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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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/* 爬樓梯：動態規劃 */
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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，用於儲存子問題的解
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const dp = new Array(n + 1).fill(-1);
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// 初始狀態：預設最小子問題的解
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dp[1] = 1;
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dp[2] = 2;
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// 狀態轉移：從較小子問題逐步求解較大子問題
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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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/* 爬樓梯：空間最佳化後的動態規劃 */
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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} 階樓梯共有 ${res} 種方案`);
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res = climbingStairsDPComp(n);
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console.log(`爬 ${n} 階樓梯共有 ${res} 種方案`);
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