二维

#include <iostream>
using namespace std;
const int N = 1010;
int weight[N], value[N], f[N][N];
int main(){
    int n, bag;
    cin >> n >> bag;
    for(int i = 1; i <= n; i ++ )   cin >> weight[i] >> value[i];
    for(int i = 1; i <= n; i ++ ){
        for(int j = 1; j <= bag; j ++ ){    # 顺序无关，可以从1 - bag，也可以从bag - 1，二维所以状态均存储了
            f[i][j] = f[i - 1][j];
            if(weight[i] <= j)  f[i][j] = max(f[i-1][j], f[i-1][j - weight[i]] + value[i]);
        }
    }
    cout << f[n][bag] << endl;
    return 0;
}

一维优化

不同的地方在于枚举时候的顺序，必须从bag开始

#include <iostream>
using namespace std;
const int N = 1010;
int weight[N], value[N], f[N];
int main(){
    int n, bag;
    cin >> n >> bag;
    for(int i = 1; i <= n; i ++ ){
        cin >> weight[i] >> value[i];
    }
    for(int i = 1; i <= n; i ++ ){
        for(int j = bag; j >= weight[i]; j -- ){
            f[j] = max(f[j], f[j - weight[i]] + value[i]);
        }
    }
    cout << f[bag] << endl;
    return 0;
}