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49 lines
1.1 KiB
C++
49 lines
1.1 KiB
C++
/**
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* File: climbing_stairs_dp.cpp
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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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#include "../utils/common.hpp"
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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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vector<int> dp(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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/* Driver Code */
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int main() {
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int n = 9;
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int res = climbingStairsDP(n);
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cout << "爬 " << n << " 阶楼梯共有 " << res << " 种方案" << endl;
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res = climbingStairsDPComp(n);
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cout << "爬 " << n << " 阶楼梯共有 " << res << " 种方案" << endl;
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return 0;
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}
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