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