Saturday, 3 June 2017

Proving Equivalences (UVa 12167, UVaLive 4287, Regionals 2008 >> Europe - Northwestern) 


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///     Raihan Ruhin
///     CSE, Jahangirnagar University.
///     Dhaka-Bangladesh.
///     id: raihanruhin (topcoder / codeforces / codechef / uva), 3235 (lightoj)
///     mail: raihanruhin@ (yahoo / gmail / facebook)
///     blog: ruhinraihan.blogspot.com

#include<bits/stdc++.h>
using namespace std;

#define SET(a) memset(a,-1,sizeof(a))
#define CLR(a) memset(a,0,sizeof(a))
#define PI acos(-1.0)

#define MOD 1000000007
#define MX 100010

vector<int>adj[20002];
stack<int>stk;

int t, lo[20002], tim[20002], vis[20002], sccrm[20002], scc, done;

void tarjan_scc(int u)
{
    t++;
    vis[u]=1;
    lo[u]=tim[u]=t;
    stk.push(u);

    for(int i=0;i<adj[u].size();i++)
    {
        int v = adj[u][i];
        if(!vis[v])
        {
            tarjan_scc(v);
            lo[u]=min(lo[u], lo[v]);
        }
        else if(vis[v]==1)
            lo[u]=min(lo[u], tim[v]);
    }

    if(lo[u]==tim[u])
    {
        scc++;
        do{
            done = stk.top();
            stk.pop();
            sccrm[done]=scc;
            vis[done]=2;
        }while(done!=u);
    }
return;
}

int main()
{
    ios_base::sync_with_stdio(0);cin.tie(0);
    int kk=1, tc, n, m, u, v;
    string s;
    cin>>tc;
    while(tc--)
    {
        cin>>n>>m;
        t=scc=0;
        while(!stk.empty()) stk.pop();
        for(int i=1;i<=n;i++)
        {
            adj[i].clear();
            vis[i]=0;
        }

        while(m--)
        {
            cin>>u>>v;
            adj[u].push_back(v);
        }
        for(int i=1;i<=n;i++)
            if(!vis[i])
                tarjan_scc(i);

        // checking zero indegree and outdegree of scc
        bool hasIndegree[scc+2], hasOutdegree[scc+2];
        CLR(hasIndegree);
        CLR(hasOutdegree);

        for(int i=1;i<=n;i++)
            for(int j=0;j<adj[i].size();j++)
                if(sccrm[i]!=sccrm[adj[i][j]]) //not in same scc
                {
                    hasIndegree[sccrm[i]]=true;
                    hasOutdegree[sccrm[adj[i][j]]]=true;
                }
        int zeroIndgree=0, zeroOutdegree=0;
        for(int i=1;i<=scc;i++)
        {
            if(!hasIndegree[i]) zeroIndgree++;
            if(!hasOutdegree[i]) zeroOutdegree++;
        }
        if(scc==1) cout<<0<<endl;
        else cout<<max(zeroIndgree, zeroOutdegree)<<endl;
        //cout<<"Case "<<kk++<<": "<< <<"\n";
    }

    return 0;
}
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