Treasure Hunt I

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Time Limit: 2 Seconds      Memory Limit: 65536 KB

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Akiba is a dangerous country since a bloodsucker living there. Sometimes the bloodsucker will appear and kill everyone who isn‘t at his hometown. One day, a brave person named CC finds a treasure map, and he wants to get as much as possible.

Akiba consists of n towns and n-1 roads. There is a way from each town to any other. Each town contains some treasure valuesV_i. CC starts from town k(his hometown), at day 0. Afterm days, the bloodsucker will appear and CC would be killed if he hasn‘t been back yet, it means CC hasm days for hunting the treasure at most. It takes CC T_i days to move from one town to another neighbour town.(Two towns called neighbour if they are the endpoint of one road.) You can assume CC will get the treasure immediately as he arrives at that town. CC wants to obtain as much value as possible, keeping him alive at the same time.

Input

There are multiple cases, about 50 cases.
The first line of each case contains an integer n, indicating there are n towns.
The following line describe the treasure‘s value in each town. "V₁ V₂ ...V_n". V_i is the value of the treasure in ith town. Each value is separated by one blank.
The next n-1 lines describe the n-1 roads in Akiba. "i j T_i" Means theith town and the jth town are endpoints of that road. It takes T_i days to get through this road.
The last line has two integer k and m as described above.

1<=n<=100, 0<=V_i<=1000 , 1<=T_i<=10
1<=k<=n, 1<=m<=200
All the inputs are integers.

Output

Just output the max value CC can get, and you should keep CC alive after m days.

Sample Input

2
1 3
1 2 1
1 2
2
1 3
2 1 1
2 1
2
3 3
1 2 1
2 5

Sample Output

4
3
6

Hint

Sample 1: CC can go to town 2 and return at day 2.
Sample 2: CC can‘t come back within 1 day. So he can only take the treasure in his hometown.
Sample 3: CC only need 2 days to collect all the treasure.

树形dp,　设dp[u][i]表示用ｉ天时间去访问以u为根的子树并且最后回到u，能够得到的最多的宝藏
dp[u][i] = max(dp[v][ j - cost[u, v] ] + dp[u][i - j] + val[v]);

/*************************************************************************
    > File Name: zoj3626.cpp
    > Author: ALex
    > Mail: 405045132@qq.com 
    > Created Time: 2015年01月02日 星期五 14时34分00秒
 ************************************************************************/

#include <map>
#include <set>
#include <queue>
#include <stack>
#include <vector>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>

using namespace std;

int dp[110][220];
int val[110], head[110];
int n, tot, m, k;

struct node
{
	int weight;
	int next;
	int to;
}edge[220];

void addedge(int from, int to, int weight)
{
	edge[tot].weight = weight;
	edge[tot].to = to;
	edge[tot].next = head[from];
	head[from] = tot++;
}

void dfs(int u, int fa)
{
	for (int i = head[u]; ~i; i = edge[i].next)
	{
		int v = edge[i].to;
		if (v == fa)
		{
			continue;
		}
		dfs(v, u);
		for (int j = m; j >= 0; --j)
		{
			for (int k = 2 * edge[i].weight; k <= j; ++k)
			{
				dp[u][j] = max(dp[u][j], dp[v][k - 2 * edge[i].weight] + dp[u][j - k] + val[v]);
			}
		}
	}
}

int main()
{
	int u, v, w;
	while (~scanf("%d", &n))
	{
		tot = 0;
		memset (head, -1, sizeof(head));
		memset (dp, 0, sizeof(dp));
		for (int i = 1; i <= n; ++i)
		{
			scanf("%d", &val[i]);
		}
		for (int i = 1; i <= n - 1; ++i)
		{
			scanf("%d%d%d", &u, &v, &w);
			addedge(u, v, w);
			addedge(v, u, w);
		}
		scanf("%d%d", &k, &m);
		dfs(k, -1);
		printf("%d\n", dp[k][m] + val[k]);
	}
	return 0;
}

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