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;
}