【题解】p1064 金明的预算方案

总结：
1.尝试设计多个状态转移方程

2.这道题记录分组的思想与分组背包由异曲同工之妙

#include<bits/stdc++.h>
using namespace std;
int dp[32005], val[65], w[65], sum[65], c[65][20], p[65];
int n, m;
int main()
{
    cin >> n >> m;
    for(int i = 1; i <= m; i++)
    {
        cin >> w[i] >> val[i] >> p[i];        
        if(p[i] != 0)
        {
            sum[p[i]]++;
            c[p[i]][sum[p[i]]] = i;
        }
    }
    for(int i = 1; i <= m; i++)
        for(int j = n; j >= 0; j--)
            if(p[i] == 0) 
            {
                if(j >= w[i]) dp[j] = max(dp[j], dp[j-w[i]]+val[i]*w[i]);
                if(sum[i] > 0)
                {
                    if(sum[i] == 1)
                    {
                        if(j >= w[i]+w[c[i][1]])
                            dp[j] = max(dp[j], dp[j-w[i]-w[c[i][1]]]+val[i]*w[i]+val[c[i][1]]*w[c[i][1]]);
                    }
                    if(sum[i] == 2)
                    {
                        if(j >= w[i]+w[c[i][1]])
                            dp[j] = max(dp[j], dp[j-w[i]-w[c[i][1]]]+val[i]*w[i]+val[c[i][1]]*w[c[i][1]]);
                        if(j >= w[i]+w[c[i][2]])
                            dp[j] = max(dp[j], dp[j-w[i]-w[c[i][2]]]+val[i]*w[i]+val[c[i][2]]*w[c[i][2]]);
                        if(j >= w[i]+w[c[i][1]]+w[c[i][2]])
                            dp[j] = max(dp[j], dp[j-w[i]-w[c[i][1]]-w[c[i][2]]]+val[i]*w[i]+val[c[i][1]]*w[c[i][1]]+val[c[i][2]]*w[c[i][2]]);
                    }
                }
            }
    cout << dp[n];
    return 0;
}