【算法】完全背包

三重循环

#include <iostream>

using namespace std;

const int N = 1010;

int n, m;
int v[N], w[N];
int f[N][N];

// TLE
int main() {

    cin >> n >> m;
    for (int i = 1; i <= n; i++) cin >> v[i] >> w[i];

    for (int i = 1; i <= n; i++)  // 先循环物品
        for (int j = 0; j <= m; j++)  // 再循环容量
            for (int k = 0; k * v[i] <= j; k++)  // 最后循环决策
                f[i][j] = max(f[i][j], f[i - 1][j - k * v[i]] + k * w[i]);
    cout << f[n][m] << endl;
    return 0;
}

二维数组

#include <iostream>

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++) {
            f[i][j] = f[i - 1][j];
            if (j >= v[i]) f[i][j] = max(f[i][j], f[i][j - v[i]] + w[i]);
        }
    cout << f[n][m] << endl;
    return 0;
}

一维数组

#include <iostream>

using namespace std;

const int N = 1010;

int n, m;
int v[N], w[N];
int f[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 = v[i]; j <= m; j++)
            f[j] = max(f[j], f[j - v[i]] + w[i]);
    cout << f[m] << endl;
    return 0;
}