[BE] Code challenge - La Thanh Tam

.gitignore

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+# Dependencies
+*node_modules/
+
+# TypeScript build output
+dist/
+*.tsbuildinfo
+
+# Tests / coverage
+coverage/
+
+# Logs & env
+*.log
+.env
+.env.*
+!.env.example
+
+# OS
+.DS_Store
+Thumbs.db
+.history/
+*.db
+*.db-journal

src/problem4/README.md

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+# Problem 4: Summation to n
+
+This folder contains three TypeScript implementations of the **triangular number** (sum of integers from 1 through n inclusive)
+
+Example: `sum_to_n(5) === 1 + 2 + 3 + 4 + 5 === 15`.
+
+**Assumption:** The mathematical result is always less than `Number.MAX_SAFE_INTEGER` (so you stay in the range where double-precision arithmetic in JavaScript is exact for these integers).
+
+## Files
+
+| File               | Purpose                                                                       |
+| ------------------ | ----------------------------------------------------------------------------- |
+| `sum_to_n.ts`      | Three exported functions: `sum_to_n_a`, `sum_to_n_b`, `sum_to_n_c`            |
+| `sum_to_n.test.ts` | Vitest checks against known values and cross-checks all three implementations |
+| `tsconfig.json`    | Strict TypeScript; `module` / `moduleResolution` set to `Node16`              |
+| `vitest.config.ts` | Runs tests in Node against `*.test.ts`                                        |
+
+## Implementations
+
+| Function     | Approach                 | Time | Extra space  |
+| ------------ | ------------------------ | ---- | ------------ |
+| `sum_to_n_a` | Closed form \(n(n+1)/2\) | O(1) | O(1)         |
+| `sum_to_n_b` | Iterative `for` loop     | O(n) | O(1)         |
+| `sum_to_n_c` | `Array.from` + `reduce`  | O(n) | O(n) (array) |
+
+For large nonnegative `n`, **`sum_to_n_a`** does the least work. **`sum_to_n_b`** is straightforward and allocation-free. **`sum_to_n_c`** mirrors a functional style but pays for building an array.
+
+## Setup
+
+From this directory:
+
+```bash
+npm install
+```
+
+## Tests
+
+```bash
+npm test
+```
+
+Runs Vitest once (`vitest run`). For watch mode while editing:
+
+```bash
+npx vitest
+```
+
+## Compile (optional)
+
+Emit JavaScript into `dist/`:
+
+```bash
+npx tsc -p .
+```