feature: solve problem4 & 5 & 6

.gitignore

@@ -0,0 +1 @@
+node_modules/

readme.md

@@ -5,6 +5,6 @@ Please submit your application along with the solutions attached or linked.
 
 It is important that you minimally attempt the problems, even if you do not arrive at a working solution.
 
-## Submission ##
+## Submission
 You can either provide a link to an online repository, attach the solution in your application, or whichever method you prefer.
 We're cool as long as we can view your solution without any pain.

src/problem4/README.md

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+# Problem 4: Sum to N
+
+Three ways to calculate the sum of integers from 1 to n.
+
+## Solutions
+
+**A. Math formula** — O(1) time, O(1) space  
+Uses the formula `n * (n + 1) / 2`
+
+**B. Iterative** — O(n) time, O(1) space  
+Loops from 1 to n, accumulating the sum
+
+**C. Recursive** — O(n) time, O(n) space  
+Calls itself with `n-1` until reaching the base case
+
+## Test
+
+```bash
+npx tsx src/problem4/index.test.ts
+```

src/problem4/index.test.ts

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+import { sum_to_n_a, sum_to_n_b, sum_to_n_c } from "./index";
+
+function assertEquals(actual: number, expected: number, name: string) {
+  if (actual !== expected) {
+    throw new Error(`${name}: expected ${expected}, got ${actual}`);
+  }
+  console.log(`${name}: PASS`);
+}
+
+assertEquals(sum_to_n_a(5), 15, "sum_to_n_a(5)");
+assertEquals(sum_to_n_a(10), 55, "sum_to_n_a(10)");
+assertEquals(sum_to_n_a(0), 0, "sum_to_n_a(0)");
+
+assertEquals(sum_to_n_b(5), 15, "sum_to_n_b(5)");
+assertEquals(sum_to_n_b(10), 55, "sum_to_n_b(10)");
+assertEquals(sum_to_n_b(0), 0, "sum_to_n_b(0)");
+
+assertEquals(sum_to_n_c(5), 15, "sum_to_n_c(5)");
+assertEquals(sum_to_n_c(10), 55, "sum_to_n_c(10)");
+assertEquals(sum_to_n_c(0), 0, "sum_to_n_c(0)");
+
+console.log("All tests passed!");

src/problem4/index.ts

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+/**
+ * 1st solution
+ * O(1) time, O(1) space
+ */
+export const sum_to_n_a = (n: number): number => {
+  return (n * (n + 1)) / 2;
+};
+
+/**
+ * 2nd solution: Iterative
+ * O(n) time, O(1) space
+ */
+export const sum_to_n_b = (n: number): number => {
+  let sum = 0;
+
+  for (let i = 1; i <= n; i++) {
+    sum += i;
+  }
+
+  return sum;
+};
+
+/**
+ * 3rd solution: Recursive
+ * O(n) time, O(n) space
+ */
+export const sum_to_n_c = (n: number): number => {
+  if (n <= 1) {
+    return n;
+  }
+
+  return n + sum_to_n_c(n - 1);
+};

src/problem5/.env.example

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+MONGODB_URI=mongodb://localhost:27017/99problem5
+PORT=3000
+X_API_KEY=your-secret-api-key