完全背包

一、思路

二、代码

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#include <bits/stdc++.h>
using namespace std;
int f[1010][1010];
int v[1010], w[1010];

int main() {
    int n, m;
    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 = 1; j <= m; j++)
            for (int k = 0; k <= j / v[i]; k++)
                f[i][j] = max(f[i][j], f[i - 1][j - k * v[i]] + k * w[i]);
                
    cout << f[n][m] << endl;
    return 0;
}

三、时间优化代码

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#include <bits/stdc++.h>
using namespace std;
int f[1010][1010];
int v[1010], w[1010];

int main() {
    int n, m;
    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 = 1; j <= m; j++) {
            f[i][j] = max(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;
}

四、空间优化代码

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#include <bits/stdc++.h>
using namespace std;
int f[1010];
int v[1010], w[1010];

int main() {
    int n, m;
    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;
}