feat(chapter_dynamic_programming): Add js and ts codes for chapter 14.1 (#658)

* feat(chapter_dynamic_programming): Add js and ts codes for chapter 14.1

* style(chapter_dynamic_programming): format code

* refactor(chapter_dynamic_programming): remove main definition and add type

codes/javascript/chapter_dynamic_programming/climbing_stairs_backtrack.js

@@ -0,0 +1,35 @@
+/**
+ * File: climbing_stairs_backtrack.js
+ * Created Time: 2023-07-26
+ * Author: yuan0221 (yl1452491917@gmail.com)
+ */
+
+/* 回溯 */
+function backtrack(choices, state, n, res) {
+    // 当爬到第 n 阶时，方案数量加 1
+    if (state === n) res.set(0, res.get(0) + 1);
+    // 遍历所有选择
+    for (choice of choices) {
+        // 剪枝：不允许越过第 n 阶
+        if (state + choice > n) break;
+        // 尝试：做出选择，更新状态
+        backtrack(choices, state + choice, n, res);
+        // 回退
+    }
+}
+
+/* 爬楼梯：回溯 */
+function climbingStairsBacktrack(n) {
+    const choices = [1, 2]; // 可选择向上爬 1 或 2 阶
+    const state = 0; // 从第 0 阶开始爬
+    const res = new Map();
+    res.set(0, 0); // 使用 res[0] 记录方案数量
+    backtrack(choices, state, n, res);
+    return res.get(0);
+}
+
+/* Driver Code */
+const n = 9;
+const res = climbingStairsBacktrack(n);
+console.log(`爬 ${n} 阶楼梯共有 ${res} 种方案`);
+