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37 lines
1.0 KiB
37 lines
1.0 KiB
/**
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* File: climbing_stairs_constraint_dp.java
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* Created Time: 2023-07-01
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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_constraint_dp {
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/* 带约束爬楼梯：动态规划 */
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static int climbingStairsConstraintDP(int 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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int[][] dp = new int[n + 1][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 (int 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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public static void main(String[] args) {
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int n = 9;
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int res = climbingStairsConstraintDP(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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