[BE] Code challenge submission

src/problem4/index.ts

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+/**
+ * Problem 4: Three ways to sum to n
+ * Summation from 1 to n: sum_to_n(5) === 1 + 2 + 3 + 4 + 5 === 15
+ * Handles positive integers, negative integers, and zero.
+ */
+
+/**
+ * Implementation A: Gauss closed-form formula
+ *
+ * For n >= 0: n * (n + 1) / 2  (standard arithmetic series)
+ * For n <  0: -(|n| * (|n| + 1) / 2)  (symmetric signed sum toward -1)
+ *
+ * Time complexity:  O(1) — single arithmetic expression, no iteration
+ * Space complexity: O(1) — no additional memory
+ */
+export function sum_to_n_a(n: number): number {
+  const abs = Math.abs(n);
+  return Math.sign(n) * (abs * (abs + 1)) / 2;
+}
+
+/**
+ * Implementation B: Iterative loop
+ *
+ * Accumulates the sum by iterating from 1 to n (or n to -1 for negatives).
+ *
+ * Time complexity:  O(n) — linear, one pass through all integers up to n
+ * Space complexity: O(1) — only a single accumulator variable
+ */
+export function sum_to_n_b(n: number): number {
+  let sum = 0;
+  if (n >= 0) {
+    for (let i = 1; i <= n; i++) {
+      sum += i;
+    }
+  } else {
+    for (let i = -1; i >= n; i--) {
+      sum += i;
+    }
+  }
+  return sum;
+}
+
+/**
+ * Implementation C: Recursive
+ *
+ * Recursively sums by reducing n toward 0 on each call.
+ *
+ * Time complexity:  O(n) — n recursive calls on the call stack
+ * Space complexity: O(n) — each call frame is kept on the stack until unwinding;
+ *                          this can cause a stack overflow for very large |n|
+ */
+export function sum_to_n_c(n: number): number {
+  if (n === 0) return 0;
+  if (n > 0) return n + sum_to_n_c(n - 1);
+  return n + sum_to_n_c(n + 1);
+}

src/problem5/.env.example

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+PORT=3000
+NODE_ENV=development
+DB_PATH=./data/dev.db

src/problem5/.gitignore

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+node_modules/
+dist/
+.env
+*.db
+*.db-shm
+*.db-wal

src/problem5/.npmrc

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+legacy-peer-deps=true

src/problem5/README.md

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+# Problem 5 – Crude Server
+
+A production-quality REST API built with **Express.js**, **TypeScript**, **TypeORM**, and **SQLite**.
+
+## Stack
+
+| Layer | Technology |
+|---|---|
+| Framework | Express.js |
+| Language | TypeScript |
+| ORM | TypeORM |
+| Database | SQLite (via sqlite3) |
+| Validation | Zod |
+| Testing | Jest + ts-jest |
+
+## Project Structure
+
+```
+src/
+├── app.ts                          # Express app setup
+├── server.ts                       # Entry point
+├── config/
+│   ├── env.ts                      # Environment variables
+│   └── database.ts                 # TypeORM DataSource
+├── modules/
+│   └── resource/
+│       ├── resource.model.ts       # TypeORM entity
+│       ├── resource.dto.ts         # Types / interfaces
+│       ├── resource.validation.ts  # Zod schemas
+│       ├── resource.repository.ts  # Database queries
+│       ├── resource.service.ts     # Business logic
+│       ├── resource.controller.ts  # Request / response handling
+│       └── resource.routes.ts      # Express router
+├── common/
+│   ├── middleware/
+│   │   ├── error.middleware.ts     # Centralized error handler
+│   │   └── validate.middleware.ts  # Zod validation middleware
+│   ├── utils/logger.ts
+│   ├── types/express.d.ts
+│   └── constants/httpStatus.ts
+├── routes/
+│   └── index.ts                    # Combines all routes
+└── database/
+    └── seed/index.ts               # Seed data
+```
+
+## Prerequisites
+
+- Node.js >= 18
+- npm
+
+## Configuration
+
+Copy `.env.example` to `.env`:
+
+```bash
+cp .env.example .env
+```
+
+| Variable | Default | Description |
+|---|---|---|
+| `PORT` | `3000` | HTTP port |
+| `NODE_ENV` | `development` | Environment |
+| `DB_PATH` | `./data/dev.db` | SQLite file path |
+
+## Running
+
+### Development
+
+```bash
+npm install
+npm run dev
+```
+
+The database tables are created automatically on first start (`synchronize: true`).
+
+### Production
+
+```bash
+npm run build
+npm start
+```
+
+### Seed (optional)
+
+```bash
+npm run db:seed
+```
+
+## Testing
+
+```bash
+# Run all tests
+npm test
+
+# Watch mode
+npm run test:watch
+```
+
+### Test coverage
+
+| File | What is tested |
+|---|---|
+| `resource.validation.ts` | All Zod schemas — valid input, edge cases, cross-field rules (`minPrice ≤ maxPrice`) |
+| `resource.service.ts` | All service methods with mocked repository — happy path and 404 error cases |
+
+Tests are located in `src/modules/resource/__tests__/`.
+
+## API Reference
+
+Base URL: `http://localhost:3000/api`
+
+### List resources
+
+```
+GET /resources
+```
+
+Query parameters:
+
+| Param | Type | Description |
+|---|---|---|
+| `name` | string | Partial name match |
+| `minPrice` | number | Minimum price |
+| `maxPrice` | number | Maximum price |
+| `page` | number | Page number (default: 1) |
+| `limit` | number | Page size (default: 20, max: 100) |
+
+**Response**
+```json
+{
+  "data": [...],
+  "total": 10,
+  "page": 1,
+  "limit": 20,
+  "totalPages": 1
+}
+```
+
+### Get resource
+
+```
+GET /resources/:id
+```
+
+### Create resource
+
+```
+POST /resources
+Content-Type: application/json
+
+{
+  "name": "Laptop",
+  "description": "High performance laptop",
+  "price": 999.99
+}
+```
+
+**Response:** `201 Created`
+
+### Update resource
+
+```
+PATCH /resources/:id
+Content-Type: application/json
+
+{
+  "price": 899.99
+}
+```
+
+### Delete resource
+
+```
+DELETE /resources/:id
+```
+
+**Response:** `204 No Content`
+
+## Example curl commands
+
+```bash
+# Create
+curl -X POST http://localhost:3000/api/resources \
+  -H "Content-Type: application/json" \
+  -d '{"name":"Laptop","description":"Gaming laptop","price":999.99}'
+
+# List with filters
+curl "http://localhost:3000/api/resources?minPrice=100&maxPrice=1000&page=1&limit=10"
+
+# Get by id
+curl http://localhost:3000/api/resources/1
+
+# Update
+curl -X PATCH http://localhost:3000/api/resources/1 \
+  -H "Content-Type: application/json" \
+  -d '{"price":899.99}'
+
+# Delete
+curl -X DELETE http://localhost:3000/api/resources/1
+```

src/problem5/jest.config.ts

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+import type { Config } from 'jest';
+
+const config: Config = {
+  preset: 'ts-jest',
+  testEnvironment: 'node',
+  rootDir: 'src',
+  testMatch: ['**/__tests__/**/*.test.ts'],
+  moduleNameMapper: {
+    '^reflect-metadata$': '<rootDir>/../node_modules/reflect-metadata',
+  },
+};
+
+export default config;