diff --git a/codes/javascript/chapter_dynamic_programming/climbing_stairs_backtrack.js b/codes/javascript/chapter_dynamic_programming/climbing_stairs_backtrack.js new file mode 100644 index 00000000..d8703e31 --- /dev/null +++ b/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`); + diff --git a/codes/javascript/chapter_dynamic_programming/climbing_stairs_dfs.js b/codes/javascript/chapter_dynamic_programming/climbing_stairs_dfs.js new file mode 100644 index 00000000..5e9cef34 --- /dev/null +++ b/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`); diff --git a/codes/javascript/chapter_dynamic_programming/climbing_stairs_dfs_mem.js b/codes/javascript/chapter_dynamic_programming/climbing_stairs_dfs_mem.js new file mode 100644 index 00000000..17860ed7 --- /dev/null +++ b/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`); diff --git a/codes/javascript/chapter_dynamic_programming/climbing_stairs_dp.js b/codes/javascript/chapter_dynamic_programming/climbing_stairs_dp.js new file mode 100644 index 00000000..fd0ccc9d --- /dev/null +++ b/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`); + diff --git a/codes/typescript/chapter_dynamic_programming/climbing_stairs_backtrack.ts b/codes/typescript/chapter_dynamic_programming/climbing_stairs_backtrack.ts new file mode 100644 index 00000000..1bb5734a --- /dev/null +++ b/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 {}; diff --git a/codes/typescript/chapter_dynamic_programming/climbing_stairs_dfs.ts b/codes/typescript/chapter_dynamic_programming/climbing_stairs_dfs.ts new file mode 100644 index 00000000..7f6de3ff --- /dev/null +++ b/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 {}; diff --git a/codes/typescript/chapter_dynamic_programming/climbing_stairs_dfs_mem.ts b/codes/typescript/chapter_dynamic_programming/climbing_stairs_dfs_mem.ts new file mode 100644 index 00000000..0820e8b5 --- /dev/null +++ b/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 {}; diff --git a/codes/typescript/chapter_dynamic_programming/climbing_stairs_dp.ts b/codes/typescript/chapter_dynamic_programming/climbing_stairs_dp.ts new file mode 100644 index 00000000..8dfdfb33 --- /dev/null +++ b/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 {};