[BE] Code Challenge - Hung Nguyen

src/problem4/README.md

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+# Problem 4 — Three Ways to Sum to N (TypeScript)
+
+Three idiomatic implementations of `sum_to_n(n)`.
+
+| File             | Approach                            | Time     | Space    | When to use                                          |
+| ---------------- | ----------------------------------- | -------- | -------- | ---------------------------------------------------- |
+| `sumToN_iter`    | iterative accumulator               | **O(n)** | **O(1)** | clearest implementation; fine for any reasonable `n` |
+| `sumToN_formula` | closed-form Gauss `n*(n+1)/2`       | **O(1)** | **O(1)** | best — always prefer in production                   |
+| `sumToN_reduce`  | functional `Array.from(...).reduce` | **O(n)** | **O(n)** | composable but allocates; demonstrative              |
+
+All three handle:
+
+- `n = 0` → `0`
+- positive `n`
+- **negative `n`** (sums `-1 + -2 + … + n`)
+- non-integer / `NaN` input → `TypeError`
+
+The closed-form implementation also guards against `n` large enough that
+`n * (n+1)` would exceed `Number.MAX_SAFE_INTEGER`, throwing `RangeError`
+instead of returning a silently wrong number.
+
+## Run
+
+```bash
+pnpm install
+pnpm test          # vitest run
+pnpm typecheck     # tsc --noEmit
+```
+
+## Notes
+
+- Source: `sum_to_n.ts`
+- Tests : `sum_to_n.test.ts` — parametric, asserts all three impls agree on a battery of inputs
+- The three impls are exported as named exports so a consumer can pick whichever
+  suits their constraints.

src/problem4/package.json

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+{
+  "name": "problem4-sum-to-n",
+  "version": "1.0.0",
+  "private": true,
+  "description": "Three TypeScript implementations of sum_to_n with complexity analysis.",
+  "type": "module",
+  "scripts": {
+    "test": "vitest run",
+    "test:watch": "vitest",
+    "typecheck": "tsc --noEmit"
+  },
+  "devDependencies": {
+    "typescript": "^5.4.5",
+    "vitest": "^1.6.0"
+  },
+  "engines": {
+    "node": ">=20"
+  }
+}