POJ 1797 Heavy Transportation (Prime 最大生成树)

Heavy Transportation

Time Limit: 3000MS		Memory Limit: 30000K
Total Submissions: 16701		Accepted: 4384

Description

Background 
Hugo Heavy is happy. After the breakdown of the Cargolifter project he can now expand business. But he needs a clever man who tells him whether there really is a way from the place his customer has build his giant steel crane to the place where it is needed on which all streets can carry the weight. 
Fortunately he already has a plan of the city with all streets and bridges and all the allowed weights.Unfortunately he has no idea how to find the the maximum weight capacity in order to tell his customer how heavy the crane may become. But you surely know. 

Problem 
You are given the plan of the city, described by the streets (with weight limits) between the crossings, which are numbered from 1 to n. Your task is to find the maximum weight that can be transported from crossing 1 (Hugo's place) to crossing n (the customer's place). You may assume that there is at least one path. All streets can be travelled in both directions.

Input

The first line contains the number of scenarios (city plans). For each city the number n of street crossings (1 <= n <= 1000) and number m of streets are given on the first line. The following m lines contain triples of integers specifying start and end crossing of the street and the maximum allowed weight, which is positive and not larger than 1000000. There will be at most one street between each pair of crossings.

Output

The output for every scenario begins with a line containing "Scenario #i:", where i is the number of the scenario starting at 1. Then print a single line containing the maximum allowed weight that Hugo can transport to the customer. Terminate the output for the scenario with a blank line.

Sample Input

1
3 3
1 2 3
1 3 4
2 3 5

Sample Output

Scenario #1:
4

Source

TUD Programming Contest 2004, Darmstadt, Germany

题意：求最大能够承受的重量，使得1~N的每条路径都能承受该重量

从1到N求最大生成树，我们不需要理会其他点，只要1能到 N 的最大生成树得到后，返回生成树的路径，遍历生成树边的权值，求出最大生成树的最小边即可。

#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
const int maxn=1001;
const int oo=10000000;
int dis[maxn],n,m,map[maxn][maxn];
int pre[maxn];
bool vis[maxn];
void build()
{
    int u,v,c;
    memset(map,0,sizeof(map));
    while(m--)
    {
        scanf("%d%d%d",&u,&v,&c);
        map[u][v]=map[v][u]=c;
    }
}
void prime()
{
    int i,j,k,mn;
    for(i=1; i<=n; i++) pre[i]=1;
    for(i=2; i<=n; i++)
    {
        dis[i]=map[1][i];
        vis[i]=0;
    }
    vis[1]=1;
    dis[1]=0;
    for(i=0; i<n-1; i++)
    {
        k=1,mn=0;
        for(j=2; j<=n; j++)
            if(!vis[j]&&dis[j]>mn)
                k=j,mn=dis[j];
        vis[k]=1;
        if(k==n) return ;
        for(j=2; j<=n; j++)
            if(!vis[j]&&map[k][j]>0&&map[k][j]>dis[j])
            {
                dis[j]=map[k][j];
                pre[j]=k;
            }
    }
}
int main()
{
    int ca,t=1,u,v;
    scanf("%d",&ca);
    while(ca--)
    {
        scanf("%d%d",&n,&m);
        build();
        prime();
        int mn=oo;
        u=pre[n];
        v=n;
        while(v!=1)
        {
            mn=min(mn,map[u][v]);
            v=u;
            u=pre[u];
        }
        printf("Scenario #%d:\n",t++);
        printf("%d\n\n",mn);
    }
    return 0;
}