背包问题

01背包

#include <iostream>
#include <algorithm>
using namespace std;
#define N 1010
int dp[N];
int main()
{
    int n,m;
    cin >> n >> m;
    for(int i = 1; i<=n; i++)
    {
        int v,w;
        cin >> v >> w;
        for(int j = m; j>=v ; j--)
            dp[j]=max(dp[j],dp[j-v]+w);
    }
    cout << dp[m];
    return 0;
}

完全背包

#include <iostream>
#include <algorithm>

using namespace std;

int main()
{
    int dp[1010] ={0};
    int n,m;
    cin >> n >> m;
    for(int i = 1; i <= n; i++)
    {
        int v, w;
        cin >> v >> w;
        for(int j = v; j <= m; j++)
        {
            dp[j] = max(dp[j] , dp[j-v] + w);
        }
    }
    cout << dp[m] << endl;
    return 0;
}

多重背包

#include <iostream>
#include <algorithm>

using namespace std;

int main()
{
    int dp[110] = {0};
    int n, m;
    cin >> n >> m;
    for(int i = 1; i <= n; ++i)
    {
        int v,w,s;
        cin >> v >> w >> s;
        
        for(int i = 1; i <= s; i++)
            for(int j = m; j >= v*i; j--)
                dp[j] = max(dp[j] , dp[j-v] + w);
    }
    cout << dp[m] << endl;
    return 0;
}

// 二进制优化
#include<iostream>
#include<algorithm>
#define N 2010
using namespace std;

int main()
{
    int n,v;
    cin >> n >> v;
    int dp[N] = {0};
    for(int i = 0; i < n; i++)
    {
        int x,y,z;
        cin >> x >> y >> z;
        int s[N] = {0};
        int cnt = 0, tmp = z;
        for(int j = 1; j <= tmp; j *= 2)
        {
            if(z > j)
            {
                z -= j;
                s[cnt++] = j;
            }
            else
                break;
        }
        if(z)   s[cnt++] = z;
        for(int q = 0; q < cnt; q++)
        {
            if(s[q]* x > v) break;
            for(int j = v; j >= s[q]*x; j--)
                dp[j] = max(dp[j], dp[j - s[q]*x] + y*s[q]); 
        }
    }
    cout << dp[v];
    return 0;
}

分组背包

#include <iostream>
#include <algorithm>
#define N 110
using namespace std;

int main()
{
    int dp[N] = {0};
    int n, v;
    cin >>  n >> v;
    while(n--)
    {
        int s; cin >> s;
        for(int i = 0; i < s; i++)
        {
            int x,y; cin >> x >> y;
            for(int j = v; j >= x; j--)
                dp[j] = max(dp[j], dp[j - x] + y);
        }
    }
    cout << dp[v];
    return 0;
}