[BE] Hung Pham

src/problem4/index.ts

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+// Time Complexity: O(1) - constant time, just arithmetic operations
+// Space Complexity: O(1) - no extra memory used
+function sum_to_n_a(n: number): number {
+	return (n * (n + 1)) / 2;
+}
+
+// Time Complexity: O(n) - iterates through all numbers from 1 to n
+// Space Complexity: O(1) - only a single accumulator variable
+function sum_to_n_b(n: number): number {
+	let sum = 0;
+	for (let i = 1; i <= n; i++) {
+		sum += i;
+	}
+	return sum;
+}
+
+// Time Complexity: O(n) - makes n recursive calls
+// Space Complexity: O(n) - each recursive call adds a frame to the call stack
+function sum_to_n_c(n: number): number {
+	if (n <= 0) return 0;
+	return n + sum_to_n_c(n - 1);
+}
+

src/problem5/.gitignore

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+node_modules/
+dist/
+data/
+

src/problem5/README.md

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+# Problem 5 - Todo CRUD API
+
+A RESTful CRUD API for managing todos, built with **Express.js** and **TypeScript**, using a **JSON file-based database** for data persistence.
+
+## Architecture
+
+The project follows a **layered architecture** for maintainability and scalability:
+
+```
+Request → Routes → Controllers → Services → Repositories → Database
+```
+
+| Layer          | Responsibility                                                 |
+| -------------- | -------------------------------------------------------------- |
+| **Routes**     | HTTP verb → controller method mapping (no logic)               |
+| **Controllers**| Parse HTTP request, delegate to service, send HTTP response    |
+| **Services**   | Business logic, validation rules, orchestration                |
+| **Repositories** | Data access abstraction (swap DB by implementing interface)  |
+| **Middleware** | Cross-cutting concerns (error handling, auth, logging)         |
+
+## Prerequisites
+
+- [Node.js](https://nodejs.org/) (v16 or higher)
+- npm (comes with Node.js)
+
+## Installation
+
+```bash
+cd src/problem5
+npm install
+```
+
+## Running the Application
+
+### Development mode (with ts-node)
+
+```bash
+npm run dev
+```
+
+### Production mode (compile and run)
+
+```bash
+npm run build
+npm start
+```
+
+The server will start on `http://localhost:3000` by default. You can change the port by setting the `PORT` environment variable:
+
+```bash
+PORT=8080 npm run dev
+```
+
+## Database
+
+The application uses a **JSON file-based database** for simplicity and zero external dependencies. The database file is automatically created at `data/todos.json` on first run. No external database setup is required.
+
+To swap to a real database (e.g. PostgreSQL, MongoDB), implement the `ITodoRepository` interface in `src/repositories/todo.repository.ts` and inject it in `src/routes/index.ts`.
+
+## API Endpoints
+
+### Health Check
+
+```
+GET /
+```
+
+### Create a Todo
+
+```
+POST /todos
+Content-Type: application/json
+
+{
+  "title": "Buy groceries",
+  "description": "Milk, eggs, bread"
+}
+```
+
+**Response:** `201 Created`
+
+### List Todos (with filters)
+
+```
+GET /todos
+```
+
+**Query Parameters:**
+
+| Parameter   | Type    | Description                                |
+| ----------- | ------- | ------------------------------------------ |
+| `completed` | boolean | Filter by completion status                |
+| `search`    | string  | Search in title and description            |
+| `limit`     | number  | Number of results per page (default: 20, max: 100) |
+| `offset`    | number  | Offset for pagination (default: 0)         |
+
+**Examples:**
+
+```
+GET /todos?completed=true
+GET /todos?search=groceries
+GET /todos?limit=10&offset=0
+```
+
+**Response:** `200 OK`
+
+```json
+{
+  "data": [...],
+  "pagination": {
+    "total": 25,
+    "limit": 20,
+    "offset": 0
+  }
+}
+```
+
+### Get Todo Details
+
+```
+GET /todos/:id
+```
+
+**Response:** `200 OK` or `404 Not Found`
+
+### Update a Todo
+
+```
+PUT /todos/:id
+Content-Type: application/json
+
+{
+  "title": "Buy groceries (updated)",
+  "completed": true
+}
+```
+
+All fields are optional. Only provided fields will be updated.
+
+**Response:** `200 OK` or `404 Not Found`
+
+### Delete a Todo
+
+```
+DELETE /todos/:id
+```
+
+**Response:** `200 OK` or `404 Not Found`
+
+## Project Structure
+
+```
+src/problem5/
+├── package.json
+├── tsconfig.json
+├── README.md
+├── data/                        # Auto-created at runtime
+│   └── todos.json
+└── src/
+    ├── index.ts                 # App bootstrap & middleware registration
+    ├── config/
+    │   └── index.ts             # Centralized configuration
+    ├── errors/
+    │   └── index.ts             # Custom error classes (AppError, NotFoundError, etc.)
+    ├── middleware/
+    │   └── errorHandler.ts      # Global error handling middleware
+    ├── types/
+    │   └── todo.types.ts        # Shared TypeScript interfaces & DTOs
+    ├── repositories/
+    │   └── todo.repository.ts   # Data access layer (ITodoRepository interface + JSON impl)
+    ├── services/
+    │   └── todo.service.ts      # Business logic layer
+    ├── controllers/
+    │   └── todo.controller.ts   # HTTP request/response handling
+    └── routes/
+        ├── index.ts             # Central route registration & dependency wiring
+        └── todo.routes.ts       # Route definitions (verb → controller)
+```