uva 10816(二分+Dijkstra)

题意：在一张图中会有重边，然后每条边上有两个权值，一个温度一个距离，让你找一条温度的最小瓶颈路，让这条最小瓶颈路距离最短。

思路：二分温度，然后用Dijkstra判断，最后输出答案。虽然想到思路后很简单，但是我一开始没注意看会有重边所以错了好多次。

代码如下：

/**************************************************
 * Author     : xiaohao Z
 * Blog     : http://www.cnblogs.com/shu-xiaohao/
 * Last modified : 2014-02-06 12:38
 * Filename     : uva_10816.cpp
 * Description     : 
 * ************************************************/

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <queue>
#include <stack>
#include <vector>
#include <set>
#include <map>
#define MP(a, b) make_pair(a, b)
#define PB(a) push_back(a)

using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<unsigned int,unsigned int> puu;
typedef pair<int, double> pid;
typedef pair<double, int> pdi;
typedef pair<ll, int> pli;
typedef pair<int, ll> pil;

const int INF = 0x3f3f3f3f;
const double eps = 1E-6;
const int LEN = 110;
struct P{
    int v;
    double t, d;
};
vector<P> Map[LEN];
int n, m, st, ed, pre[LEN];
double dis[LEN];

struct cmp{
    bool operator() (pdi a, pdi b){ return a.first > b.first;}
};

P M_P(int a, double b, double c){
     P ret;ret.v = a, ret.d = b, ret.t = c;return ret;
}

double Dijkstra(int vex, double tt){
    priority_queue<pdi, vector<pdi>, cmp> q;
    int vis[LEN] = {0};
    for(int i=0; i<LEN; i++) dis[i] = INF;
    memset(pre, 0, sizeof pre);
    dis[vex] = 0;
    pre[vex] = -1;
    q.push(MP(dis[vex], vex));
    while(!q.empty()){
        pdi nvex = q.top();q.pop();
        int nv = nvex.second;
        if(vis[nv]) continue;
        vis[nv] = 1;
        for(int i=0; i<Map[nv].size(); i++){
            int x = Map[nv][i].v;
               double y = Map[nv][i].d;
            if(dis[x] > dis[nv] + y && Map[nv][i].t<=tt){
                 dis[x] = dis[nv] + y;
                 pre[x] = nv;
                 q.push(MP(dis[x], x));
            }
        }
    }
    return dis[ed];
}

void out(int v){
     if(pre[v] < 0){
         printf("%d", v);
         return ;
     }
     out(pre[v]);
     printf(" %d", v);
}

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

    int a, b;
    double c, d;
    while(scanf("%d%d", &n, &m)!=EOF){
        for(int i=0; i<LEN; i++)Map[i].clear();
        scanf("%d%d", &st, &ed);
        double l = INF, r = 0, ans;
        for(int i=0; i<m; i++){
            scanf("%d%d%lf%lf", &a, &b, &c, &d);
            Map[a].PB(M_P(b, d, c));
            Map[b].PB(M_P(a, d, c));
            l = min(l, c);
            r = max(r, c);
        }
        while(r-l > eps){
            double m = (l+r)/2;
            double ta = Dijkstra(st, m);
            if(ta != INF) r = m;
            else l = m;
         }
        ans = Dijkstra(st, r);
        out(ed);puts("");
        printf("%.1lf %.1lf
", ans, r);
    }
    return 0;
}