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38 lines
924 B
38 lines
924 B
/**
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* File: climbing_stairs_constraint_dp.cpp
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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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#include "../utils/common.hpp"
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/* 带约束爬楼梯：动态规划 */
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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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vector<vector<int>> dp(n + 1, vector<int>(3, 0));
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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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/* Driver Code */
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int main() {
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int n = 9;
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int res = climbingStairsConstraintDP(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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