Add climbing-stairs solution in TypeScript

Author: Jeehay28

climbing-stairs/Jeehay28.ts

@@ -0,0 +1,43 @@
+// Approach 2: DFS with Memoization
+// 🗓️ 2025-04-06
+// ⏳ Time Complexity: O(n)
+// 💾 Space Complexity: O(n)
+
+function climbStairs(n: number): number {
+  const memo = new Map<number, number>();
+
+  const dfs = (step: number) => {
+    if (step > n) return 0;
+    if (step === n) return 1;
+    if (memo.has(step)) return memo.get(step);
+
+    const result = dfs(step + 1) + dfs(step + 2);
+    memo.set(step, result);
+    return result;
+  };
+
+  return dfs(0);
+}
+
+
+// Approach 1: DFS (depth-first search)
+// ❌ Time Limit Exceeded (TLE) error!
+// ⏳ Time Complexity: O(2^n)
+// 💾 Space Complexity: O(n)
+// The maximum depth of the recursive call stack is n, because we go from step = 0 to step = n.
+
+// function climbStairs(n: number): number {
+//   // 1 -> 1 -> 1
+//   // 1 -> 2
+//   // 2 -> 1
+
+//   const dfs = (step: number) => {
+//     // reach the top
+//     if (step > n) return 0;
+//     if (step === n) return 1;
+
+//     return dfs(step + 1) + dfs(step + 2);
+//   };
+
+//   return dfs(0);
+// }