#include <iostream>
#include <fstream>
#include <vector>
#include <stack>
#include <algorithm>
#include <unordered_map>
#include <deque>
#include <queue>
#define PROBLEMA 8
#define inf INT_MAX
using namespace std;
ifstream f;
ofstream g;
int ap[5000][5000];
int ap_sol[5000][5000];
class graf
{
    unsigned int n,m;
    vector< vector<unsigned int> > lista_vecini;
    void BFS(unsigned int);
    void DFS(unsigned int, bool*,unsigned int&);
    void biconex(unsigned int, int*, int*, unsigned int&, stack<pair<unsigned int, unsigned int>>&, vector<unsigned int>&);
    void ctc(unsigned int, int*, int*, bool*, unsigned int&, unsigned int&, stack<unsigned int>&, vector <unsigned int>&);
    void sortaret(unsigned int, bool*, stack<unsigned int>&);
    vector<vector<int>> criticalConnections(int,vector<vector<int>>&);
public:
    graf(const unsigned int &);
    ~graf();
    void setn(const unsigned int &);
    void setm(const unsigned int &);
    int getn();
    int getm();
    void getvecini();
    void sortvecini();
    void StartBFS();
    void StartDFS();
    void Startbiconex();
    void Startctc();
    void Startsortaret();
    void havelhakimi();
    void StartcriticalConnections();
    void apm();
};


graf::graf(const unsigned int &opt=0)
{

    switch (opt)
    {
    case 1:
    case 3:
    {
        unsigned int x,y;
        f>>this->n>>this->m;
        if (opt==1)
            f>>x;
        this->lista_vecini.resize(n+1);
        for (unsigned int i=0; i<this->m; ++i)
        {
            f>>x>>y;
            this->lista_vecini[x].push_back(y);
        }
        break;
    }
    case 2:
    {
        unsigned int x,y;
        f>>this->n>>this->m;
        this->lista_vecini.resize(n+1);
        for (unsigned int i=0; i<this->m; ++i)
        {
            f>>x>>y;
            this->lista_vecini[x].push_back(y);
            this->lista_vecini[y].push_back(x);
        }
        break;
    }
    default:
        break;
    }
}

graf::~graf()
{
    //simbolic
    this->n=this->m=0;
    for (size_t i=0; i<this->lista_vecini.size(); ++i)
        this->lista_vecini[i].clear();
    this->lista_vecini.clear();
}

void graf::setn(const unsigned int &n)
{
    this->n=n;
}

void graf::setm(const unsigned int &m)
{
    this->m=m;
}

int graf::getm()
{
    return this->m;
}

int graf::getn()
{
    return this->n;
}

void graf::getvecini()
{
    for (unsigned int i=1-min(1,int(lista_vecini[0].size())); i<this->lista_vecini.size()-min(1,int(lista_vecini[0].size())); ++i)
    {
        cout<<i<<": ";
        for (unsigned int j=0; j<this->lista_vecini[i].size(); ++j)
            cout<<this->lista_vecini[i][j]<<" ";
        cout<<"\n";
    }
}

void graf::sortvecini()
{
    unsigned int j,k;
    unsigned int ap[this->n+1];
    for (j=0; j<=this->n; ++j)
        ap[j]=0;
    for (unsigned int i=1; i<this->lista_vecini.size(); ++i)
    {
        k=0;
        for (j=0; j<this->lista_vecini[i].size(); ++j)
            ++ap[this->lista_vecini[i][j]];
        for (j=1; j<=this->n; ++j)
        {
            if (ap[j])
            {
                this->lista_vecini[i][k++]=j;
                ap[j]=0;
            }
        }
    }
}

void graf::StartBFS()
{
    ifstream h;
    unsigned int start;
    h.open("bfs.in",std::ifstream::in);
    h>>start>>start>>start;
    h.close();
    BFS(start);
}

void graf::BFS(unsigned int nod_start)
{
    int d[this->n+1];
    for (unsigned int i=1; i<=n; ++i)
        d[i]=-1;
    unsigned int index=0;
    vector <int> coada;
    coada.push_back(nod_start);
    d[nod_start]=0;
    while (index<coada.size())
    {
        int nod_curent=coada[index++];
        for (unsigned int i=0; i<this->lista_vecini[nod_curent].size(); ++i)
            if (d[this->lista_vecini[nod_curent][i]]==-1)
            {
                coada.push_back(this->lista_vecini[nod_curent][i]);
                d[this->lista_vecini[nod_curent][i]]=d[nod_curent]+1;

            }
    }
    for (unsigned int i=1; i<=n; ++i)
    {
        g<<d[i]<<" ";
    }
}

void graf::StartDFS()
{
    bool viz[this->n+1];
    unsigned int nrconex;
    for (unsigned int i=1; i<=this->n; ++i)
        viz[i]=false;
    nrconex=0;
    for (unsigned int i=1; i<=this->n; ++i)
        if (!viz[i])
        {
            nrconex++;
            DFS(i,viz,nrconex);
        }
    g<<nrconex;

}

void graf::DFS(unsigned int nod_curent,bool viz[],unsigned int &nrconex)
{
    viz[nod_curent]=true;
    for (unsigned int i=0; i<this->lista_vecini[nod_curent].size(); ++i)
        if (!viz[this->lista_vecini[nod_curent][i]])
            DFS(this->lista_vecini[nod_curent][i],viz,nrconex);
}

void graf::Startbiconex()
{
    int niv[this->n+1];
    int niv_int[this->n+1];
    unsigned int nrbiconex=0;
    stack <pair<unsigned int,unsigned int>> stiva;
    vector <unsigned int> sol;
    for (unsigned int i=1; i<=this->n; ++i)
    {
        niv[i]=-1;
        niv_int[i]=0;
    }
    niv[1]=0;
    biconex(1,niv,niv_int,nrbiconex,stiva,sol);
    g<<nrbiconex<<"\n";
    for (auto i = sol.begin(); i != sol.end(); ++ i)
        if (*i!=0)
            g<<*i<<" ";
        else
            g<<"\n";
}

void graf::biconex(unsigned int nod_curent,int niv[],int niv_int[],unsigned int &nrbiconex,stack <pair<unsigned int,unsigned int>> &stiva,vector <unsigned int> &sol)
{
    for (unsigned int i=0; i<this->lista_vecini[nod_curent].size(); ++i)
        if (niv[this->lista_vecini[nod_curent][i]]==-1)
        {
            niv[this->lista_vecini[nod_curent][i]]=niv[nod_curent]+1;
            niv_int[this->lista_vecini[nod_curent][i]]=niv[nod_curent]+1;
            stiva.push(make_pair(nod_curent,this->lista_vecini[nod_curent][i]));
            biconex(this->lista_vecini[nod_curent][i],niv,niv_int,nrbiconex,stiva,sol);
            niv_int[nod_curent]=min(niv_int[nod_curent],niv_int[this->lista_vecini[nod_curent][i]]);
            if (niv_int[this->lista_vecini[nod_curent][i]]>=niv[nod_curent])
            {
                nrbiconex++;
                unordered_map<unsigned int,bool> ap;
                unsigned int aux1;
                unsigned int aux2;
                do
                {

                    aux1=stiva.top().first;
                    aux2=stiva.top().second;
                    if (!ap[aux1])
                    {
                        sol.push_back(aux1);
                        ap[aux1]=1;
                    }
                    if (!ap[aux2])
                    {
                        sol.push_back(aux2);
                        ap[aux2]=1;
                    }
                    stiva.pop();
                }
                while(aux1!=nod_curent || aux2!=this->lista_vecini[nod_curent][i]);
                sol.push_back(0);
            }
        }
        else if (niv[nod_curent]-1!=niv[this->lista_vecini[nod_curent][i]])
            niv_int[nod_curent]=min(niv_int[nod_curent],niv[this->lista_vecini[nod_curent][i]]);
    //scadem 1 ca sa nu luam in considerare si tatal nodului
}

void graf::Startctc()
{
    int indx[this->n+1];
    int indx_min[this->n+1];
    bool peStiva[this->n+1];
    unsigned int nrctc=0;
    unsigned int it=1;
    unsigned int i;
    stack <unsigned int> stiva;
    vector <unsigned int> sol;
    for (i=1; i<=this->n; ++i)
    {
        indx[i]=-1;
        indx_min[i]=0;
        peStiva[i]=false;
    }
    for(i=1; i<=this->n; ++i)
        if (indx[i]==-1)
            ctc(i,indx,indx_min,peStiva,nrctc,it,stiva,sol);
    g<<nrctc<<"\n";
    for (auto i = sol.begin(); i != sol.end(); ++ i)
        if (*i!=0)
            g<<*i<<" ";
        else
            g<<"\n";

}

void graf::ctc(unsigned int nod_curent,int indx[], int indx_min[], bool peStiva[], unsigned int &nrctc, unsigned int &it, stack<unsigned int> &stiva, vector<unsigned int> &sol)
{
    indx[nod_curent]=it;
    indx_min[nod_curent]=it++;
    stiva.push(nod_curent);
    peStiva[nod_curent]=true;
    for (unsigned int i=0; i<this->lista_vecini[nod_curent].size(); ++i)
        if (indx[this->lista_vecini[nod_curent][i]]==-1)
        {
            ctc(this->lista_vecini[nod_curent][i],indx,indx_min,peStiva,nrctc,it,stiva,sol);
            indx_min[nod_curent]=min(indx_min[nod_curent],indx_min[this->lista_vecini[nod_curent][i]]);
        }
        else if (peStiva[this->lista_vecini[nod_curent][i]])
            indx_min[nod_curent]=min(indx_min[nod_curent],indx[this->lista_vecini[nod_curent][i]]);
    if (indx_min[nod_curent]==indx[nod_curent])
    {
        ++nrctc;
        unsigned int nod_aux;
        do
        {
            nod_aux=stiva.top();
            peStiva[nod_aux]=false;
            sol.push_back(nod_aux);
            stiva.pop();
        }
        while (nod_aux!=nod_curent);
        sol.push_back(0);
    }

}

void graf::Startsortaret()
{
    bool viz[this->n+1];
    stack <unsigned int> sol;
    unsigned int i;
    for (i=1; i<=this->n; ++i)
        viz[i]=false;
    for (i=1; i<=this->n; ++i)
        if (!viz[i])
            sortaret(i, viz, sol);
    while (!sol.empty())
    {
        //afisam in postordine invers
        g<<sol.top()<<" ";
        sol.pop();
    }
}

void graf::sortaret(unsigned int nod_curent, bool viz[], stack<unsigned int> &sol)
{
    viz[nod_curent]=true;
    for (unsigned int i=0; i<this->lista_vecini[nod_curent].size(); ++i)
        if (!viz[lista_vecini[nod_curent][i]])
        {
            sortaret(lista_vecini[nod_curent][i], viz, sol);
        }
    //introducem nodurile in postordine (dupa ce ies din stiva) in stiva solutie
    sol.push(nod_curent);
}

void graf::havelhakimi()
{
    bool zero=false;
    vector <int> grad;
    unsigned int x;
    while (f>>x)
        grad.push_back(x);
    while (!zero)
    {
        zero=true;
        sort(grad.begin(),grad.end());
        unsigned int nrs=grad[grad.size()-1];
        grad.pop_back();
        if (nrs>grad.size())
        {
            cout<<"Nu";
            g<<"Nu";
            return;
        }
        for (unsigned int i=grad.size()-1; (int)(i)>(int)(grad.size()-nrs-1); --i)
        {
            --grad[i];
            if (grad[i]<0)
            {
                cout<<"Nu";
                g<<"Nu";
                return;
            }
            if (grad[i]!=0)
                zero=false;
        }
    }
    cout<<"Da";
    g<<"Da";
}

void graf::StartcriticalConnections()
{
    vector<vector<int>> muchii;
    int n,x,y,m;
    unsigned int nrt;
    f>>nrt;
    for (unsigned int t=0; t<nrt; ++t)
    {
        muchii.resize(0);
        f>>n>>m;
        for (int i=0; i<m; ++i)
        {
            f>>x>>y;
            muchii.push_back(vector<int> {x,y});
        }
        vector<vector<int>> sol(this->criticalConnections(n,muchii));
        for (size_t i=0; i<sol.size(); ++i)
        {
            cout<<"("<<sol[i][0]<<","<<sol[i][1]<<") ";
            g<<"("<<sol[i][0]<<","<<sol[i][1]<<") ";
        }
        cout<<"\n\n";
        g<<"\n\n";
    }
}

vector<vector<int>> graf::criticalConnections(int n, vector<vector<int>>& connections)
{
    unsigned int i;
    this->setn(n);
    this->setm(connections.size());
    stack <unsigned int> stiva;
    vector<vector<int>> sol;
    unsigned int icopil[n];
    this->lista_vecini.clear();
    this->lista_vecini.resize(n);
    int niv[n];
    int niv_int[n];
    for (int i=0; i<n; ++i)
    {
        niv[i]=-1;
        niv_int[i]=0;
        icopil[i]=0;
    }
    for (i=0; i<connections.size(); ++i)
    {
        this->lista_vecini[connections[i][0]].push_back(connections[i][1]);
        this->lista_vecini[connections[i][1]].push_back(connections[i][0]);
    }
    niv[0]=1;
    stiva.push(0);
    while (!stiva.empty())
    {
        unsigned int nod_curent=stiva.top();
        for (i=icopil[nod_curent]; i<lista_vecini[nod_curent].size(); ++i)
        {
            ++icopil[nod_curent];
            if (niv[lista_vecini[nod_curent][i]]==-1)
            {
                niv[lista_vecini[nod_curent][i]]=niv[nod_curent]+1;
                niv_int[lista_vecini[nod_curent][i]]=niv[nod_curent]+1;
                stiva.push(lista_vecini[nod_curent][i]);
                nod_curent=lista_vecini[nod_curent][i];
                break;
            }
            else if (niv[nod_curent]-1!=niv[lista_vecini[nod_curent][i]])
                niv_int[nod_curent]=min(niv_int[nod_curent],niv[lista_vecini[nod_curent][i]]);
        }
        if (icopil[nod_curent]==lista_vecini[nod_curent].size())
        {
            unsigned int copil=stiva.top();
            stiva.pop();
            if (!stiva.empty())
            {
                niv_int[stiva.top()]=min(niv_int[copil],niv_int[stiva.top()]);
                if (niv_int[copil]>niv[stiva.top()])
                    sol.push_back({int(stiva.top()),int(copil)});
            }

        }
    }
    return sol;
}


void graf::apm()
{
    unsigned int x,y;
    unsigned int i;
    int cost=0;
    f>>this->n>>this->m;
    int C[this->n+1][this->n+1];
    int d[this->n+1];
    int t[this->n+1];
    bool viz[this->n+1];
    this->lista_vecini.resize(this->n+1);
    priority_queue<pair<int,int>> noduri;
    vector<pair<int,int>> sol;
    for (unsigned int i=0; i<this->m; ++i)
    {
        f>>x>>y;
        this->lista_vecini[x].push_back(y);
        this->lista_vecini[y].push_back(x);
        f>>C[x][y];
        C[y][x]=C[x][y];
    }


    unsigned int s=1;
    for (i=1; i<=this->n; ++i)
    {
        d[i]=inf;
        t[i]=0;
        viz[i]=false;
    }
    d[s]=0;
    noduri.push(make_pair(-1*d[1],1));
    for (i=0; i<this->n; ++i)
    {
        unsigned int nod;
        do
        {
            nod=noduri.top().second;
            //cout<<"Verificam daca nodul cu costul minim, "<<nod<<", e in heap\n";
            noduri.pop();
        }
        while (viz[nod]);
        //cout<<nod<<" e in heap\n";
        viz[nod]=true;
        //cout<<"Costul la nodul "<<nod<<" e "<<d[nod]<<" si nodul are tatal "<<t[nod]<<"\n";
        cost+=d[nod];
        for (unsigned int i=0; i<this->lista_vecini[nod].size(); ++i)
        {
            //cout<<"Vecinul "<<this->lista_vecini[nod][i]<<"\n";
            if (!viz[this->lista_vecini[nod][i]] && C[nod][this->lista_vecini[nod][i]]<d[this->lista_vecini[nod][i]])
            {
                //cout<<"Actualizam vecinul care nu e in heap "<< this->lista_vecini[nod][i]<<" cu distanta "<<C[nod][this->lista_vecini[nod][i]]<<" si tatal "<<nod<<"\n";
                d[this->lista_vecini[nod][i]]=C[nod][this->lista_vecini[nod][i]];
                t[this->lista_vecini[nod][i]]=nod;
                //cout<<"actualizam nodul in heap\n";
                noduri.push(make_pair(-1*d[this->lista_vecini[nod][i]],this->lista_vecini[nod][i]));
            }
        }

        if (nod!=s)
        {
            //cout<<"Adaugam in solutie muchia "<<nod<<" - "<<t[nod]<<"\n";
            sol.push_back(make_pair(nod,t[nod]));
        }
    }
    g<<cost<<"\n"<<this->n-1<<"\n";
    for (unsigned int i=0; i<sol.size(); ++i)
        g<<sol[i].first<<" "<<sol[i].second<<"\n";

}

int main()
{
    switch (PROBLEMA)
    {
    case 1:
    {
        f.open ("bfs.in", std::ifstream::in);
        g.open ("bfs.out", std::ifstream::out);
        graf a(1);
        a.StartBFS();
        f.close();
        g.close();
        break;
    }
    case 2:
    {
        f.open ("dfs.in", std::ifstream::in);
        g.open ("dfs.out", std::ifstream::out);
        graf a(2);
        a.StartDFS();
        f.close();
        g.close();
        break;
    }
    case 3:
    {
        f.open("biconex.in",std::fstream::in);
        g.open("biconex.out",std::fstream::out);
        graf a(2);
        a.Startbiconex();
        f.close();
        g.close();
        break;
    }
    case 4:
    {
        f.open("ctc.in",std::fstream::in);
        g.open("ctc.out",std::fstream::out);
        graf a(3);
        a.Startctc();
        f.close();
        g.close();
        break;
    }
    case 5:
    {
        f.open("sortaret.in",std::fstream::in);
        g.open("sortaret.out",std::fstream::out);
        graf a(3);
        a.Startsortaret();
        f.close();
        g.close();
        break;
    }
    case 6:
    {
        f.open("havelhakimi.in",std::fstream::in);
        g.open("havelhakimi.out",std::fstream::out);
        graf a;
        a.havelhakimi();
        f.close();
        g.close();
        break;
    }
    case 7:
    {
        f.open("criticalConnections.in",std::fstream::in);
        g.open("criticalConnections.out",std::fstream::out);
        graf a;
        a.StartcriticalConnections();
        f.close();
        g.close();
        break;
    }
    case 8:
    {
        f.open("apm.in",std::fstream::in);
        g.open("apm.out",std::fstream::out);
        graf a;
        a.apm();
        f.close();
        g.close();
        break;
    }
    default:
        break;
    }
}