Vijos P1313 金明的预算方案（树形DP）

思路：

树形DP，和选课那题一模一样。有依赖的背包，也叫做泛化背包。

 

#include <iostream>

#include <cstdio>

#include <algorithm>

using namespace std;



const int MAXD = 3210;

const int MAXN = 64;



int dp[MAXN][MAXD];

int val[MAXN], deg[MAXN], pre[MAXN];



void treedp(int u, int vol, int n)

{

    if (!vol)

        return ;



    for (int i = 1; i <= n; ++i)

    {

        if (pre[i] == u)

        {

            for (int v = 0; v <= vol; ++v)

                dp[i][v] = dp[u][v];



            treedp(i, vol - val[i], n);



            for (int v = vol; v >= val[i]; --v)

                dp[u][v] = max(dp[u][v], dp[i][v - val[i]] + val[i] * deg[i]);

        }

    }

}



int main()

{

    int n, vol;

    while (scanf("%d %d", &vol, &n) != EOF)

    {

        vol /= 10;

        for (int i = 1; i <= n; ++i)

            scanf("%d %d %d", &val[i], &deg[i], &pre[i]), val[i] /= 10;



        for (int v = 0; v <= vol; ++v)

            dp[0][v] = 0;



        treedp(0, vol, n);

        printf("%d\n", dp[0][vol] * 10);

    }

    return 0;

}