transaction transaction transaction 最大费用最大流转化到SPFA最长路

Posted 2020-10-06 joeylee97

//当时比赛的时候没有想到可以用SPFA做，TLE！

Problem Description

Kelukin is a businessman. Every day, he travels around cities to do some business. On August 17th, in memory of a great man, citizens will read a book named "the Man Who Changed China". Of course, Kelukin wouldn‘t miss this chance to make money, but he doesn‘t have this book. So he has to choose two city to buy and sell. 
As we know, the price of this book was different in each city. It is ai yuan in it city. Kelukin will take taxi, whose price is 1yuan per km and this fare cannot be ignored.
There are n?1 roads connecting n cities. Kelukin can choose any city to start his travel. He want to know the maximum money he can get.

 

 

Input

The first line contains an integer T (1≤T≤10) , the number of test cases. 
For each test case:
first line contains an integer n (2≤n≤100000) means the number of cities;
second line contains n numbers, the ith number means the prices in ith city; (1≤Price≤10000) 
then follows n?1 lines, each contains three numbers x, y and z which means there exists a road between x and y, the distance is zkm (1≤z≤1000). 

 

 

Output

For each test case, output a single number in a line: the maximum money he can get.

 

 

Sample Input

1 4 10 40 15 30 1 2 30 1 3 2 3 4 10

 

 

Sample Output

8

 

 

Source

2017 ACM/ICPC Asia Regional Shenyang Online

 

 

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#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<sstream>
#include<algorithm>
#include<queue>
#include<deque>
#include<iomanip>
#include<vector>
#include<cmath>
#include<map>
#include<stack>
#include<set>
#include<functional>
#include<fstream>
#include<memory>
#include<list>
#include<string>
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;

//最大费用最大流 简化到SPFA上特例
const int MAXN = 100000 + 65;
struct edge
{
    int to, next, cost;
}E[MAXN << 2];
int head[MAXN], tot, n;
int val[MAXN];
bool vis[MAXN];
int lowcost[MAXN];
void init()
{
    memset(head, -1, sizeof(head));
    tot = 0;
}
void addedge(int u, int v, int d)
{
    E[tot].to = v;
    E[tot].cost = d;
    E[tot].next = head[u];
    head[u] = tot++;
}
int spfa(int st, int ed)
{
    memset(vis, false, sizeof(vis));
    memset(lowcost, 0, sizeof(lowcost));
    queue<int> q;
    q.push(st);
    vis[st] = true;
    lowcost[st] = 0;
    while (!q.empty())
    {
        int f = q.front();
        q.pop();
        vis[f] = false;
        for (int i = head[f]; i != -1; i = E[i].next)
        {
            int v = E[i].to, d = E[i].cost;
            if (lowcost[v] < lowcost[f] + d)
            {
                lowcost[v] = lowcost[f] + d;
                if (!vis[v])
                {
                    vis[v] = true;
                    q.push(v);
                }
            }
        }
    }
    return lowcost[ed];
}
int main()
{
    int T;
    scanf("%d", &T);
    while (T--)
    {
        init();
        scanf("%d", &n);
        for (int i = 1; i <= n; i++)
        {
            scanf("%d", &val[i]);
            addedge(0, i, val[i]);
            addedge(i, n + 1, -val[i]);
        }
        int u, v, d;
        for (int i = 0; i < n - 1; i++)
        {
            scanf("%d%d%d", &u, &v, &d);
            addedge(u, v, -d);
            addedge(v, u, -d);
        }
        printf("%d\n", spfa(0, n + 1));
    }
}