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_dp.js

@@ -0,0 +1,41 @@
+/**
+ * File: climbing_stairs_dp.js
+ * Created Time: 2023-07-26
+ * Author: yuan0221 (yl1452491917@gmail.com)
+ */
+
+/* 爬楼梯：动态规划 */
+function climbingStairsDP(n) {
+    if (n == 1 || n == 2) return n;
+    // 初始化 dp 表，用于存储子问题的解
+    const dp = new Array(n + 1).fill(-1);
+    // 初始状态：预设最小子问题的解
+    dp[1] = 1;
+    dp[2] = 2;
+    // 状态转移：从较小子问题逐步求解较大子问题
+    for (let i = 3; i <= n; i++) {
+        dp[i] = dp[i - 1] + dp[i - 2];
+    }
+    return dp[n];
+}
+
+/* 爬楼梯：状态压缩后的动态规划 */
+function climbingStairsDPComp(n) {
+    if (n == 1 || n == 2) return n;
+    let a = 1,
+        b = 2;
+    for (let i = 3; i <= n; i++) {
+        const tmp = b;
+        b = a + b;
+        a = tmp;
+    }
+    return b;
+}
+
+/* Driver Code */
+const n = 9;
+let res = climbingStairsDP(n);
+console.log(`爬 ${n} 阶楼梯共有 ${res} 种方案`);
+res = climbingStairsDPComp(n);
+console.log(`爬 ${n} 阶楼梯共有 ${res} 种方案`);
+