poj1904 完美匹配+Tarjan

Posted Billyshuai

tags:

篇首语:本文由小常识网(cha138.com)小编为大家整理,主要介绍了poj1904 完美匹配+Tarjan相关的知识,希望对你有一定的参考价值。

 
King\'s Quest
Time Limit: 15000MS   Memory Limit: 65536K
Total Submissions: 9460   Accepted: 3497
Case Time Limit: 2000MS

Description

Once upon a time there lived a king and he had N sons. And there were N beautiful girls in the kingdom and the king knew about each of his sons which of those girls he did like. The sons of the king were young and light-headed, so it was possible for one son to like several girls.

So the king asked his wizard to find for each of his sons the girl he liked, so that he could marry her. And the king\'s wizard did it -- for each son the girl that he could marry was chosen, so that he liked this girl and, of course, each beautiful girl had to marry only one of the king\'s sons.

However, the king looked at the list and said: "I like the list you have made, but I am not completely satisfied. For each son I would like to know all the girls that he can marry. Of course, after he marries any of those girls, for each other son you must still be able to choose the girl he likes to marry."

The problem the king wanted the wizard to solve had become too hard for him. You must save wizard\'s head by solving this problem.

Input

The first line of the input contains N -- the number of king\'s sons (1 <= N <= 2000). Next N lines for each of king\'s sons contain the list of the girls he likes: first Ki -- the number of those girls, and then Ki different integer numbers, ranging from 1 to N denoting the girls. The sum of all Ki does not exceed 200000.

The last line of the case contains the original list the wizard had made -- N different integer numbers: for each son the number of the girl he would marry in compliance with this list. It is guaranteed that the list is correct, that is, each son likes the girl he must marry according to this list.

Output

Output N lines.For each king\'s son first print Li -- the number of different girls he likes and can marry so that after his marriage it is possible to marry each of the other king\'s sons. After that print Li different integer numbers denoting those girls, in ascending order.

Sample Input

4
2 1 2
2 1 2
2 2 3
2 3 4
1 2 3 4

Sample Output

2 1 2
2 1 2
1 3
1 4
题解这里

#include<vector>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int N=4080;
const int M=4e6+88;
vector<int>sc[N];
vector<int>G[N];
int head[N],dfn[N],low[N],q[N];
bool instack[N],mp[2008][2008];
int tot,scnt,l,cnt;
struct node
{
    int to,next;
} e[M];
void add(int u,int v)
{
    e[tot].to=v;
    e[tot].next=head[u];
    head[u]=tot++;
}
void Tarjan(int u)
{
    dfn[u]=low[u]=++cnt;
    q[l++]=u;
    instack[u]=1;
    for(int i=head[u]; ~i; i=e[i].next)
    {
        int v=e[i].to;
        if(!dfn[v])
        {
            Tarjan(v);
            low[u]=min(low[u],low[v]);
        }
        else if(instack[v]&&dfn[v]<low[u]) low[u]=dfn[v];
    }
    if(low[u]==dfn[u])
    {
        ++scnt;
        int t;
        do
        {
            t=q[--l];
            sc[scnt].push_back(t);
            instack[t]=0;
        }
        while(t!=u);
    }
}
int main()
{
    int n,x,y;
    while(scanf("%d",&n)!=EOF)
    {
        tot=scnt=cnt=l=0;
        memset(head,-1,sizeof(head));
        memset(dfn,0,sizeof(dfn));
        memset(mp,0,sizeof(mp));
        for(int i=1; i<=n; ++i)
        {
            scanf("%d",&x);
            while(x--)
            {
                scanf("%d",&y);
                add(i,y+n);
                G[i].clear();
                sc[i].clear();
                mp[i][y]=1;
            }
        }
        for(int i=1; i<=n; ++i)
        {
            scanf("%d",&x);
            add(x+n,i);
        }
        for(int i=1; i<=n; ++i) if(!dfn[i]) Tarjan(i);
        for(int i=1; i<=scnt; ++i) sort(sc[i].begin(),sc[i].end());
        for(int i=1; i<=scnt; ++i)
        {
            int tc=upper_bound(sc[i].begin(),sc[i].end(),n)-sc[i].begin();
            for(int j=0; j<tc; ++j) for(int k=tc; k<(int)sc[i].size(); ++k) if(mp[sc[i][j]][sc[i][k]-n] ) G[sc[i][j]].push_back(sc[i][k]-n);
        }
        for(int i=1; i<=n; ++i)
        {
            printf("%d",(int)G[i].size());
            for(int j=0; j<(int)G[i].size(); ++j) printf(" %d",G[i][j]);
            puts("");
        }
    }
}

 

以上是关于poj1904 完美匹配+Tarjan的主要内容,如果未能解决你的问题,请参考以下文章

Poj 1904 King's Quest 强连通分量

poj 1904 King's Quest

King's Quest POJ - 1904(强连通分量)

BZOJ 2140 Tarjan

poj 1904(强连通)

hdu3861他的子问题是poj2762二分匹配+Tarjan+有向图拆点 其实就是求DAG的最小覆盖点