SGU 242 Student's Morning (网络流+打印路径，Dinic)

http://acm.sgu.ru/problem.php?contest=0&problem=242

网络流+打印路径

原点和人建立权为1的边，人和学校建立权为1的边，学校和汇点建权为2的边

最大流是2*k则yes,否则no

顺便附上修改自他人的带各种优化的Dinic模板~

/**
*网络流+打印路径
*原点和人建立权为1的边，学校和汇点建权为2的边
*最大流是2*k则yes,否则no
*
*@Author: xysmlx xiaohai
*/
//#pragma comment(linker, "/STACK:102400000,102400000")
#include<cstdio>
#include<iostream>
#include<cstring>
#include<string>
#include<cmath>
#include<set>
#include<list>
#include<map>
#include<iterator>
#include<cstdlib>
#include<vector>
#include<queue>
#include<stack>
#include<algorithm>
#include<functional>
using namespace std;
typedef long long LL;
#define ROUND(x) round(x)
#define FLOOR(x) floor(x)
#define CEIL(x) ceil(x)
const int maxn=510;
const int inf=0x3f3f3f3f;
const LL inf64=0x3f3f3f3f3f3f3f3fLL;
const double INF=1e30;
const double eps=1e-6;

/**
*最大流：加各种优化的Dinic算法($O(V^2E)$)
*输入：图(链式前向星),n(顶点个数,包含源汇),st(源),ed(汇)
*输出：MaxFlow()(最大流)
*/
//const int maxn=0;
const int maxm=50010;
//const int inf=0x3f3f3f3f;
struct Edge
{
    int v;
    int cap;
    int next;
} edge[maxm];
int head[maxn],edgeNum;//需初始化
int n,m,d[maxn],cur[maxn];
int st,ed;
void addSubEdge(int u,int v,int cap)
{
    edge[edgeNum].v=v;
    edge[edgeNum].cap=cap;
    edge[edgeNum].next=head[u];
    head[u]=edgeNum++;
    cur[u]=head[u];
}
void addEdge(int u,int v,int cap)
{
    addSubEdge(u,v,cap);
    addSubEdge(v,u,0);//注意加反向0边
}
bool BFS()
{
    queue<int> Q;
    memset(d, -1, sizeof(d));
    Q.push(st);
    d[st]=0;
    while (!Q.empty())
    {
        int u=Q.front();
        Q.pop();
        for(int i=head[u]; i!=-1; i=edge[i].next)
        {
            int v=edge[i].v;
            int cap=edge[i].cap;
            if(cap&&d[v]==-1)
            {
                Q.push(v);
                d[v]=d[u]+1;
                if(v==ed) return 1;
            }
        }
    }
    return false;
}
int Aug(int u, int a)
{
    if (u==ed) return a;
    int aug=0, delta;
    for(int &i=cur[u]; i!=-1; i=edge[i].next)
    {
        int v=edge[i].v;
        int cap=edge[i].cap;
        if (cap && d[v]==d[u]+1)
        {
            delta = Aug(v, min(a,cap));
            if (delta)
            {
                edge[i].cap -= delta;
                edge[i^1].cap += delta;
                aug += delta;
                if (!(a-=delta)) break;
            }
        }
    }
    if (!aug) d[u]=-1;
    return aug;
}
int MaxFlow()
{
    int flow=0;
    while (BFS())
    {
        memcpy(cur,head,sizeof(int)*(n+1));
        flow += Aug(st,inf);
    }
    return flow;
}

int N,M;
void init()
{
    memset(head,-1,sizeof(head));
    edgeNum=0;
    st=0,ed=N+M+1;
    n=N+M+1;
}
void input()
{
    for(int i=1;i<=N;i++)
    {
        addEdge(st,i,1);
        int u,v;
        scanf("%d",&u);
        for(int j=0;j<u;j++)
        {
            scanf("%d",&v);
            addEdge(i,N+v,1);
        }
    }
    for(int i=1;i<=M;i++) addEdge(N+i,ed,2);
}
void solve()
{
    int f=MaxFlow();
    if(f!=2*M)
    {
        puts("NO");
        return;
    }
    puts("YES");
    for(int v=1;v<=M;v++)
    {
        printf("2");
        for(int i=head[N+v];i!=-1;i=edge[i].next)
        {
            if((i&1)&&edge[i].cap==1) printf(" %d",edge[i].v);
        }
        puts("");
    }
}
int main()
{
//    std::ios_base::sync_with_stdio(false);
//    freopen("in.cpp","r",stdin);
    while(~scanf("%d%d",&N,&M))
    {
        init();
        input();
        solve();
    }
    return 0;
}