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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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/* 爬楼梯：动态规划 */
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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，用于存储子问题的解
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int[] dp = new int[n + 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 (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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/* 爬楼梯：空间优化后的动态规划 */
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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 阶楼梯共有 %d 种方案", n, res));
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res = climbingStairsDPComp(n);
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System.out.println(String.format("爬 %d 阶楼梯共有 %d 种方案", n, res));
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}
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}
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