網路流處理無向圖 二分+網路流

題意：給定一張無向圖，有n個節點p條邊，
要求在圖中從1到n找到t條路徑，並且使這t條路徑中的最長邊最小，
輸出這個最小的最長邊

思路：讓所有的邊值為1，即可知道從s到t有多少條路，二分處理最大值的最小值即可。

#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);}