2023-9-12 01背包问题

题目链接：

朴素版本

#include 
#include 

using namespace std;

const int N = 1010;

int n, m;
int f[N][N];
int v[N], w[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 - 1][j - v[i]] + w[i]);
        }
        
    cout << f[n][m] << endl;
    
    return 0;
}

优化版本

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