HDU 3836 - Equivalent Sets【强连通分量 基础题】

Description

To prove two sets A and B are equivalent, we can first prove A is a subset of B, and then prove B is a subset of A, so finally we got that these two sets are equivalent.
You are to prove N sets are equivalent, using the method above: in each step you can prove a set X is a subset of another set Y, and there are also some sets that are already proven to be subsets of some other sets.
Now you want to know the minimum steps needed to get the problem proved.

 

Input

The input file contains multiple test cases, in each case, the first line contains two integers N <= 20000 and M <= 50000.
Next M lines, each line contains two integers X, Y, means set X in a subset of set Y.

 

Output

For each case, output a single integer: the minimum steps needed.

 

Sample Input

     
     
     
     

      
      
      
      4 0
3 2
1 2
1 3 
     
     
     
     

 

Sample Output

     
     
     
     

      
      
      
      4
2 
     
     
     
     

Hint

Case 2: First prove set 2 is a subset of set 1 and then prove set 3 is a subset of set 1. 

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#include<cstdio>
#include<cstring>
#include<vector>
#include<stack>
using namespace std;
#define maxn 20000
vector<int>G[maxn];
int pre[maxn],lowlink[maxn],sccno[maxn],dfs_clock,scc_cnt;
stack<int>S;
int min(int a,int b){if(a<b)return a;return b;}
void dfs(int u)
{
    pre[u]=lowlink[u]=++dfs_clock;
    S.push(u);
    for(int i=0;i<G[u].size();i++)
    {
        int v=G[u][i];
        if(!pre[v])
        {
            dfs(v);
            lowlink[u]=min(lowlink[u],lowlink[v]);
        }
        else if(!sccno[v])
            lowlink[u]=min(lowlink[u],pre[v]);
    }
    if(lowlink[u]==pre[u])
    {
        scc_cnt++;
        for(;;)
        {
            int x=S.top();S.pop();
            sccno[x]=scc_cnt;
            if(x==u) break;
        }
    }
}
void find_scc(int n)
{
    dfs_clock=scc_cnt=0;
    memset(sccno,0,sizeof(sccno));
    memset(pre,0,sizeof(pre));
    for(int i=0;i<n;i++)
    if(!pre[i]) dfs(i);
}
int in0[maxn],out0[maxn];
int main()
{
    int T,n,m;
    while(~scanf("%d%d",&n,&m))
    {
        for(int i=0;i<n;i++) G[i].clear();
        for(int i=0;i<m;i++)
        {
            int u,v;
            scanf("%d%d",&u,&v);
            u--;v--;
            G[u].push_back(v);
        }
        find_scc(n);
        for(int i=1;i<=scc_cnt;i++)in0[i]=out0[i]=1;
        for(int u=0;u<n;u++)
        {
            for(int i=0;i<G[u].size();i++)
            {
                int v=G[u][i];
                if(sccno[u]!=sccno[v])in0[sccno[v]]=out0[sccno[u]]=0;
            }
        }
        int a=0,b=0;
        for(int i=1;i<=scc_cnt;i++)
        {
            if(in0[i])a++;
            if(out0[i]) b++;
        }
        int ans=a;
        if(ans<b) ans=b;
        if(scc_cnt==1) ans=0;
        printf("%d\n",ans);

    }return 0;
}