hihocode#1378 : 網絡流二·最大流最小割定理(最大流求最小割集)

題目鏈接

EK求最小割集模板

代碼：

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>
#include<string>
#include<vector>
#include<stack>
#include<bitset>
#include<cstdlib>
#include<cmath>
#include<set>
#include<list>
#include<deque>
#include<map>
#include<queue>
using namespace std;
typedef long long ll;
const double PI = acos(-1.0);
const double eps = 1e-6;
const int INF = 1000000000;
const int maxn = 123456;
int T,n,m;
int tot,s,t;
int head[maxn],vis[maxn],path[maxn];
set<int>st;

struct EDGE
{
    int from,to;
    int cap,flow;
    int next;
}e[maxn];

void init()
{
    tot=0;
    s=1;
    t=n;
    memset(head,-1,sizeof(head));
    memset(vis,0,sizeof(vis));
    memset(path,0,sizeof(path));
}


void add_edge(int u,int v,int w)
{
    e[tot].from=u;
    e[tot].to=v;
    e[tot].cap=w;
    e[tot].flow=0;
    e[tot].next=head[u];
    head[u]=tot++;
}

int bfs()
{
    queue<int>q;
    q.push(s);
    vis[s]=1;
    path[s]=-1;
    while(!q.empty())
    {
        int u=q.front();
        q.pop();
        for(int i=head[u];i!=-1;i=e[i].next)
        {
            int v=e[i].to;
            if(e[i].cap-e[i].flow>0&&!vis[v])
            {
                path[v]=i;
                vis[v]=1;
                if(v==t)
                    return 1;
                q.push(v);
            }
        }
    }
    return 0;
}

int EK()
{
    int maxFlow=0;
    int flow,i;
    while(bfs())
    {
        memset(vis,0,sizeof(vis));
        i=path[t];
        flow=INF;
        while(i!=-1)
        {
            flow=min(flow,e[i].cap-e[i].flow);
            i=path[e[i].from];
        }
        i=path[t];
        while(i!=-1)
        {
            e[i].flow+=flow;
            e[i^1].flow-=flow;
            i=path[e[i].from];
        }
        maxFlow+=flow;
    }
    return maxFlow;
}

void Get_set()//求割集
{
    memset(vis,0,sizeof(vis));
    queue<int>q;
    q.push(1);
    vis[1]=1;
    while(!q.empty())
    {
        int u=q.front();
        q.pop();
        st.insert(u);
        for(int i=head[u];i!=-1;i=e[i].next)
        {
            int v=e[i].to;
            if(vis[v]==0&&e[i].cap-e[i].flow>0)
            {
                vis[v]=1;
                q.push(v);
            }
        }
    }
}

int main()
{
    while(scanf("%d%d",&n,&m)!=EOF)
    {
        init();
        for(int i=0;i<m;i++)
        {
            int u,v,c;
            scanf("%d%d%d",&u,&v,&c);
            add_edge(u,v,c);
            add_edge(v,u,0);
        }
        int maxFlow=EK();
        Get_set();
        printf("%d %d\n",maxFlow,st.size());
        for(set<int>::iterator it = st.begin();it!=st.end();it++)
        {
            if(it!=st.begin())
                printf(" ");
            printf("%d",*it);
        }
        printf("\n");
    }
    return 0;
}