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49 lines
1.3 KiB
49 lines
1.3 KiB
/**
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* File: climbing_stairs_dp.java
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* Created Time: 2023-06-30
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* Author: krahets (krahets@163.com)
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*/
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package chapter_dynamic_programming;
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public class climbing_stairs_dp {
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/* 爬樓梯：動態規劃 */
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public static int climbingStairsDP(int n) {
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if (n == 1 || n == 2)
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return n;
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// 初始化 dp 表，用於儲存子問題的解
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int[] dp = new int[n + 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 (int 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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public static int climbingStairsDPComp(int n) {
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if (n == 1 || n == 2)
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return n;
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int a = 1, b = 2;
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for (int i = 3; i <= n; i++) {
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int 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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public static void main(String[] args) {
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int n = 9;
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int res = climbingStairsDP(n);
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System.out.println(String.format("爬 %d 階樓梯共有 %d 種方案", n, res));
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res = climbingStairsDPComp(n);
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System.out.println(String.format("爬 %d 階樓梯共有 %d 種方案", n, res));
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}
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}
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