54 lines
1.3 KiB
C++
54 lines
1.3 KiB
C++
/**
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* File: min_cost_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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/* 爬楼梯最小代价：动态规划 */
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int minCostClimbingStairsDP(vector<int> &cost) {
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int n = cost.size() - 1;
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if (n == 1 || n == 2)
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return cost[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] = cost[1];
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dp[2] = cost[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] = min(dp[i - 1], dp[i - 2]) + cost[i];
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}
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return dp[n];
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}
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/* 爬楼梯最小代价：空间优化后的动态规划 */
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int minCostClimbingStairsDPComp(vector<int> &cost) {
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int n = cost.size() - 1;
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if (n == 1 || n == 2)
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return cost[n];
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int a = cost[1], b = cost[2];
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for (int i = 3; i <= n; i++) {
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int tmp = b;
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b = min(a, tmp) + cost[i];
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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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vector<int> cost = {0, 1, 10, 1, 1, 1, 10, 1, 1, 10, 1};
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cout << "输入楼梯的代价列表为 ";
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printVector(cost);
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int res = minCostClimbingStairsDP(cost);
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cout << "爬完楼梯的最低代价为 " << res << endl;
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res = minCostClimbingStairsDPComp(cost);
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cout << "爬完楼梯的最低代价为 " << res << endl;
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return 0;
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}
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