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50 lines
1.3 KiB
50 lines
1.3 KiB
/**
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* File: climbing_stairs_dp.cs
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* Created Time: 2023-06-30
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* Author: hpstory (hpstory1024@163.com)
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*/
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namespace hello_algo.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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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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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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[Test]
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public void Test() {
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int n = 9;
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int res = ClimbingStairsDP(n);
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Console.WriteLine($"爬 {n} 阶楼梯共有 {res} 种方案");
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res = ClimbingStairsDPComp(n);
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Console.WriteLine($"爬 {n} 阶楼梯共有 {res} 种方案");
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}
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}
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