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`);
+

codes/javascript/chapter_dynamic_programming/climbing_stairs_dfs.js

@@ -0,0 +1,24 @@
+/**
+ * File: climbing_stairs_dfs.js
+ * Created Time: 2023-07-26
+ * Author: yuan0221 (yl1452491917@gmail.com)
+ */
+
+/* 搜索 */
+function dfs(i) {
+    // 已知 dp[1] 和 dp[2] ，返回之
+    if (i == 1 || i == 2) return i;
+    // dp[i] = dp[i-1] + dp[i-2]
+    const count = dfs(i - 1) + dfs(i - 2);
+    return count;
+}
+
+/* 爬楼梯：搜索 */
+function climbingStairsDFS(n) {
+    return dfs(n);
+}
+
+/* Driver Code */
+const n = 9;
+const res = climbingStairsDFS(n);
+console.log(`爬 ${n} 阶楼梯共有 ${res} 种方案`);

codes/javascript/chapter_dynamic_programming/climbing_stairs_dfs_mem.js

@@ -0,0 +1,30 @@
+/**
+ * File: climbing_stairs_dfs_mem.js
+ * Created Time: 2023-07-26
+ * Author: yuan0221 (yl1452491917@gmail.com)
+ */
+
+/* 记忆化搜索 */
+function dfs(i, mem) {
+    // 已知 dp[1] 和 dp[2] ，返回之
+    if (i == 1 || i == 2) return i;
+    // 若存在记录 dp[i] ，则直接返回之
+    if (mem[i] != -1) return mem[i];
+    // dp[i] = dp[i-1] + dp[i-2]
+    const count = dfs(i - 1, mem) + dfs(i - 2, mem);
+    // 记录 dp[i]
+    mem[i] = count;
+    return count;
+}
+
+/* 爬楼梯：记忆化搜索 */
+function climbingStairsDFSMem(n) {
+    // mem[i] 记录爬到第 i 阶的方案总数，-1 代表无记录
+    const mem = new Array(n + 1).fill(-1);
+    return dfs(n, mem);
+}
+
+/* Driver Code */
+const n = 9;
+const res = climbingStairsDFSMem(n);
+console.log(`爬 ${n} 阶楼梯共有 ${res} 种方案`);

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`);
+

codes/typescript/chapter_dynamic_programming/climbing_stairs_backtrack.ts

@@ -0,0 +1,41 @@
+/**
+ * File: climbing_stairs_backtrack.ts
+ * Created Time: 2023-07-26
+ * Author: yuan0221 (yl1452491917@gmail.com)
+ */
+
+/* 回溯 */
+function backtrack(
+    choices: number[],
+    state: number,
+    n: number,
+    res: Map<0, any>
+): void {
+    // 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 (let 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: number): number {
+    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`);
+
+export {};

codes/typescript/chapter_dynamic_programming/climbing_stairs_dfs.ts

@@ -0,0 +1,26 @@
+/**
+ * File: climbing_stairs_dfs.ts
+ * Created Time: 2023-07-26
+ * Author: yuan0221 (yl1452491917@gmail.com)
+ */
+
+/* 搜索 */
+function dfs(i: number): number {
+    // 已知 dp[1] 和 dp[2] ，返回之
+    if (i == 1 || i == 2) return i;
+    // dp[i] = dp[i-1] + dp[i-2]
+    const count = dfs(i - 1) + dfs(i - 2);
+    return count;
+}
+
+/* 爬楼梯：搜索 */
+function climbingStairsDFS(n: number): number {
+    return dfs(n);
+}
+
+/* Driver Code */
+const n = 9;
+const res = climbingStairsDFS(n);
+console.log(`爬 ${n} 阶楼梯共有 ${res} 种方案`);
+
+export {};

codes/typescript/chapter_dynamic_programming/climbing_stairs_dfs_mem.ts

@@ -0,0 +1,32 @@
+/**
+ * File: climbing_stairs_dfs_mem.ts
+ * Created Time: 2023-07-26
+ * Author: yuan0221 (yl1452491917@gmail.com)
+ */
+
+/* 记忆化搜索 */
+function dfs(i: number, mem: number[]): number {
+    // 已知 dp[1] 和 dp[2] ，返回之
+    if (i == 1 || i == 2) return i;
+    // 若存在记录 dp[i] ，则直接返回之
+    if (mem[i] != -1) return mem[i];
+    // dp[i] = dp[i-1] + dp[i-2]
+    const count = dfs(i - 1, mem) + dfs(i - 2, mem);
+    // 记录 dp[i]
+    mem[i] = count;
+    return count;
+}
+
+/* 爬楼梯：记忆化搜索 */
+function climbingStairsDFSMem(n: number): number {
+    // mem[i] 记录爬到第 i 阶的方案总数，-1 代表无记录
+    const mem = new Array(n + 1).fill(-1);
+    return dfs(n, mem);
+}
+
+/* Driver Code */
+const n = 9;
+const res = climbingStairsDFSMem(n);
+console.log(`爬 ${n} 阶楼梯共有 ${res} 种方案`);
+
+export {};

codes/typescript/chapter_dynamic_programming/climbing_stairs_dp.ts

@@ -0,0 +1,42 @@
+/**
+ * File: climbing_stairs_dp.ts
+ * Created Time: 2023-07-26
+ * Author: yuan0221 (yl1452491917@gmail.com)
+ */
+
+/* 爬楼梯：动态规划 */
+function climbingStairsDP(n: number): number {
+    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: number): number {
+    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`);
+
+export {};