2023-9-12 完全背包问题

题目链接：完全背包问题

初版(时间复杂度拉满)

#include 
#include 

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 - k * v[i]] + k * w[i]);
    cout << f[n][m] << endl;

    return 0;
}

改良版

#include 
#include 

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;
}

最终版

#include 
#include 

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;
}