#include <iostream>
#include <fstream>
#include <vector>
#include <queue>
#include <unordered_set>
#include <stack>
#include <map>
#include <algorithm>

std::ifstream f("graful.in");
std::ofstream g("graful.out");
//std::ifstream f("sortaret.in");
//std::ofstream g("sortaret.out");

int start = 0, contor;   // contorul il vom folosi in mai multe probleme;  start va aparea eventual ca nod de start
const int nodgol = 0;

class vecin
{
	int index;  // eticheta sa
	int cost;	 // costul muchiei catre acest vecin

	vecin(int idx = 0, int costul = 0) : index(idx), cost(costul) {}

	friend class graf;
};

template <typename moneda>
class muchie
{
	int vf1;
	int vf2;
	moneda cost;

public:
	muchie(int varf1 = 0, int varf2 = 0, int costul = 0) : vf1(varf1), vf2(varf2), cost(costul) {}
	friend class graf;


	void setAll(int varf1, int varf2, int costul)
	{
		vf1 = varf1;
		vf2 = varf2;
		cost = costul;
	}
	moneda getcost() const
	{
		return cost;
	}

	bool operator < (const muchie& m)
	{
		if (cost < m.getcost())
			return true;
		return false;
	}
};

typedef std::stack< std::pair <int, int > > stackpair;
typedef std::unordered_set< int > multime;
typedef std::vector< std::vector < int > > vector_vectori;
typedef std::vector < vecin > vector_vecini;


class graf
{
private:
	const bool orientat;
	const bool areCosturi;
	const bool areListaMuchii;

	int nrvf, nrmuchii;
	vector_vecini* vecini;

	muchie<int>* lista_muchii;
	int size_lista_muchii;
	bool lista_muchii_sortata;

	void DFS(int nod, bool* viz);
	void biconexe(int nod, int tata, bool* viz, multime* wayback, stackpair& muchiiviz, vector_vectori& comp_biconexe);
	void tareconexe(int nod, int& freeorder, int* order, int* leastbackorder, bool* pestiva, std::stack<int>& noduriviz, vector_vectori& comp_tareconexe);
	void mCrits(int nod, int tata, bool* viz, multime* wayback, stackpair& muchiiviz, vector_vectori& connections, vector_vectori& solutia);
	void DFS_SortareTopologica(int nod, bool* viz, int* finished, int& idxfinished);
public:
	graf(bool orientat_param = true, bool areCosturi_param = true, bool areListaMuchii_param = true);

	int get_nrvf() { return nrvf; }
	void copiaza_listeAdiacenta(vector_vectori& solution);
	void verifvecini();

	void BFS();
	void cadruDFS();
	void cadru_biconexe();
	void cadru_tareconexe();
	vector_vectori criticalConnections(int n, vector_vectori& connections);
	void cadruSortareTopologica();

	int tataMare(int nod, int tata[]);
	void kruskal();

	~graf()
	{
		delete[]vecini;
		if (lista_muchii)
			delete[] lista_muchii;
	}
};

graf::graf(bool orientat_param, bool areCosturi_param, bool areListaMuchii_param) : orientat(orientat_param), areCosturi(areCosturi_param), areListaMuchii(areListaMuchii_param)
{
	f >> nrvf >> nrmuchii;
	if (start)	// daca start este nenul, inseamna ca avem de citit un nod de start...
		f >> start;

	vecini = new vector_vecini[nrvf + 1];
	if (areListaMuchii)
	{
		//if (orientat)
			size_lista_muchii = nrmuchii;
		//else
		// 	size_lista_muchii = 2 * nrmuchii;

		lista_muchii = new muchie<int>[size_lista_muchii];
	}
	else
	{
		size_lista_muchii = 0;
		lista_muchii = NULL;
	}
	lista_muchii_sortata = false;

	int idxListaMuchii = 0;
	for (int i = 0; i < nrmuchii; i++)
	{
		int x, y, c = 0;
		f >> x >> y;
		if (areCosturi)
			f >> c;

		vecin aux(y, c);
		vecini[x].push_back(aux);
		if (!orientat)
		{
			vecin aux(x, c);
			vecini[y].push_back(aux);
		}

		if (areListaMuchii)
		{
			lista_muchii[idxListaMuchii].setAll(x, y, c);
			idxListaMuchii++;
			//if (!orientat)
			//{
			//	lista_muchii[idxListaMuchii].setAll(y, x, c);
			//	idxListaMuchii++;
			//}
		}
	}
}

#pragma region Functii graf
void graf::verifvecini()
{
	for (int i = 1; i <= nrvf; i++)
	{
		std::cout << "\n  vecinii lui " << i << " :  ";
		for (unsigned int j = 0; j < vecini[i].size(); j++)
			std::cout << vecini[i][j].index << " ";
	}
}

void graf::BFS()
{
	int* dist = new int[nrvf + 1]{ 0 };	// initializam distantele cu 0 (le decrementam ulterior)
	std::queue <int> qBFS;	  // coada pt BFS
	qBFS.push(start);
	dist[start] = 1;

	while (!qBFS.empty())
	{
		const int nod = qBFS.front();
		for (unsigned int i = 0; i < vecini[nod].size(); i++)
		{
			const int nod_urm = vecini[nod][i].index;
			if (dist[nod_urm] == 0)
			{
				qBFS.push(nod_urm);
				dist[nod_urm] = dist[nod] + 1;
			}
		}

		qBFS.pop();
	}

	for (int i = 1; i <= nrvf; i++)
		g << dist[i] - 1 << " ";

	delete[] dist;
}

void graf::DFS(int nod, bool* viz)
{
	viz[nod] = true;
	for (unsigned int i = 0; i < vecini[nod].size(); i++)
	{
		const int nod_urm = vecini[nod][i].index;
		if (!viz[nod_urm])
			DFS(nod_urm, viz);
	}
}
void graf::cadruDFS()
{
	contor = 0;
	bool* viz = new bool[nrvf + 1]{ 0 };
	for (int i = 1; i <= nrvf; i++)
		if (!viz[i])
		{
			contor++;
			DFS(i, viz);
		}
	g << contor;
	delete[]viz;
}

void graf::biconexe(int nod, int tata, bool* viz, multime* wayback, stackpair& muchiiviz, vector_vectori& comp_biconexe)
{
	viz[nod] = true;

	for (unsigned int i = 0; i < vecini[nod].size(); i++)
	{
		const int nod_urm = vecini[nod][i].index;

		if (viz[nod_urm])
		{
			if (nod_urm != tata and nod_urm != nod)
			{
				wayback->insert(nod_urm);
				for (unsigned int i = 0; i < vecini[nod_urm].size(); i++)
					if (vecini[nod_urm][i].index == nod)
					{
						vecini[nod_urm][i].index = nod_urm;
						break;
					}
			}
		}
		else
		{
			muchiiviz.push({ nod, nod_urm });
			multime* wayback_fiu = new multime;
			biconexe(nod_urm, nod, viz, wayback_fiu, muchiiviz, comp_biconexe);

			wayback_fiu->erase(nod);
			if (wayback_fiu->size() == 0)
			{
				contor++;
				std::vector< int > aux;
				comp_biconexe.push_back(aux);
				while (muchiiviz.top().first != nod)
				{
					comp_biconexe.back().push_back(muchiiviz.top().second);
					muchiiviz.pop();
				}
				comp_biconexe.back().push_back(muchiiviz.top().second);
				comp_biconexe.back().push_back(muchiiviz.top().first);
				muchiiviz.pop();
			}
			else
				wayback->insert(wayback_fiu->begin(), wayback_fiu->end());

			delete wayback_fiu;
		}
	}
}
void graf::cadru_biconexe()
{
	contor = 0;
	vector_vectori comp_biconexe;		// solutia, de forma unui vector cu alti vectori ce reprezinta componentele biconexe
	bool* viz = new bool[nrvf + 1]{ 0 };	// nodurile vizitate deja
	stackpair muchiiviz;							// stiva de muchii vizitate
	multime* setgol = new multime;		// un set "wayback" pe care il pasez fiului pentru a-mi returna caile de intoarcere disponibile
	biconexe(1, -1, viz, setgol, muchiiviz, comp_biconexe);
	delete setgol;
	delete[]viz;

	g << contor << "\n";
	for (unsigned int i = 0; i < comp_biconexe.size(); i++)
	{
		for (unsigned int j = 0; j < comp_biconexe[i].size(); j++) {
			g << comp_biconexe[i][j] << " ";
		}
		g << "\n";
	}
}

void graf::tareconexe(int nod, int& freeorder, int* order, int* leastbackorder, bool* pestiva, std::stack<int>& noduriviz, vector_vectori& comp_tareconexe)
{
	order[nod] = freeorder;
	leastbackorder[nod] = freeorder;
	freeorder++;
	noduriviz.push(nod);
	pestiva[nod] = true;

	for (unsigned int i = 0; i < vecini[nod].size(); i++)
	{
		const int nod_urm = vecini[nod][i].index;

		if (order[nod_urm] == 0)			// nevizitat
		{
			tareconexe(nod_urm, freeorder, order, leastbackorder, pestiva, noduriviz, comp_tareconexe);
			leastbackorder[nod] = std::min(leastbackorder[nod], leastbackorder[nod_urm]);
		}
		else if (pestiva[nod_urm])		// vizitat, dar inca pe stiva
			leastbackorder[nod] = std::min(leastbackorder[nod], order[nod_urm]);
	}

	if (leastbackorder[nod] == order[nod])   //  nodul nu se poate intoarce mai sus de el
	{
		contor++;
		std::vector< int > aux;
		comp_tareconexe.push_back(aux);

		int varf = noduriviz.top();
		while (varf != nod)
		{
			noduriviz.pop();
			pestiva[varf] = false;
			comp_tareconexe.back().push_back(varf);

			varf = noduriviz.top();
		}
		noduriviz.pop();
		pestiva[varf] = false;
		comp_tareconexe.back().push_back(varf);
	}
}
void graf::cadru_tareconexe()
{
	if (!orientat)
	{
		std::cout << "\n   Graful dat trebuie sa fie orientat pentru a rezolva aceasta problema";
		g << "\n   Graful dat trebuie sa fie orientat pentru a rezolva aceasta problema";
		return;
	}

	contor = 0;
	vector_vectori comp_tareconexe;				// solutia, de forma unui vector cu alti vectori ce reprezinta componentele tareconexe
	std::stack<int> noduriviz;								// stiva de noduri vizitate
	bool* pestiva = new bool[nrvf + 1]{ 0 };
	int* order = new int[nrvf + 1]{ 0 };				// ordinea intrarii pe stiva a nodurilor
	int freeorder = 1;
	int* leastbackorder = new int[nrvf + 1]{ 0 };		// cel mai mic ordin accesibil din urma, de pe stiva

	for (int i = 1; i <= nrvf; i++)
		if (order[i] == 0)		//  nod nevizitat 
			tareconexe(i, freeorder, order, leastbackorder, pestiva, noduriviz, comp_tareconexe);

	g << contor << "\n";
	for (unsigned int i = 0; i < comp_tareconexe.size(); i++)
	{
		for (unsigned int j = 0; j < comp_tareconexe[i].size(); j++)
			g << comp_tareconexe[i][j] << " ";
		g << "\n";
	}

	delete[] leastbackorder;
	delete[] order;
	delete[] pestiva;
}

void graf::copiaza_listeAdiacenta(vector_vectori& solution)
{
	// Obs: ^ asta face doar o copie a listelor de adiacenta din graf
	// e un design incurcat pt a adapta antetul functiei cerute pe leetcode, dar eu am preferat sa folosesc connections pe post de g.vecini ca sa reutilizez algoritmul de la ex precedent

	std::vector< int > aux;
	solution.push_back(aux);
	for (int i = 1; i <= nrvf; i++)
	{
		std::vector< int > aux;
		solution.push_back(aux);
		for (unsigned int j = 0; j < vecini[i].size(); j++)
			solution.back().push_back(vecini[i][j].index);
	}
}
void graf::mCrits(int nod, int tata, bool* viz, multime* wayback, stackpair& muchiiviz, vector_vectori& connections, vector_vectori& solutia)
{
	viz[nod] = true;
	for (unsigned int i = 0; i < connections[nod].size(); i++)
	{
		const int nod_urm = connections[nod][i];
		if (viz[nod_urm])
		{
			if (nod_urm != tata and nod_urm != nod)
			{
				wayback->insert(nod_urm);
				for (unsigned int i = 0; i < connections[nod_urm].size(); i++)
					if (connections[nod_urm][i] == nod)
					{
						connections[nod_urm][i] = nod_urm;
						break;
					}
			}
		}
		else
		{
			muchiiviz.push({ nod, nod_urm });
			multime* wayback_fiu = new multime;
			mCrits(nod_urm, nod, viz, wayback_fiu, muchiiviz, connections, solutia);

			if (wayback_fiu->size() == 0)
			{
				std::vector< int > aux;
				solutia.push_back(aux);
				while (muchiiviz.top().first != nod)
					muchiiviz.pop();

				solutia.back().push_back(muchiiviz.top().first);
				solutia.back().push_back(muchiiviz.top().second);
				muchiiviz.pop();
			}
			else
			{
				wayback_fiu->erase(nod);
				wayback->insert(wayback_fiu->begin(), wayback_fiu->end());
			}

			delete wayback_fiu;
		}
	}
}
std::vector< std::vector< int > > graf::criticalConnections(int n, vector_vectori& connections)
{
	vector_vectori solutia;		// solutia, de forma unui vector cu alti vectori ce reprezinta muchiile critice
	bool* viz = new bool[nrvf + 1]{ 0 };	// nodurile vizitate deja
	stackpair muchiiviz;							// stiva de muchii vizitate
	multime* setgol = new multime;		// un set "wayback" pe care il pasez fiului pentru a-mi returna caile de intoarcere disponibile
	mCrits(1, -1, viz, setgol, muchiiviz, connections, solutia);
	delete setgol;
	delete[]viz;

	return solutia;
}

void graf::DFS_SortareTopologica(int nod, bool* viz, int* finished, int& idxfinished)
{
	viz[nod] = true;
	for (unsigned int i = 0; i < vecini[nod].size(); i++)
	{
		const int nod_urm = vecini[nod][i].index;
		if (!viz[nod_urm])
			DFS_SortareTopologica(nod_urm, viz, finished, idxfinished);
	}
	finished[idxfinished] = nod;
	idxfinished++;
}
void graf::cadruSortareTopologica()
{
	if (!orientat)
	{
		std::cout << "\n   Graful dat trebuie sa fie orientat pentru a rezolva aceasta problema";
		g << "\n   Graful dat trebuie sa fie orientat pentru a rezolva aceasta problema";
		return;
	}

	bool* viz = new bool[nrvf + 1]{ 0 };
	int* finished = new int[nrvf + 1]{ 0 };
	int idxfinished = 1;
	for (int i = 1; i <= nrvf; i++)
		if (!viz[i])
			DFS_SortareTopologica(i, viz, finished, idxfinished);

	for (int i = nrvf; i >= 1; i--)
		g << finished[i] << " ";
	delete[]finished;
	delete[]viz;
}

int graf::tataMare(int nod, int tata[])
{
	// implementam un algoritm "tataMare()" care imi trece recursiv prin tati si la intoarcere imi seteaza peste tot cel mai batran nod ca fiind tata direct

	if (tata[nod] == nodgol)
		return nod;	// l-am gasit pe tataMare
	tata[nod] = tataMare(tata[nod], tata);		// toate nodurile de pe drum il vor primi ca tata pe tataMare
	return tata[nod];		// dau inapoi in recursie informatia pe care am primit-o eu despre cine e tataMare in arborele acesta
}

void graf::kruskal()
{
	if (!areCosturi)
	{
		std::cout << "\n   Muchiile din graful dat trebuie sa  pentru a rezolva aceasta problema";
		g << "\n   Muchiile din graful dat trebuie sa  pentru a rezolva aceasta problema";
		return;
	}
	
	if (! lista_muchii_sortata)
	{
		std::sort(lista_muchii, lista_muchii + size_lista_muchii);
		lista_muchii_sortata = true;
	}
	std::vector<int> indecsii_muchii;
	contor = 0;   // folosim contor sa stocam costul APM;

	//construim un vector de tati in care, pt eficienta, tatal fiecarui nod va fi initializat cu zero.
	int* tata = new int[nrvf + 1]{ 0 };
	int* h_subarbore = new int[nrvf + 1]{ 0 }; // ne va interesa in general doar inaltimea pt nodurile returnate de tataMare

	for (int i = 0; i < size_lista_muchii; i++)
	{
		const int tataMare1 = tataMare(lista_muchii[i].vf1, tata);
		const int tataMare2 = tataMare(lista_muchii[i].vf2, tata);
		if (tataMare1 != tataMare2)
		{
			// avem o muchie buna
			indecsii_muchii.push_back(i);
			contor += lista_muchii[i].cost;

			const int h1 = h_subarbore[tataMare1];
			const int h2 = h_subarbore[tataMare2];
			if (h1 == h2)
			{
				tata[tataMare2] = tataMare1;
				h_subarbore[tataMare1]++;
			}
			else if (h1 > h2)
				tata[tataMare2] = tataMare1;
			else
				tata[tataMare1] = tataMare2;
		}
	}
	delete[]tata;

	g << contor << "\n" << nrvf - 1;	// cost si nr muchii APM 
	for (unsigned int i = 0; i < indecsii_muchii.size(); i++)
		g << "\n" << lista_muchii[i].vf1 << " " << lista_muchii[i].vf2;
}
#pragma endregion

bool HavelHakimi()
{
	int nrnod, sumgrade = 0;
	f >> nrnod;
	std::map< int, int, std::greater< int > > grad;		//   grad  :  nr_noduri_cu_acel_grad  | sortat descresc

	grad.insert(std::pair< int, int >(0, 0));
	for (int i = 1; i <= nrnod; i++)
	{
		int gradaux;		// gradul nodului curent
		f >> gradaux;
		if (gradaux >= nrnod)
		{
			std::cout << "\n grad prea mare introdus! ";
			return false;
		}
		sumgrade += gradaux;

		if (grad.find(gradaux) == grad.end())	// daca nu avem inca o clasa de noduri pentru gradul curent
		{
			grad.insert(std::pair< int, int >(gradaux, 1));		// facem una, ce retine contorul pt un nod
			std::cout << "\n clasa " << gradaux << " a fost creata si contine " << grad[gradaux] << " nod(uri)";
		}
		else
		{
			grad[gradaux]++;		// else, crestem contorul
			std::cout << "\n clasa " << gradaux << " contine acum " << grad[gradaux] << " nod(uri)";
		}
	}
	if (sumgrade % 2 != 0)
	{
		std::cout << "\n suma gradelor este impara! ";
		return false;
	}

	while (grad[0] < nrnod)
	{
		int maxgr = grad.begin()->first;	// cel mai mare grad existent
		if (maxgr == 0)
			break;
		std::cout << "\n\n | incepere iteratie pentru legare nod din clasa " << maxgr;
		std::map< int, int >::iterator lastgr = grad.begin();
		// ultimul grad care va avea noduri legate de un nod din maxgr
		int contor = maxgr;			// nr noduri ce trb legate de acest nod in cauza
		grad[0] ++;						// rezolvam un nod din maxgr
		grad[maxgr]--;

		bool intrat_in_grad0 = false;
		while (contor and lastgr != grad.end())
		{
			if (lastgr->first == 0)
				intrat_in_grad0 = true;

			if (contor - lastgr->second >= 0)
			{
				contor -= lastgr->second;		// voi lega nodul de nodurile din lastgr
				lastgr++;
			}
			else
				break;
		}
		if (intrat_in_grad0)
		{
			std::cout << "\n nu am avut suficiente noduri ramase pt a lega nodul curent";
			return false;
		}
		std::cout << "\n clasa cea mai mica la care ne-am oprit: " << lastgr->first;

		if (contor)  // daca avem o clasa din care trb sa "mutam" doar o parte din valori
		{
			// pornim din dreapta si "mutam" valorile intr-o clasa mai mica
			if (grad.find(lastgr->first - 1) == grad.end())
				grad.insert(std::pair< int, int >(lastgr->first - 1, contor));
			else
				grad[lastgr->first - 1] += contor;
			// in contor au ramas o parte din nodurile ce trb "mutate" din lastgr
			lastgr->second -= contor;

			std::cout << "\n am legat nodul de " << contor << " nod( uri ) din clasa " << lastgr->first;
		}

		int auxleft = 0, auxright = 0;
		for (auto it = grad.begin(); it != lastgr; it++)
		{
			auxright = it->second;	// salvam nr noduri din clasa curenta
			it->second = auxleft;	// luam nr de noduri din stanga
			auxleft = auxright;		// val din auxright se salveaza in auxleft pt pasul urm
			std::cout << "\n am legat nodul de " << auxleft << " nod(uri) din clasa " << it->first;

			if (grad.find(it->first - 1) == grad.end())
			{
				// daca nu avem clasa coresp etichetei curente minus 1, o cream si ii dam direct auxleft
				grad.insert(std::pair< int, int >(it->first - 1, auxleft));
				auxleft = 0;
				it++;  // sarim clasa noua
			}
		}
		lastgr->second += auxleft;  // am scos deja din lastgr, acum ii si aducem (eventual) cv din stanga

		while (grad[maxgr] == 0)		// daca nu mai avem noduri in maxgr dupa ce rezolvam unul
		{
			std::cout << "\n clasa " << maxgr << " a fost epuizata";
			grad.erase(maxgr);			// nu ne va mai trebui clasa cu eticheta "maxgr"
			maxgr = grad.begin()->first;
		}
	}
	return true;
}


int main()
{
	start = 0;		// daca start e setat la zero, nu se va mai citi un nod de start

	//graf g(false, false, false);
	//g.verifvecini();

	//graf g(false, false, false);
	//g.cadru_biconexe();

	//	//// muchii critice:
	//graf g(false, false, false);
	//vector_vectori* connections = new vector_vectori;
	//g.copiaza_listeAdiacenta(*connections);
	//vector_vectori vector_afisare = g.criticalConnections(g.get_nrvf(), *connections);
	//for (int i = 0; i < vector_afisare.size(); i++)
	//	std::cout << vector_afisare[i][0] << " " << vector_afisare[i][1] << "\n";
	//delete connections;

	//graf g(true, false, false);
	//g.cadru_tareconexe();

	//std::cout << "\n\n Status final Havel Hakimi: " << HavelHakimi() << "\n\n";

	//graf g(true, false, false);
	//g.cadruSortareTopologica();

	graf g(false, true, true);
	g.kruskal();

	return 0;
}