1-й найменший: \"",[5541,12811,7751],{"class":6263},[5541,12813,10804],{"class":6272},[5541,12815,5514],{"class":6263},[5541,12817,12818],{"class":6325},"kthSmallest",[5541,12820,6328],{"class":6263},[5541,12822,10338],{"class":10337},[5541,12824,10878],{"class":6263},[5541,12826,9475],{"class":6441},[5541,12828,7767],{"class":7766},[5541,12830,9475],{"class":6441},[5541,12832,6276],{"class":6263},[5541,12834,12835],{"class":6279},"  \u002F\u002F 20\n",[5541,12837,12838,12840,12842,12844,12846,12849,12851,12853,12855,12857,12859,12862,12864,12866,12868,12870,12872],{"class":5543,"line":5617},[5541,12839,9465],{"class":6257},[5541,12841,7181],{"class":6263},[5541,12843,9470],{"class":6272},[5541,12845,7751],{"class":6263},[5541,12847,12848],{"class":6441},"\"4-й найменший: \"",[5541,12850,7751],{"class":6263},[5541,12852,10804],{"class":6272},[5541,12854,5514],{"class":6263},[5541,12856,12818],{"class":6325},[5541,12858,6328],{"class":6263},[5541,12860,12861],{"class":10337},"4",[5541,12863,10878],{"class":6263},[5541,12865,9475],{"class":6441},[5541,12867,7767],{"class":7766},[5541,12869,9475],{"class":6441},[5541,12871,6276],{"class":6263},[5541,12873,12874],{"class":6279},"  \u002F\u002F 50\n",[5541,12876,12877,12879,12881,12883,12885,12888,12890,12892,12894,12896,12898,12901,12903,12905,12907,12909,12911],{"class":5543,"line":5623},[5541,12878,9465],{"class":6257},[5541,12880,7181],{"class":6263},[5541,12882,9470],{"class":6272},[5541,12884,7751],{"class":6263},[5541,12886,12887],{"class":6441},"\"7-й найменший: \"",[5541,12889,7751],{"class":6263},[5541,12891,10804],{"class":6272},[5541,12893,5514],{"class":6263},[5541,12895,12818],{"class":6325},[5541,12897,6328],{"class":6263},[5541,12899,12900],{"class":10337},"7",[5541,12902,10878],{"class":6263},[5541,12904,9475],{"class":6441},[5541,12906,7767],{"class":7766},[5541,12908,9475],{"class":6441},[5541,12910,6276],{"class":6263},[5541,12912,12913],{"class":6279},"  \u002F\u002F 80\n",[5541,12915,12916],{"class":5543,"line":5628},[5541,12917,6315],{"class":6263},[5541,12919,12920,12922,12924],{"class":5543,"line":5634},[5541,12921,7790],{"class":6418},[5541,12923,11155],{"class":10337},[5541,12925,6465],{"class":6263},[5541,12927,12928],{"class":5543,"line":5640},[5541,12929,5620],{"class":6263},[11163,12931,12933,12940,12947],{"title":12932},".\u002Fkth_smallest",[11167,12934,12936,12937],{"className":12935},[5543],"1-й найменший: ",[5541,12938,5886],{"className":12939},[11208],[11167,12941,12943,12944],{"className":12942},[5543],"4-й найменший: ",[5541,12945,5816],{"className":12946},[11208],[11167,12948,12950,12951],{"className":12949},[5543],"7-й найменший: ",[5541,12952,5895],{"className":12953},[11208],[11749,12955,12957,12969,12981,12991],{"icon":11751,"label":12956},"📋 Завдання 3: Пошук діапазону значень",[5390,12958,12959,11758,12961,12964,12965,12968],{},[5271,12960,11757],{},[5538,12962,12963],{},"void printRange(int min, int max)",", який виводить усі елементи BST у діапазоні ",[5538,12966,12967],{},"[min, max]"," (включно).",[5390,12970,12971,12973,12974,12977,12978,5514],{},[5271,12972,11767],{}," Модифікуйте in-order обхід — пропускайте ліве піддерево, якщо ",[5538,12975,12976],{},"node->data \u003C min",", та праве, якщо ",[5538,12979,12980],{},"node->data > max",[5390,12982,12983,12257,12985,12987,12988,6012],{},[5271,12984,12256],{},[5538,12986,9623],{}," та діапазону ",[5538,12989,12990],{},"[35, 65]",[5531,12992,12995],{"className":12993,"code":12994,"language":6061},[6059],"Виведе: 40 50 60\n",[5538,12996,12994],{"__ignoreMap":5536},[11749,12998,13000,13384,13388,13600],{"icon":11791,"label":12999},"✅ Розв'язок завдання 3",[5531,13001,13003],{"className":6244,"code":13002,"language":6246,"meta":5536,"style":5536},"class BinarySearchTree\n{\nprivate:\n    void printRangeRecursive(TreeNode* node, int min, int max) const\n    {\n        if (node == nullptr)\n        {\n            return;\n        }\n        \n        \u002F\u002F Якщо поточне значення > min — може бути щось корисне ліворуч\n        if (node->data > min)\n        {\n            printRangeRecursive(node->left, min, max);\n        }\n        \n        \u002F\u002F Якщо поточне значення в діапазоні — виводимо\n        if (node->data >= min && node->data \u003C= max)\n        {\n            std::cout \u003C\u003C node->data \u003C\u003C \" \";\n        }\n        \n        \u002F\u002F Якщо поточне значення \u003C max — може бути щось корисне праворуч\n        if (node->data \u003C max)\n        {\n            printRangeRecursive(node->right, min, max);\n        }\n    }\n\npublic:\n    void printRange(int min, int max) const\n    {\n        std::cout \u003C\u003C \"Елементи у діапазоні [\" \u003C\u003C min \u003C\u003C \", \" \u003C\u003C max \u003C\u003C \"]: \";\n        printRangeRecursive(root, min, max);\n        std::cout \u003C\u003C '\\n';\n    }\n};\n",[5538,13004,13005,13011,13015,13019,13050,13054,13068,13072,13078,13082,13086,13091,13109,13113,13136,13140,13144,13149,13179,13183,13206,13210,13214,13219,13237,13241,13263,13267,13271,13275,13279,13302,13306,13339,13358,13376,13380],{"__ignoreMap":5536},[5541,13006,13007,13009],{"class":5543,"line":5544},[5541,13008,6550],{"class":6253},[5541,13010,6553],{"class":6257},[5541,13012,13013],{"class":5543,"line":5550},[5541,13014,6264],{"class":6263},[5541,13016,13017],{"class":5543,"line":5556},[5541,13018,6562],{"class":6253},[5541,13020,13021,13023,13026,13028,13030,13032,13034,13036,13038,13040,13042,13044,13046,13048],{"class":5543,"line":5562},[5541,13022,6696],{"class":6253},[5541,13024,13025],{"class":6325}," printRangeRecursive",[5541,13027,6328],{"class":6263},[5541,13029,6599],{"class":6257},[5541,13031,6288],{"class":6253},[5541,13033,6604],{"class":6272},[5541,13035,5742],{"class":6263},[5541,13037,6331],{"class":6253},[5541,13039,11833],{"class":6272},[5541,13041,5742],{"class":6263},[5541,13043,6331],{"class":6253},[5541,13045,11840],{"class":6272},[5541,13047,6658],{"class":6263},[5541,13049,8115],{"class":6253},[5541,13051,13052],{"class":5543,"line":5569},[5541,13053,6373],{"class":6263},[5541,13055,13056,13058,13060,13062,13064,13066],{"class":5543,"line":5575},[5541,13057,8438],{"class":6418},[5541,13059,5285],{"class":6263},[5541,13061,7291],{"class":6272},[5541,13063,7294],{"class":6263},[5541,13065,6358],{"class":6253},[5541,13067,6337],{"class":6263},[5541,13069,13070],{"class":5543,"line":5581},[5541,13071,8457],{"class":6263},[5541,13073,13074,13076],{"class":5543,"line":5587},[5541,13075,8462],{"class":6418},[5541,13077,6465],{"class":6263},[5541,13079,13080],{"class":5543,"line":5593},[5541,13081,8474],{"class":6263},[5541,13083,13084],{"class":5543,"line":5599},[5541,13085,8954],{"class":6263},[5541,13087,13088],{"class":5543,"line":5605},[5541,13089,13090],{"class":6279},"        \u002F\u002F Якщо поточне значення > min — може бути щось корисне ліворуч\n",[5541,13092,13093,13095,13097,13099,13101,13103,13105,13107],{"class":5543,"line":5611},[5541,13094,8438],{"class":6418},[5541,13096,5285],{"class":6263},[5541,13098,7291],{"class":6272},[5541,13100,7336],{"class":6263},[5541,13102,6345],{"class":6272},[5541,13104,7677],{"class":6263},[5541,13106,11771],{"class":6272},[5541,13108,6337],{"class":6263},[5541,13110,13111],{"class":5543,"line":5617},[5541,13112,8457],{"class":6263},[5541,13114,13115,13118,13120,13122,13124,13126,13128,13130,13132,13134],{"class":5543,"line":5623},[5541,13116,13117],{"class":6325},"            printRangeRecursive",[5541,13119,6328],{"class":6263},[5541,13121,7291],{"class":6272},[5541,13123,7336],{"class":6263},[5541,13125,5495],{"class":6272},[5541,13127,5742],{"class":6263},[5541,13129,11771],{"class":6272},[5541,13131,5742],{"class":6263},[5541,13133,10416],{"class":6272},[5541,13135,6613],{"class":6263},[5541,13137,13138],{"class":5543,"line":5628},[5541,13139,8474],{"class":6263},[5541,13141,13142],{"class":5543,"line":5634},[5541,13143,8954],{"class":6263},[5541,13145,13146],{"class":5543,"line":5640},[5541,13147,13148],{"class":6279},"        \u002F\u002F Якщо поточне значення в діапазоні — виводимо\n",[5541,13150,13151,13153,13155,13157,13159,13161,13163,13165,13167,13169,13171,13173,13175,13177],{"class":5543,"line":5646},[5541,13152,8438],{"class":6418},[5541,13154,5285],{"class":6263},[5541,13156,7291],{"class":6272},[5541,13158,7336],{"class":6263},[5541,13160,6345],{"class":6272},[5541,13162,11921],{"class":6263},[5541,13164,11771],{"class":6272},[5541,13166,8978],{"class":6263},[5541,13168,7291],{"class":6272},[5541,13170,7336],{"class":6263},[5541,13172,6345],{"class":6272},[5541,13174,11907],{"class":6263},[5541,13176,10416],{"class":6272},[5541,13178,6337],{"class":6263},[5541,13180,13181],{"class":5543,"line":5652},[5541,13182,8457],{"class":6263},[5541,13184,13185,13188,13190,13192,13194,13196,13198,13200,13202,13204],{"class":5543,"line":5658},[5541,13186,13187],{"class":6257},"            std",[5541,13189,7181],{"class":6263},[5541,13191,9470],{"class":6272},[5541,13193,7751],{"class":6263},[5541,13195,7291],{"class":6272},[5541,13197,7336],{"class":6263},[5541,13199,6345],{"class":6272},[5541,13201,7751],{"class":6263},[5541,13203,9589],{"class":6441},[5541,13205,6465],{"class":6263},[5541,13207,13208],{"class":5543,"line":5664},[5541,13209,8474],{"class":6263},[5541,13211,13212],{"class":5543,"line":5669},[5541,13213,8954],{"class":6263},[5541,13215,13216],{"class":5543,"line":5675},[5541,13217,13218],{"class":6279},"        \u002F\u002F Якщо поточне значення \u003C max — може бути щось корисне праворуч\n",[5541,13220,13221,13223,13225,13227,13229,13231,13233,13235],{"class":5543,"line":5681},[5541,13222,8438],{"class":6418},[5541,13224,5285],{"class":6263},[5541,13226,7291],{"class":6272},[5541,13228,7336],{"class":6263},[5541,13230,6345],{"class":6272},[5541,13232,7614],{"class":6263},[5541,13234,10416],{"class":6272},[5541,13236,6337],{"class":6263},[5541,13238,13239],{"class":5543,"line":5687},[5541,13240,8457],{"class":6263},[5541,13242,13243,13245,13247,13249,13251,13253,13255,13257,13259,13261],{"class":5543,"line":5693},[5541,13244,13117],{"class":6325},[5541,13246,6328],{"class":6263},[5541,13248,7291],{"class":6272},[5541,13250,7336],{"class":6263},[5541,13252,5499],{"class":6272},[5541,13254,5742],{"class":6263},[5541,13256,11771],{"class":6272},[5541,13258,5742],{"class":6263},[5541,13260,10416],{"class":6272},[5541,13262,6613],{"class":6263},[5541,13264,13265],{"class":5543,"line":5699},[5541,13266,8474],{"class":6263},[5541,13268,13269],{"class":5543,"line":5704},[5541,13270,6378],{"class":6263},[5541,13272,13273],{"class":5543,"line":5710},[5541,13274,5566],{"emptyLinePlaceholder":5565},[5541,13276,13277],{"class":5543,"line":5716},[5541,13278,6804],{"class":6253},[5541,13280,13281,13283,13286,13288,13290,13292,13294,13296,13298,13300],{"class":5543,"line":5722},[5541,13282,6696],{"class":6253},[5541,13284,13285],{"class":6325}," printRange",[5541,13287,6328],{"class":6263},[5541,13289,6331],{"class":6253},[5541,13291,11833],{"class":6272},[5541,13293,5742],{"class":6263},[5541,13295,6331],{"class":6253},[5541,13297,11840],{"class":6272},[5541,13299,6658],{"class":6263},[5541,13301,8115],{"class":6253},[5541,13303,13304],{"class":5543,"line":5727},[5541,13305,6373],{"class":6263},[5541,13307,13308,13310,13312,13314,13316,13319,13321,13323,13325,13328,13330,13332,13334,13337],{"class":5543,"line":5732},[5541,13309,7743],{"class":6257},[5541,13311,7181],{"class":6263},[5541,13313,9470],{"class":6272},[5541,13315,7751],{"class":6263},[5541,13317,13318],{"class":6441},"\"Елементи у діапазоні [\"",[5541,13320,7751],{"class":6263},[5541,13322,11771],{"class":6272},[5541,13324,7751],{"class":6263},[5541,13326,13327],{"class":6441},"\", \"",[5541,13329,7751],{"class":6263},[5541,13331,10416],{"class":6272},[5541,13333,7751],{"class":6263},[5541,13335,13336],{"class":6441},"\"]: \"",[5541,13338,6465],{"class":6263},[5541,13340,13341,13344,13346,13348,13350,13352,13354,13356],{"class":5543,"line":6796},[5541,13342,13343],{"class":6325},"        printRangeRecursive",[5541,13345,6328],{"class":6263},[5541,13347,5351],{"class":6272},[5541,13349,5742],{"class":6263},[5541,13351,11771],{"class":6272},[5541,13353,5742],{"class":6263},[5541,13355,10416],{"class":6272},[5541,13357,6613],{"class":6263},[5541,13359,13360,13362,13364,13366,13368,13370,13372,13374],{"class":5543,"line":6801},[5541,13361,7743],{"class":6257},[5541,13363,7181],{"class":6263},[5541,13365,9470],{"class":6272},[5541,13367,7751],{"class":6263},[5541,13369,9475],{"class":6441},[5541,13371,7767],{"class":7766},[5541,13373,9475],{"class":6441},[5541,13375,6465],{"class":6263},[5541,13377,13378],{"class":5543,"line":6807},[5541,13379,6378],{"class":6263},[5541,13381,13382],{"class":5543,"line":6813},[5541,13383,6383],{"class":6263},[5390,13385,13386],{},[5271,13387,12073],{},[5531,13389,13391],{"className":6244,"code":13390,"language":6246,"meta":5536,"style":5536},"int main()\n{\n    BinarySearchTree bst;\n    bst.insert(50);\n    bst.insert(30);\n    bst.insert(70);\n    bst.insert(20);\n    bst.insert(40);\n    bst.insert(60);\n    bst.insert(80);\n    \n    bst.printRange(35, 65);  \u002F\u002F Виведе: 40 50 60\n    bst.printRange(10, 90);  \u002F\u002F Виведе: 20 30 40 50 60 70 80\n    bst.printRange(55, 75);  \u002F\u002F Виведе: 60 70\n    \n    return 0;\n}\n",[5538,13392,13393,13401,13405,13413,13427,13441,13455,13469,13483,13497,13511,13515,13539,13561,13584,13588,13596],{"__ignoreMap":5536},[5541,13394,13395,13397,13399],{"class":5543,"line":5544},[5541,13396,6331],{"class":6253},[5541,13398,10483],{"class":6325},[5541,13400,7186],{"class":6263},[5541,13402,13403],{"class":5543,"line":5550},[5541,13404,6264],{"class":6263},[5541,13406,13407,13409,13411],{"class":5543,"line":5556},[5541,13408,6816],{"class":6257},[5541,13410,10496],{"class":6272},[5541,13412,6465],{"class":6263},[5541,13414,13415,13417,13419,13421,13423,13425],{"class":5543,"line":5562},[5541,13416,10555],{"class":6272},[5541,13418,5514],{"class":6263},[5541,13420,5299],{"class":6325},[5541,13422,6328],{"class":6263},[5541,13424,5816],{"class":10337},[5541,13426,6613],{"class":6263},[5541,13428,13429,13431,13433,13435,13437,13439],{"class":5543,"line":5569},[5541,13430,10555],{"class":6272},[5541,13432,5514],{"class":6263},[5541,13434,5299],{"class":6325},[5541,13436,6328],{"class":6263},[5541,13438,5845],{"class":10337},[5541,13440,6613],{"class":6263},[5541,13442,13443,13445,13447,13449,13451,13453],{"class":5543,"line":5575},[5541,13444,10555],{"class":6272},[5541,13446,5514],{"class":6263},[5541,13448,5299],{"class":6325},[5541,13450,6328],{"class":6263},[5541,13452,5849],{"class":10337},[5541,13454,6613],{"class":6263},[5541,13456,13457,13459,13461,13463,13465,13467],{"class":5543,"line":5581},[5541,13458,10555],{"class":6272},[5541,13460,5514],{"class":6263},[5541,13462,5299],{"class":6325},[5541,13464,6328],{"class":6263},[5541,13466,5886],{"class":10337},[5541,13468,6613],{"class":6263},[5541,13470,13471,13473,13475,13477,13479,13481],{"class":5543,"line":5587},[5541,13472,10555],{"class":6272},[5541,13474,5514],{"class":6263},[5541,13476,5299],{"class":6325},[5541,13478,6328],{"class":6263},[5541,13480,5889],{"class":10337},[5541,13482,6613],{"class":6263},[5541,13484,13485,13487,13489,13491,13493,13495],{"class":5543,"line":5593},[5541,13486,10555],{"class":6272},[5541,13488,5514],{"class":6263},[5541,13490,5299],{"class":6325},[5541,13492,6328],{"class":6263},[5541,13494,5892],{"class":10337},[5541,13496,6613],{"class":6263},[5541,13498,13499,13501,13503,13505,13507,13509],{"class":5543,"line":5599},[5541,13500,10555],{"class":6272},[5541,13502,5514],{"class":6263},[5541,13504,5299],{"class":6325},[5541,13506,6328],{"class":6263},[5541,13508,5895],{"class":10337},[5541,13510,6613],{"class":6263},[5541,13512,13513],{"class":5543,"line":5605},[5541,13514,6315],{"class":6263},[5541,13516,13517,13519,13521,13524,13526,13529,13531,13534,13536],{"class":5543,"line":5611},[5541,13518,10555],{"class":6272},[5541,13520,5514],{"class":6263},[5541,13522,13523],{"class":6325},"printRange",[5541,13525,6328],{"class":6263},[5541,13527,13528],{"class":10337},"35",[5541,13530,5742],{"class":6263},[5541,13532,13533],{"class":10337},"65",[5541,13535,8311],{"class":6263},[5541,13537,13538],{"class":6279},"  \u002F\u002F Виведе: 40 50 60\n",[5541,13540,13541,13543,13545,13547,13549,13551,13553,13556,13558],{"class":5543,"line":5617},[5541,13542,10555],{"class":6272},[5541,13544,5514],{"class":6263},[5541,13546,13523],{"class":6325},[5541,13548,6328],{"class":6263},[5541,13550,11340],{"class":10337},[5541,13552,5742],{"class":6263},[5541,13554,13555],{"class":10337},"90",[5541,13557,8311],{"class":6263},[5541,13559,13560],{"class":6279},"  \u002F\u002F Виведе: 20 30 40 50 60 70 80\n",[5541,13562,13563,13565,13567,13569,13571,13574,13576,13579,13581],{"class":5543,"line":5623},[5541,13564,10555],{"class":6272},[5541,13566,5514],{"class":6263},[5541,13568,13523],{"class":6325},[5541,13570,6328],{"class":6263},[5541,13572,13573],{"class":10337},"55",[5541,13575,5742],{"class":6263},[5541,13577,13578],{"class":10337},"75",[5541,13580,8311],{"class":6263},[5541,13582,13583],{"class":6279},"  \u002F\u002F Виведе: 60 70\n",[5541,13585,13586],{"class":5543,"line":5628},[5541,13587,6315],{"class":6263},[5541,13589,13590,13592,13594],{"class":5543,"line":5634},[5541,13591,7790],{"class":6418},[5541,13593,11155],{"class":10337},[5541,13595,6465],{"class":6263},[5541,13597,13598],{"class":5543,"line":5640},[5541,13599,5620],{"class":6263},[11163,13601,13603,13611,13618],{"title":13602},".\u002Fprint_range",[11167,13604,13606,13607],{"className":13605},[5543],"Елементи у діапазоні [35, 65]: ",[5541,13608,13610],{"className":13609},[11208],"40 50 60",[11167,13612,13614,13615],{"className":13613},[5543],"Елементи у діапазоні [10, 90]: ",[5541,13616,11209],{"className":13617},[11208],[11167,13619,13621,13622],{"className":13620},[5543],"Елементи у діапазоні [55, 75]: ",[5541,13623,13625],{"className":13624},[11208],"60 70",[5382,13627],{},[5390,13629,13630,13631,13634,13635,5742,13638,5742,13641,5742,13643,13645,13646,5514],{},"Ця стаття завершує серію власних структур даних перед переходом до ",[5271,13632,13633],{},"стандартної бібліотеки C++ (STL)",". Ми опанували лінійні (масиви, списки, стеки, черги) та ієрархічні (дерева) структури. У наступних лекціях вивчимо професійні реалізації цих концепцій у ",[5538,13636,13637],{},"std::vector",[5538,13639,13640],{},"std::list",[5538,13642,5741],{},[5538,13644,5745],{}," та алгоритми ",[5538,13647,11738],{},[13649,13650,13651],"style",{},"html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: 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.sJj4R{--shiki-light:#098658;--shiki-default:#B5CEA8;--shiki-dark:#B5CEA8}",{"title":5536,"searchDepth":5550,"depth":5550,"links":13653},[13654,13655,13660,13665,13666,13670,13676,13681,13682,13683,13687,13688,13689],{"id":5387,"depth":5550,"text":5388},{"id":5750,"depth":5550,"text":5751,"children":13656},[13657,13658,13659],{"id":5755,"depth":5556,"text":5756},{"id":5981,"depth":5556,"text":5982},{"id":6141,"depth":5556,"text":6142},{"id":6225,"depth":5550,"text":6226,"children":13661},[13662,13663,13664],{"id":6229,"depth":5556,"text":6230},{"id":6402,"depth":5556,"text":6403},{"id":7146,"depth":5556,"text":7147},{"id":7393,"depth":5550,"text":7394},{"id":8072,"depth":5550,"text":8073,"children":13667},[13668,13669],{"id":8082,"depth":5556,"text":8083},{"id":8360,"depth":5556,"text":8361},{"id":8601,"depth":5550,"text":8602,"children":13671},[13672,13673,13674,13675],{"id":8615,"depth":5556,"text":8616},{"id":8630,"depth":5556,"text":8631},{"id":8643,"depth":5556,"text":8644},{"id":8689,"depth":5556,"text":8690},{"id":9401,"depth":5550,"text":9402,"children":13677},[13678,13679,13680],{"id":9414,"depth":5556,"text":9415},{"id":9632,"depth":5556,"text":9633},{"id":9836,"depth":5556,"text":9837},{"id":10216,"depth":5550,"text":10217},{"id":10454,"depth":5550,"text":10455},{"id":11302,"depth":5550,"text":11303,"children":13684},[13685,13686],{"id":11306,"depth":5556,"text":11307},{"id":11444,"depth":5556,"text":11445},{"id":11516,"depth":5550,"text":11517},{"id":11641,"depth":5550,"text":11642},{"id":11743,"depth":5550,"text":11744},"Проєктування та реалізація бінарного дерева пошуку (BST) з нуля: ієрархічна структура, рекурсивні операції вставки, пошуку та видалення, обходи дерева (in-order, pre-order, post-order), логарифмічна складність O(log n)","md",null,{},{"title":2077,"description":13690},"T7utfkeAT-bQ1JxqyXeblD1FG8JVwHgnD9JOB23X1og",[13697,13699],{"title":2073,"path":2074,"stem":2075,"description":13698,"children":-1},"Проєктування та реалізація однозв'язаного списку з нуля: вузли, покажчики, динамічне виділення пам'яті, операції вставки, видалення, пошуку за O(1) або O(n), ітеративний обхід",{"title":2081,"path":2082,"stem":2083,"description":13700,"children":-1},"Проєктування та реалізація хеш-таблиці з нуля: принципи хешування, розв'язання колізій методом ланцюгів, динамічне збільшення розміру (rehashing), коефіцієнт завантаження, середня складність O(1) для операцій вставки, пошуку та видалення",1792589358945]