朴素
#include<iostream> #include<algorithm> using namespace std ; const int N=1010; int n,m; int v[N],w[N]; int f[N][N]; int main() { cin>>n>>m;//n个物品 最大体积位m for(int i=1; i<=n; i++) cin>>v[i]>>w[i]; for(int i=1; i<=n; i++) for(int j=0; j<=m; j++) for(int k=0; k*v[i]<=j; k++)//选k个第i个物品 f[i][j]=max(f[i][j],f[i-1][j-v[i]*k]+k*w[i]); cout<<f[n][m]<<endl; return 0; }
优化二维
//01背包从i-1转移过来 而完全背包是从第
i层转移过来 #include <iostream> #include <algorithm> using namespace std; const int N = 1010; int n, m; int v[N], w[N]; int f[N][N]; int main() { cin >> n >> m; for (int i = 1; i <= n; i ++ ) cin >> v[i] >> w[i]; for (int i = 1; i <= n; i ++ ) for (int j = 0; j <= m; j ++ ) for(int k=0; k*v[i]<=j; k++) f[i][j] = max(f[i][j], f[i-1][j - v[i]*k] + w[i]*k); cout << f[n][m] << endl; return 0; }
终极一维
//一维 #include <iostream> #include <algorithm> using namespace std; const int N = 1010; int n, m; int v[N], w[N]; int f[N]; int main() { cin >> n >> m;//n是数量,m是体积 for (int i = 1; i <= n; i ++ ) cin >> v[i] >> w[i]; for (int i = 1; i <= n; i ++ ) for (int j = v[i]; j <= m; j ++ ) f[j] = max(f[j], f[j - v[i]] + w[i]); cout << f[m] << endl; return 0; }