Telephone Lines POJ - 3662(spfa+二分）

Farmer John wants to set up a telephone line at his farm. Unfortunately, the phone company is uncooperative, so he needs to pay for some of the cables required to connect his farm to the phone system.

There are $N (1 ≤ N ≤ 1,000)$ forlorn telephone poles conveniently numbered 1..N that are scattered around Farmer John’s property; no cables connect any them. A total of$P (1 ≤ P ≤ 10,000)$ pairs of poles can be connected by a cable; the rest are too far apart.

The i-th cable can connect the two distinct poles Ai and Bi, with length $Li (1 ≤ Li ≤ 1,000,000)$ units if used. The input data set never names any {Ai, Bi} pair more than once. Pole 1 is already connected to the phone system, and pole N is at the farm. Poles 1 and N need to be connected by a path of cables; the rest of the poles might be used or might not be used.

As it turns out, the phone company is willing to provide Farmer John with $K (0 ≤ K < N)$ lengths of cable for free. Beyond that he will have to pay a price equal to the length of the longest remaining cable he requires (each pair of poles is connected with a separate cable), or 0 if he does not need any additional cables.

Determine the minimum amount that Farmer John must pay.

Input
* Line 1: Three space-separated integers: N, P, and K
* Lines 2..P+1: Line i+1 contains the three space-separated integers: Ai, Bi, and Li

Output
* Line 1: A single integer, the minimum amount Farmer John can pay. If it is impossible to connect the farm to the phone company, print -1.

Sample Input
5 7 1
1 2 5
3 1 4
2 4 8
3 2 3
5 2 9
3 4 7
4 5 6
Sample Output
4
评价：好题，spfa的变式原因，因为答案存在单调行（假设答案存在），而且必然是从已知边里选择，关键怎么判断边的可行，只要把边大于mid的地阿亮看作长度为1，反正变为0，然后做spfa，如果num[n]的值小于等于k，则合法。
代码

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<queue>
#include<cstring>
#define maxx 1005
#define maxn 10005
#define INF 0x3f3f3f3f
using namespace std;
int n,m,k;
int head[maxx],_next[maxn<<1],to[maxn<<1],w[maxn<<1];
int num[maxx];
char inQ[maxx];
int cnt;
void addEdge(int x,int y,int r)
{
    to[++cnt]=y,w[cnt]=r,_next[cnt]=head[x],head[x]=cnt;
    to[++cnt]=x,w[cnt]=r,_next[cnt]=head[y],head[y]=cnt;
}
int b[maxn];
bool spfa(int x)
{
    queue<int> que;
    memset(num,INF,sizeof(num));
    num[1]=0;
    que.push(1);
    inQ[1]=true;
    while(que.size())
    {
        int now=que.front();
        que.pop();
        inQ[now]=false;
        for(int i=head[now];i;i=_next[i])
        {
            int L=w[i]>x?1:0;
            int v=to[i];
            if(num[v]>num[now]+L)
            {
                num[v]=num[now]+L;
                if(!inQ[v])
                {
                    que.push(v);
                    inQ[v]=true;
                }
            }
        }
    }
    return num[n]<=k;
}
int main()
{
    cin>>n>>m>>k;
    int x,y,w;
    cnt=0;
    for(int i=0;i<m;i++)
    {
        scanf("%d%d%d",&x,&y,&w);
        addEdge(x,y,w);
        b[i]=w;
    }
    if(spfa(0))
        cout<<0<<endl;
    else
    {
        sort(b,b+m);
        //cout<<"haha"<<spfa(4)<<endl;
        int l=0,r=m-1;
        while(l<=r)
        {
            int mid=(l+r)>>1;
            if(spfa(b[mid]))
                r=mid-1;
            else
                l=mid+1;
        }
        if(l==m)
            cout<<-1<<endl;
        else
            cout<<b[l]<<endl;
    }
    return 0;
}