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31 lines
886 B
31 lines
886 B
/**
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* File: climbing_stairs_constraint_dp.js
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* Created Time: 2023-08-23
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* Author: Gaofer Chou (gaofer-chou@qq.com)
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*/
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/* 带约束爬楼梯：动态规划 */
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function climbingStairsConstraintDP(n) {
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if (n === 1 || n === 2) {
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return 1;
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}
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// 初始化 dp 表，用于存储子问题的解
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const dp = Array.from(new Array(n + 1), () => new Array(3));
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// 初始状态：预设最小子问题的解
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dp[1][1] = 1;
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dp[1][2] = 0;
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dp[2][1] = 0;
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dp[2][2] = 1;
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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][1] = dp[i - 1][2];
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dp[i][2] = dp[i - 2][1] + dp[i - 2][2];
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}
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return dp[n][1] + dp[n][2];
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}
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/* Driver Code */
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const n = 9;
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const res = climbingStairsConstraintDP(n);
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console.log(`爬 ${n} 阶楼梯共有 ${res} 种方案`);
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