es un Arbol?

///https://trello.com/c/GF5EGjZq/18-2012n2p1-es-un-%C3%A1rbol
///http://www.oia.unsam.edu.ar/_media/prob/c3a12n2p1.pdf
#include <iostream>
#include <vector>
using namespace std;

struct grafo {

    vector< vector<int> > ady;
    vector< vector<int> > p;
    vector<bool> visit;
    int n, m;
    bool arbol = true;

    void leer()
    {
        cin>>n>>m;

        ady.resize(n+1);
        p.resize(n+1);
        visit = vector<bool> (n+1, false);

        int a, b;
        for (int i=0; i<m; i++)
        {
            cin>>a>>b;
            ady[a].push_back(b);
            p[b].push_back(a);
        }
    }

    void DFS (int nodo)
    {
        visit[nodo] = true;

        for (int i=0; i<ady[nodo].size(); i++)
        {
            int vecino = ady[nodo][i];

            if ( !visit[vecino] )
                DFS(vecino);
            else arbol = false;
        }
    }

    void resp ()
    {
        int raiz, raices=0, raras=0;

        for (int i=1; i<=n; i++)
        {
            if ( !p[i].size() )
                raices++, raiz=i;
            if ( p[i].size() > 1 )
                raras++;
        }

        if  ( (m+1) != n || raras || raices != 1 )
            arbol = false;


        if (arbol)
            cout<<"Si";
        else
        {
            cout<<"No"<<endl;

            for (int i=1; i<=n; i++)
                if ( !p[i].size() )
                    cout<<i<<" ";

            if (!raices)
                cout<<raices;
            cout<<endl;


            if (raices == 1)
            {
                for (int i=1; i<=n; i++)
                    if ( (i != raiz) && (p[i].size() != 1) )
                        cout<<i<<" ";

                if (!raras)
                    cout<<raras;
            }
            else
            {
                for (int i=1; i<=n; i++)
                    if ( p[i].size() != 1 )
                        cout<<i<<" ";

                if (!raices && !raras)
                    cout<<raras;
            }
            cout<<endl;

            if ( raices==1 )
            {
                DFS(raiz);
                for (int i=1; i<=n; i++)
                    if (!visit[i])
                        cout<<i<<" ";

                if (!raras)
                    cout<<"0";
            }
            else cout<<"0";
            cout<<endl;
        }
    }

};

int main()
{
    grafo g;
    g.leer();
    g.resp();

    return 0;
}