poj 2152 FIre ( tree_dp )

題意：有一棵n個點到樹，在結點上建立一些消防站，使每個結點i離最近的一個消防站到距離小於等於D[i], 每個結點建立消防站的花費爲W[i];

解法看論文 ：http://wenku.baidu.com/view/82124f74f242336c1eb95e44.html

dp[i][j] 表示在以i爲根結點的樹中建立一些消防站，且結點i依賴的消防站建立在結點j上

best[i] 表示以i爲根結點的樹中滿足題意的最小花費

#include<iostream>
#include<cstring>
#include<string>
#include<cstdio>
#include<stdio.h>
#include<algorithm>
#include<cmath>
#include<set>
#include<map>
#include<queue>
using namespace std;


#define inf 0x3f3f3f3f
#define eps 1e-9
#define mod 1000000007
#define FOR(i,s,t) for(int i = s; i < t; ++i )
#define REP(i,s,t) for( int i = s; i <= t; ++i )
#define LL unsigned long long
#define ULL unsigned long long
#define pii pair<int,int>
#define MP make_pair
#define lson id << 1 , l , m
#define rson id << 1 | 1 , m + 1 , r 
#define maxn ( 1000+100 )
#define maxe ( 2000+10 )
#define mxn 20000


int fst[maxn], vv[maxe], cost[maxe], nxt[maxe], ec;

void add ( int u, int v, int w ) {
	vv[ec] = v, cost[ec] = w;
	nxt[ec] =fst[u];
	fst[u] = ec++;

}

int dis[maxn];
void getdis ( int u, int fa ) {
	for( int i = fst[u]; i != -1; i = nxt[i] ) {
		int v = vv[i];
		if( v == fa ) continue;
		dis[v] = dis[u] + cost[i];
		getdis( v, u ) ;
	}
}

int dp[maxn][maxn], best[maxn];
int n, m;
int W[maxn], D[maxn];
void dfs ( int u, int fa ) {
	for( int i = fst[u]; i != -1; i = nxt[i] ) {
		int v = vv[i];
		if( v == fa ) continue;
		dfs ( v, u );
	}
	dis[u] = 0;
	getdis( u, -1 );
	best[u] = inf;
	for( int j = 1; j <= n; ++j ) {
		if( dis[j] > D[u] ) dp[u][j] = inf;
		else {
			dp[u][j] = W[j];
			for( int i = fst[u]; i != -1; i = nxt[i] ) {
				int v = vv[i];
				if( v == fa ) continue;
				dp[u][j] += min ( best[v], dp[v][j] - W[j] );
			}
			best[u] = min( dp[u][j], best[u] );
		}
	}
}

int main () {
	int T;
	//freopen( "in.in", "r", stdin );
	scanf("%d", &T );
	while( T-- ) {
		scanf("%d", &n );
		for( int i = 1; i <= n; ++i )
			scanf("%d", &W[i] );
		for( int i = 1; i <= n; ++i )
			scanf("%d", &D[i] );
		int u, v, w;
		memset( fst, -1, sizeof( fst ) );
		ec = 0;
		for( int i = 1; i < n; ++i ) {
			scanf("%d%d%d", &u, &v, &w );
			add( u, v, w );
			add( v, u, w );
		}
		dfs ( 1 , -1 );
		printf("%d\n", best[1] );
	}
	return 0;
}