Secret Milking Machine POJ - 2455

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题意：

给定一张无向图，有n个节点p条边，
要求在图中从1到n找到t条路径，并且使这t条路径中的最长边最小，
输出这个最小的最长边

/*题意：给定一张无向图，有n个节点p条边，
要求在图中从1到n找到t条路径，并且使这t条路径中的最长边最小，
输出这个最小的最长边
*/
#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int maxn=300;
const int maxm=50000;
const int inf=0x3f3f3f3f;
int head[maxm],cnt=0;
int n,m;
struct nodee
{   
    int u,v,w;
}aa[maxm*4+100];
struct edge
{
    int v,nxt,w;
}edge[maxm*4+100];
void add_edge(int u,int v,int w)
{
    edge[cnt].v=v;
    edge[cnt].w=w;
    edge[cnt].nxt=head[u];
    head[u]=cnt++;
}
int numh[maxn],h[maxn],curedge[maxn],pre[maxn];
int sap(int s,int t)
{
    memset(numh,0,sizeof(numh));
    memset(h,0,sizeof(h));
    memset(pre,-1,sizeof(pre));
    int cur_flow,flow_ans=0,u,tmp,neck,i;
    for(i=1;i<=n;i++)
    {
        curedge[i]=head[i];
    }
    numh[0]=n;
    u=s;
    while(h[s]<n)
    {
        if(u==t)
        {
            cur_flow=inf;
            for(i=s;i!=t;i=edge[curedge[i]].v)
            {
                if(cur_flow>edge[curedge[i]].w)
                {
                    neck=i;
                    cur_flow=edge[curedge[i]].w;
                }
            }
            for(i=s;i!=t;i=edge[curedge[i]].v)
            {
                tmp=curedge[i];
                edge[tmp].w-=cur_flow;
                edge[tmp^1].w+=cur_flow;
            }
            flow_ans+=cur_flow;
            u=neck;
        }
        for(i=curedge[u];i!=-1;i=edge[i].nxt)
        {
            if(edge[i].w&&h[u]==h[edge[i].v]+1)
            {
                break;
            }
        }
        if(i!=-1)
        {
            curedge[u]=i;
            pre[edge[i].v]=u;
            u=edge[i].v;
        }
        else
        {
            if(0==--numh[h[u]])
                break;
            curedge[u]=head[u];
            for(tmp=n,i=head[u];i!=-1;i=edge[i].nxt)
            {
                if(edge[i].w)
                {
                    tmp=min(tmp,h[edge[i].v]);
                }
            }
            h[u]=tmp+1;
            ++numh[h[u]];
            if(u!=s)
                u=pre[u];
        }
    }
    return flow_ans;
}
int main ()
{
    int t;
    scanf("%d%d%d",&n,&m,&t);
    memset(head,-1,sizeof(head));
    cnt=0;
    int maxx=0;
    for(int i=1;i<=m;i++)
    {
        scanf("%d%d%d",&aa[i].u,&aa[i].v,&aa[i].w);
        maxx=max(maxx,aa[i].w);
    }
    int l=0,r=maxx;
    int answer=maxx;
    while(l<=r)
    {
        int mid=(l+r)/2;
        memset(head,-1,sizeof(head));
        cnt=0;
        for(int i=1;i<=m;i++)
        {
            if(aa[i].w<=mid)
            {
                add_edge(aa[i].u,aa[i].v,1);
                add_edge(aa[i].v,aa[i].u,1);
            }
        }
        int anss=sap(1,n);
        //printf("%d %d\n",anss,mid);
        if(anss>=t)
        {
            r=mid-1;
            answer=min(answer,mid);
        }
        else
        {
            l=mid+1;
        }
    }
    printf("%d\n",answer);
}