uva 10099(最大生成树+搜索)

题意：给一个源点一个终点求一条路径是路径上最小的那条边最大。

思路：先求最大生成树，然后从源点搜索到终点求权值最小的边即可。

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#define INF 0x7fffffff
#define eps 1E-8
#define LEN 110

using namespace std;

int n, m, top, vis[LEN*LEN], CC = 1;

struct Edge{
    int a, b, val;
    void make_edge(int _a, int _b, int _v){
        a = _a, b = _b; val = _v;
    }
}edge[LEN*LEN];
bool cmp(Edge a, Edge b){return a.val>b.val;}

//UFSet
int parent[LEN];

void init(){for(int i=0; i<LEN; i++)parent[i] = i;}
int Find(int x){return parent[x]==x?x:Find(parent[x]);}
void Union(int a, int b){int pa=Find(a), pb=Find(b);if(pa!=pb)parent[pa]=pb;}

//kruskal
int Kruskal()
{
    memset(vis, 0 ,sizeof vis);
    init();
    int cnt = 0, ret = 0;;
    for(int i=0; i<top; i++){
        if(Find(edge[i].a)!=Find(edge[i].b)){
            cnt++;
            Union(edge[i].a, edge[i].b);
            ret+=edge[i].val;
            vis[i] = 1;
        }
        if(cnt==n-1)break;
    }
    return ret;
}

int dfs(int st, int en)
{
    int v[LEN];
    for(int i=0; i<LEN; i++){
        v[i] = INF;
    }
    queue<int> q;
    q.push(st);
    v[st] = INF-1;
    while(!q.empty()){
        int vex = q.front();q.pop();
        if(vex == en){return v[en];}
        for(int i=0; i<top; i++){
            if(vis[i] && edge[i].a==vex && v[edge[i].b] == INF){
                q.push(edge[i].b);
                v[edge[i].b] = min(v[edge[i].a], edge[i].val);
            }
            if(vis[i] && edge[i].b==vex && v[edge[i].a] == INF){
                q.push(edge[i].a);
                v[edge[i].a] = min(v[edge[i].b], edge[i].val);
            }
        }
    }
    return -1;
}

int main()
{
//    freopen("in.txt", "r", stdin);

    while(scanf("%d%d", &n, &m)!=EOF){
        if(!n && !m) break;
        top = 0;
        int a, b, v;
        for(int i=0; i<m; i++){
            scanf("%d%d%d", &a, &b, &v);
            edge[top++].make_edge(a, b, v);
        }
        int st, en, num;
        scanf("%d%d%d", &st, &en, &num);
        sort(edge, edge+top, cmp);
        Kruskal();
        int ans = dfs(st, en) - 1;
        int aa = num/ans;
        if(num%ans!=0)aa++;
        printf("Scenario #%d
", CC++);
        printf("Minimum Number of Trips = %d

", aa);
    }
    return 0;
}