hihoCoder 1043 完全背包

来源：互联网发布：淘宝名字大全男生编辑：程序博客网时间：2024/06/06 01:51

可以直接在0-1背包的基础上进行扩展，得到一个比较naive的解法

// hiho1043.cpp : Defines the entry point for the console application.//#include<iostream>#include<vector>#include<algorithm>#include<fstream>//#define DEBUGusing namespace std;int main(){#ifdef DEBUGifstream cin("E:\\cppfiles\\input.txt");#endifint n, m;cin >> n >> m;vector<int> need(n + 1, 0);vector<int> value(n + 1, 0);for (int i = 1; i <= n; ++i){cin >> need[i] >> value[i];}vector<vector<int> > dp(n + 1, vector<int>(m + 1, 0));for (int i = 1; i <= n; ++i){for (int j = 1; j <= m; ++j){if (j < need[i]){dp[i][j] = dp[i - 1][j];}else{int cnt = 1;int tmp = 0;while (j - cnt*need[i] >= 0){tmp = max(tmp, dp[i - 1][j - cnt*need[i]]+cnt*value[i]);cnt++;}dp[i][j] = max(dp[i - 1][j], tmp);}}}cout << dp[n][m] << endl;return 0;}

注意观察可以得到，其实在每次计算i物品拿j件时，不需要从1开始循环，只要比较下拿j-1时即可，因为之前已经有计算好的结果了，如果从1开始循环，就进行了多余的重复计算。最后再进行空间的优化即可得到如下代码。

// hiho1043.cpp : Defines the entry point for the console application.//#include<iostream>#include<vector>#include<algorithm>#include<fstream>//#define DEBUGusing namespace std;int main(){#ifdef DEBUGifstream cin("E:\\cppfiles\\input.txt");#endifint n, m;cin >> n >> m;vector<int> need(n + 1, 0);vector<int> value(n + 1, 0);for (int i = 1; i <= n; ++i){cin >> need[i] >> value[i];}vector<int> dp(m + 1, 0);for (int i = 1; i <= n; ++i){for (int j = need[i]; j <= m; ++j){dp[j] = max(dp[j], dp[j-need[i]]+value[i]);}}cout << dp[m] << endl;return 0;}

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