/// Lacatus Catalin-Petru, grupa 2341
#include<iostream>
#include<vector>
#include <queue>
#include<stack>
#include <utility>
#include<algorithm>
#include<fstream>
using namespace std;
const int oo = numeric_limits<int>::max();
class Graf { ///clasa abstracta graf
protected:
int Nr_noduri, Nr_muchii;
public:
Graf(int, int);
~Graf();
virtual void citire(istream& in) = 0;
virtual void afisare(ostream& out) = 0;
};
Graf::Graf(int Nr_noduri = 0, int Nr_muchii = 0) {
this->Nr_noduri = Nr_noduri;
this->Nr_muchii = Nr_muchii;
}
Graf::~Graf() {
this->Nr_noduri = 0;
this->Nr_muchii = 0;
}
/// ------------------------------------------------------------------------
class Graf_orientat : public Graf ///graf orientat
{
private:
vector<vector<int>>Lista_de_adiacenta;
vector<vector<int>> Costuri;
public:
Graf_orientat(int, int, vector<vector<int>>, vector<vector<int>>, int ok);
~Graf_orientat();
void citire(istream& in);
void afisare(ostream& out);
friend istream& operator >>(istream&, Graf_orientat&);
friend ostream& operator <<(ostream&, Graf_orientat&);
vector<int> BFS_infoarena(int) const;
vector<int> Sortare_topologica_infoarena() const;
vector<vector<int>>CTC_infoarena(int&);
void Dijkstra_infoarena(ifstream&, ofstream&);
void Bellman_ford_infoarena(ofstream&);
void Roy_Floyd(vector<vector<long long>>&);
int Flux_maxim();
private:
void DFS(int, vector<int>&, stack<int>&);
void Transpusa();
void DFS_transpusa(int, vector<int>&, int, vector<vector<int>>&);
vector<vector<int>> CTC(int&);
vector<int> BFS(int) const;
vector<int> Sortare_topologica() const;
void Dijkstra(int, vector<int>&);
void Bellman_ford(int, vector<int>&, bool&);
int Bfs_flux(const int&, const int&, vector<int>, const vector<vector<int>>&, vector<int>&);
};
Graf_orientat::Graf_orientat(int Nr_noduri = 0, int Nr_muchii = 0, vector<vector<int>>Lista_de_adiacenta = {}, vector<vector<int>>Costuri = {}, int ok = 0) :Graf(Nr_noduri, Nr_muchii) {
try {
if (Costuri.size() == 0)
throw 1;
if (ok == 1)
throw 3;
this->Lista_de_adiacenta.resize(Nr_noduri + 1);
this->Costuri.resize(Nr_noduri + 1);
if (Nr_muchii == 0)
throw 2;
for (int i = 0; i < Lista_de_adiacenta.size(); i++)
for (int j = 0; j < Lista_de_adiacenta[i].size(); j++)
{
this->Lista_de_adiacenta[i].push_back(Lista_de_adiacenta[i][j]);
this->Costuri[i].push_back(Costuri[i][j]);
}
}
catch (int x) {
if (x == 1 || x == 2)
{
this->Lista_de_adiacenta.resize(Nr_noduri + 1);
this->Costuri.resize(Nr_noduri + 1);
for (int i = 0; i < Lista_de_adiacenta.size(); i++)
for (int j = 0; j < Lista_de_adiacenta[i].size(); j++)
this->Lista_de_adiacenta[i].push_back(Lista_de_adiacenta[i][j]);
}
if (x == 3)
{
this->Lista_de_adiacenta.resize(Nr_noduri + 1);
this->Costuri.resize(Nr_noduri + 1, vector<int>(Nr_noduri, 0));
for (int i = 1; i < Lista_de_adiacenta.size(); i++)
for (int j = 0; j < Lista_de_adiacenta[i].size(); j++)
{
this->Lista_de_adiacenta[i].push_back(Lista_de_adiacenta[i][j]);
this->Costuri[i][Lista_de_adiacenta[i][j] - 1] = Costuri[i][Lista_de_adiacenta[i][j] - 1];
}
}
}
}
void Graf_orientat::citire(istream& in) {
in >> Nr_noduri;
in >> Nr_muchii;
this->Lista_de_adiacenta.resize(Nr_noduri + 1);
int stanga, dreapta;
for (int i = 1; i <= Nr_muchii; i++)
{
in >> stanga;
in >> dreapta;
Lista_de_adiacenta[stanga].push_back(dreapta);
}
}
void Graf_orientat::afisare(ostream& out) {
out << Nr_noduri << " ";
out << Nr_muchii << endl;
for (int i = 1; i < Lista_de_adiacenta.size(); i++) {
cout << endl;
for (int j = 0; j < Lista_de_adiacenta[i].size(); j++)
out << i << ":" << Lista_de_adiacenta[i][j] << " ";
}
}
istream& operator>>(istream& in, Graf_orientat& g)
{
g.citire(in);
return in;
}
ostream& operator<<(ostream& out, Graf_orientat& g)
{
g.afisare(out);
return out;
}
Graf_orientat::~Graf_orientat() {
this->Lista_de_adiacenta.clear();
}
/// ------------------------------------------------------------------------
class Graf_neorientat : public Graf ///graf neorientat
{
private:
vector<vector<int>>Lista_de_adiacenta;
vector<vector<int>> Costuri;
public:
Graf_neorientat(int, int, vector<vector<int>>, vector<vector<int>>);
~Graf_neorientat();
int get_nr_noduri();
void Adauga_in_lista_de_adiacenta(const int&, const int&, const int&);
void citire(istream& in);
void afisare(ostream& out);
friend istream& operator >>(istream&, Graf_neorientat&);
friend ostream& operator <<(ostream&, Graf_neorientat&);
int DFS_infoarena();
void Afla_noduri_critice(int, vector<int>&, vector<int>&, vector<int>&, vector<int>&, vector<int>&) const;
vector<vector<pair<int, int>>> Componente_biconexe_infoarena(int&);
void Havel_Hakimi_sol();
vector<pair<int, int>> Afla_muchii_critice_rezolvare();
void APM_infoarena(int, ofstream&);
void Pad_de_mult_dis_infoarena(ifstream&, ofstream&);
int Diametru_arbore();
bool Verif_cilcu_eulerian() const;
void Ciclu_eulerian(int, vector<bool>&, vector<int>&);
private:
void DFS(int, vector<int>&) const;
void Afla_muchii_critice(int, vector<int>&, vector<int>&, vector<int>&, vector<int>&, vector<pair<int, int>>&);
vector<pair<int, int>> AMC();
vector<int> ANC() const;
void Parcurgere_comp_biconexe(int, vector<int>&, vector<int>&, vector<int>&, vector<int>&, stack<pair<int, int>>&, vector<vector<pair<int, int>>>&, int&);
vector<vector<pair<int, int>>> Componente_biconexe(int&);
bool Havel_Hakimi_algoritm(vector<int>& Secventa_de_grade);
vector<int> Arbore_partial_de_cost_minim(int&, int&) const;
int Gaseste_tata_arbore(int, vector<int>&);
void Reuniune_de_multimi(int, int, vector<int>&);
void Afla_distante_dfs(int, vector<int>&, vector<int>&);
};
void Graf_neorientat::Adauga_in_lista_de_adiacenta(const int& nod_st, const int& nod_dr, const int& val_cost_indice) {
this->Lista_de_adiacenta[nod_st].push_back(nod_dr);
this->Lista_de_adiacenta[nod_dr].push_back(nod_st);
this->Costuri[nod_st].push_back(val_cost_indice);
this->Costuri[nod_dr].push_back(val_cost_indice);
}
Graf_neorientat::Graf_neorientat(int Nr_noduri = 0, int Nr_muchii = 0, vector<vector<int>>Lista_de_adiacenta = {}, vector<vector<int>>Costuri = {}) :Graf(Nr_noduri, Nr_muchii) {
try {
if (Lista_de_adiacenta.size() == 0 || Costuri.size() == 0)
throw 1;
if (Costuri.size() == 0)
throw 2;
this->Lista_de_adiacenta.resize(Nr_noduri + 1);
this->Costuri.resize(Nr_noduri + 1);
for (int i = 0; i < Lista_de_adiacenta.size(); i++)
for (int j = 0; j < Lista_de_adiacenta[i].size(); j++)
{
this->Lista_de_adiacenta[i].push_back(Lista_de_adiacenta[i][j]);
this->Costuri[i].push_back(Costuri[i][j]);
}
}
catch (int x) {
if (x == 2)
{
this->Lista_de_adiacenta.resize(Nr_noduri + 1);
for (int i = 1; i < Lista_de_adiacenta.size(); i++)
for (int j = 0; j < Lista_de_adiacenta[i].size(); j++)
{
this->Lista_de_adiacenta[i].push_back(Lista_de_adiacenta[i][j]);
}
}
else if (x == 1)
{
this->Lista_de_adiacenta.resize(Nr_noduri + 1);
this->Costuri.resize(Nr_noduri + 1);
}
}
}
int Graf_neorientat::get_nr_noduri() {
return Nr_noduri;
}
void Graf_neorientat::citire(istream& in) {
in >> Nr_noduri;
in >> Nr_muchii;
this->Lista_de_adiacenta.resize(Nr_noduri + 1);
int stanga, dreapta;
for (int i = 1; i <= Nr_muchii; i++)
{
in >> stanga;
in >> dreapta;
this->Lista_de_adiacenta[stanga].push_back(dreapta);
this->Lista_de_adiacenta[dreapta].push_back(stanga);
}
}
void Graf_neorientat::afisare(ostream& out) {
out << Nr_noduri << " ";
out << Nr_muchii << endl;
for (int i = 1; i < Lista_de_adiacenta.size(); i++) {
out << i << ":" << endl;
for (int j = 0; j < Lista_de_adiacenta[i].size(); j++)
out << Lista_de_adiacenta[i][j] << " ";
out << endl;
}
}
istream& operator>>(istream& in, Graf_neorientat& g)
{
g.citire(in);
return in;
}
ostream& operator<<(ostream& out, Graf_neorientat& g)
{
g.afisare(out);
return out;
}
Graf_neorientat::~Graf_neorientat() {
this->Lista_de_adiacenta.clear();
this->Costuri.clear();
}
///--------------------------------BFS-------------------------------
vector<int> Graf_orientat::BFS(int Start_nod) const {
vector<int>Distante(this->Nr_noduri + 1, -1);
deque<int>coada;
coada.push_back(Start_nod);
Distante[Start_nod] = 0;
while (!coada.empty()) {
int primul_nod_din_coada = coada.front();
for (int i = 0; i < Lista_de_adiacenta[primul_nod_din_coada].size(); i++) {
int nod_curent = Lista_de_adiacenta[primul_nod_din_coada][i];
if (Distante[nod_curent] == -1) {
coada.push_back(nod_curent);
Distante[nod_curent] = Distante[primul_nod_din_coada] + 1;
}
}
coada.pop_front();
}
return Distante;
}
///--------------------------------DFS-------------------------------
void Graf_neorientat::DFS(int Nod_start, vector<int>& Vector_vizitati) const {
Vector_vizitati[Nod_start] = 0; ///Marcam nodul de unde incepe dfs-ul ca vizitat
for (int i = 0; i < Lista_de_adiacenta[Nod_start].size(); i++)///parcurgem vecinii nodului
{
int nod_curent = Lista_de_adiacenta[Nod_start][i];
if (Vector_vizitati[nod_curent] == -1)
DFS(nod_curent, Vector_vizitati);
}
}
///--------------------------------Nr componente conexe-------------------------------
int Graf_neorientat::DFS_infoarena() {
vector<int>Vector_vizitati(Nr_noduri + 1, -1); ///Marcam toate norudrile nevizitate
///-1 =>nod nevizitat
///0 =>nod vizitat
int Nr_comp_conexe = 0;
for (int i = 1; i <= Nr_noduri; i++)
{
if (Vector_vizitati[i] == -1) { ///Daca nodul este nevizitat se aplica DFS
DFS(i, Vector_vizitati);
Nr_comp_conexe++;
}
}
return Nr_comp_conexe;
}
///--------------------------------Noduri critice-------------------------------
void Graf_neorientat::Afla_noduri_critice(int Nod_start, vector<int>& Vector_vizitati, vector<int>& Timp_curent, vector<int>& Timp_min, vector<int>& Vector_tati,
vector<int>& Noduri_critice) const {
static int timp_curent = 0;
Vector_vizitati[Nod_start] = 0;
int copii = 0;
Timp_curent[Nod_start] = Timp_min[Nod_start] = ++timp_curent;
for (int i = 0; i < Lista_de_adiacenta[Nod_start].size(); i++) {///parcurgem vecinii nodului
int nod_curent = Lista_de_adiacenta[Nod_start][i];
if (Vector_vizitati[nod_curent] == -1) {
copii++;
Vector_tati[nod_curent] = Nod_start;
Afla_noduri_critice(nod_curent, Vector_vizitati, Timp_curent, Timp_min, Vector_tati, Noduri_critice);
Timp_min[Nod_start] = min(Timp_min[Nod_start], Timp_min[nod_curent]);
if (Vector_tati[Nod_start] == 0 && copii > 1)///daca e radacina si are mai mult de un copil
Noduri_critice.push_back(Nod_start);
if (Vector_tati[Nod_start] != 0 && Timp_min[nod_curent] >= Timp_curent[Nod_start])///daca nu e radacina si fiul are gradul de intoarcere >= decat nivelul nodului
Noduri_critice.push_back(Nod_start);
}
else
if (nod_curent != Vector_tati[Nod_start])///actualizam distantele minime
Timp_min[Nod_start] = min(Timp_min[Nod_start], Timp_curent[nod_curent]);
}
}
vector<int> Graf_neorientat::ANC() const {
vector<int>Noduri_critice;
vector<int>Vector_vizitati(Nr_noduri + 1, -1);
vector<int>Timp_curent(Nr_noduri + 1);
vector<int>Timp_min(Nr_noduri + 1);
vector<int>Vector_tati(Nr_noduri + 1, 0);
for (int i = 1; i < Lista_de_adiacenta.size(); i++)
if (Vector_vizitati[i] == -1)
Afla_noduri_critice(i, Vector_vizitati, Timp_curent, Timp_min, Vector_tati, Noduri_critice);
return Noduri_critice;
}
///----------------------------------COMPONENTE BICONEXE-----------------------------------------------------------
void Graf_neorientat::Parcurgere_comp_biconexe(int Nod_start, vector<int>& Vector_vizitati, vector<int>& Timp_curent, vector<int>& Timp_min, vector<int>& Vector_tati,
stack<pair<int, int>>& Stiva, vector<vector<pair<int, int>>>& Componente_biconexe, int& Nr_componente_biconexe) {
Vector_vizitati[Nod_start] = 1;
static int timp_curent = 0;
int copii = 0;
Timp_curent[Nod_start] = Timp_min[Nod_start] = ++timp_curent;
for (int i = 0; i < Lista_de_adiacenta[Nod_start].size(); i++) {///parcurgem vecinii nodului
int nod_curent = Lista_de_adiacenta[Nod_start][i];
if (Vector_vizitati[nod_curent] == -1) {
copii++;
Vector_tati[nod_curent] = Nod_start;
pair<int, int>Muchii;
Muchii.first = Nod_start;
Muchii.second = nod_curent;
Stiva.push(Muchii);
Parcurgere_comp_biconexe(nod_curent, Vector_vizitati, Timp_curent, Timp_min, Vector_tati, Stiva, Componente_biconexe, Nr_componente_biconexe);
Timp_min[Nod_start] = min(Timp_min[Nod_start], Timp_min[nod_curent]);
if ((Timp_curent[Nod_start] == 1 && copii > 1) || (Timp_curent[Nod_start] > 1 && Timp_min[nod_curent] >= Timp_curent[Nod_start])) { ///daca e nod critic scot din stiva
while ((Stiva.top().first != Nod_start || Stiva.top().second != nod_curent) && (Stiva.top().first != nod_curent || Stiva.top().second != Nod_start)) {
pair<int, int>Muchii;
Muchii.first = Stiva.top().first;
Muchii.second = Stiva.top().second;
Componente_biconexe[Nr_componente_biconexe].push_back(Muchii);
Stiva.pop();
}
pair<int, int>Muchii;
Muchii.first = Stiva.top().first;
Muchii.second = Stiva.top().second;
Componente_biconexe[Nr_componente_biconexe].push_back(Muchii);
Stiva.pop();
Nr_componente_biconexe++;
}
}
else
if (nod_curent != Vector_tati[Nod_start]) { ///actualizam distantele minime
Timp_min[Nod_start] = min(Timp_min[Nod_start], Timp_curent[nod_curent]);
if (Timp_curent[nod_curent] < Timp_curent[Nod_start]) {
pair<int, int>Muchii;
Muchii.first = Nod_start;
Muchii.second = nod_curent;
Stiva.push(Muchii);
}
}
}
}
vector<vector<pair<int, int>>> Graf_neorientat::Componente_biconexe(int& Nr_comp_bi) {
int Nr_comp_biconexe = 0;
vector<vector<pair<int, int>>>Componente_biconexe(Nr_noduri);
stack <pair<int, int>>Stiva;
vector<int>Vector_vizitati(Nr_noduri + 1, -1);
vector<int>Timp_curent(Nr_noduri + 1, -1);
vector<int>Timp_min(Nr_noduri + 1, -1);
vector<int>Vector_tati(Nr_noduri + 1, -1);
for (int i = 1; i < Lista_de_adiacenta.size(); i++) {
if (Vector_vizitati[i] == -1)
Parcurgere_comp_biconexe(i, Vector_vizitati, Timp_curent, Timp_min, Vector_tati, Stiva, Componente_biconexe, Nr_comp_biconexe);
int verifica = 0;
while (Stiva.size() > 0) {
verifica = 1;
pair<int, int>Muchii;
Muchii.first = Stiva.top().first;
Muchii.second = Stiva.top().second;
Componente_biconexe[Nr_comp_biconexe].push_back(Muchii);
Stiva.pop();
}
if (verifica == 1) {
Nr_comp_biconexe++;
}
}
Nr_comp_bi = Nr_comp_biconexe;
return Componente_biconexe;
}
///----------------------------------------SORTARE TOPOLOGICA--------------------------------------------
vector<int> Graf_orientat::Sortare_topologica() const {
vector<int>Rezultat;
vector<int>Vector_dependente(Nr_noduri + 1, 0);
queue<int>Coada;
for (int i = 1; i < Lista_de_adiacenta.size(); i++)
for (int j = 0; j < Lista_de_adiacenta[i].size(); j++)
Vector_dependente[Lista_de_adiacenta[i][j]]++;
for (int i = 1; i < Vector_dependente.size(); i++)
if (Vector_dependente[i] == 0)
Coada.push(i);
while (!Coada.empty())
{
int nod_curent = Coada.front();
Rezultat.push_back(nod_curent);
Coada.pop();
for (int j = 0; j < Lista_de_adiacenta[nod_curent].size(); j++)
{
Vector_dependente[Lista_de_adiacenta[nod_curent][j]]--;
if (Vector_dependente[Lista_de_adiacenta[nod_curent][j]] == 0)
Coada.push(Lista_de_adiacenta[nod_curent][j]);
}
}
return Rezultat;
}
///---------------------------------------------- MUCHII CRITICE----------------------------------------------------
void Graf_neorientat::Afla_muchii_critice(int Nod_start, vector<int>& Vector_vizitati, vector<int>& Timp_curent, vector<int>& Timp_min, vector<int>& Vector_tati,
vector<pair<int, int>>& Muchii_critice) {
static int timp_curent = 0;
Vector_vizitati[Nod_start] = 0;
Timp_curent[Nod_start] = Timp_min[Nod_start] = ++timp_curent;
for (int nod_curent : Lista_de_adiacenta[Nod_start]) {///parcurgem vecinii nodului
if (nod_curent == Vector_tati[Nod_start]) continue;
if (Vector_vizitati[nod_curent] == -1) {
Vector_tati[nod_curent] = Nod_start;
Afla_muchii_critice(nod_curent, Vector_vizitati, Timp_curent, Timp_min, Vector_tati, Muchii_critice);
Timp_min[Nod_start] = min(Timp_min[Nod_start], Timp_min[nod_curent]);
if (Timp_min[nod_curent] > Timp_curent[Nod_start])
{
pair<int, int>Muchii;
Muchii.first = Nod_start;
Muchii.second = nod_curent;
Muchii_critice.push_back(Muchii);
}
}
else
///actualizam distantele minime
Timp_min[Nod_start] = min(Timp_min[Nod_start], Timp_curent[nod_curent]);
}
}
vector<pair<int, int>> Graf_neorientat::AMC() {
vector<pair<int, int>>Muchii_critice;
vector<int>Vector_vizitati(Nr_noduri + 1, -1);
vector<int>Timp_curent(Nr_noduri + 1);
vector<int>Timp_min(Nr_noduri + 1);
vector<int>Vector_tati(Nr_noduri + 1, -1);
for (int i = 0; i < Lista_de_adiacenta.size(); i++)
if (Vector_vizitati[i] == -1)
Afla_muchii_critice(i, Vector_vizitati, Timp_curent, Timp_min, Vector_tati, Muchii_critice);
return Muchii_critice;
}
///--------------------------------------Havel Hakimi------------------------------------------------------------
bool Graf_neorientat::Havel_Hakimi_algoritm(vector<int>& Secventa_de_grade) {
bool val = true;
while (val == true) {
sort(Secventa_de_grade.begin(), Secventa_de_grade.end(), greater <>());
if (Secventa_de_grade[0] == 0)
return true;
int Grad_curent = Secventa_de_grade[0];
Secventa_de_grade.erase(Secventa_de_grade.begin() + 0);
if (Grad_curent > Secventa_de_grade.size())
return false;
for (int i = 0; i < Grad_curent; i++)
{
Secventa_de_grade[i]--;
if (Secventa_de_grade[i] < 0)
return false;
}
}
}
///-------------------------------------------------------- CTC--------------------------------------------------
void Graf_orientat::DFS_transpusa(int Nod_start, vector<int>& Vector_vizitati, int Nr_componente_conexe, vector<vector<int>>& Componente_tare_conexe) {
Vector_vizitati[Nod_start] = 1; ///Marcam nodul de unde incepe dfs-ul ca vizitat
Componente_tare_conexe[Nr_componente_conexe].push_back(Nod_start);
for (int i = 0; i < Lista_de_adiacenta[Nod_start].size(); i++)///parcurgem vecinii nodului
{
int nod_curent = Lista_de_adiacenta[Nod_start][i];
if (Vector_vizitati[nod_curent] == 0)
DFS_transpusa(nod_curent, Vector_vizitati, Nr_componente_conexe, Componente_tare_conexe);
}
}
void Graf_orientat::DFS(int Nod_start, vector<int>& Vector_vizitati, stack<int>& Stiva) {
Vector_vizitati[Nod_start] = 0; ///Marcam nodul de unde incepe dfs-ul ca vizitat
for (int i = 0; i < Lista_de_adiacenta[Nod_start].size(); i++)///parcurgem vecinii nodului
{
int nod_curent = Lista_de_adiacenta[Nod_start][i];
if (Vector_vizitati[nod_curent] == -1)
DFS(nod_curent, Vector_vizitati, Stiva);
}
Stiva.push(Nod_start);
}
void Graf_orientat::Transpusa() {
vector<vector<int>>Lista_de_adiacenta_transpusa(Nr_noduri + 1);
for (int i = 1; i < Lista_de_adiacenta.size(); i++)
for (int j = 0; j < Lista_de_adiacenta[i].size(); j++)
{
Lista_de_adiacenta_transpusa[Lista_de_adiacenta[i][j]].push_back(i);
}
this->Lista_de_adiacenta.clear();
Lista_de_adiacenta.resize(Nr_noduri + 1);
for (int i = 1; i < Lista_de_adiacenta_transpusa.size(); i++)
for (int j = 0; j < Lista_de_adiacenta_transpusa[i].size(); j++)
this->Lista_de_adiacenta[i].push_back(Lista_de_adiacenta_transpusa[i][j]);
}
vector<vector<int>> Graf_orientat::CTC(int& Nr_componente_conexe) {
vector<vector<int>>Componente_tare_conexe(Nr_noduri + 1);
vector<int>Vector_vizitati(Nr_noduri + 1, -1);
stack<int>Stiva;
for (int i = 1; i < Lista_de_adiacenta.size(); i++)
if (Vector_vizitati[i] == -1)
DFS(i, Vector_vizitati, Stiva);
Transpusa();
while (!Stiva.empty())
{
int nod_curent = Stiva.top();
Stiva.pop();
if (Vector_vizitati[nod_curent] == 0)
{
Nr_componente_conexe++;
DFS_transpusa(nod_curent, Vector_vizitati, Nr_componente_conexe, Componente_tare_conexe);
}
}
return Componente_tare_conexe;
}
///----------------------------------------------APM--------------------------------------------------------
vector<int> Graf_neorientat::Arbore_partial_de_cost_minim(int& costuri, int& nr_muchii) const {
vector<int>Vector_tati(Nr_noduri + 1, -1);
vector<bool>In_MST(Nr_noduri + 1, false);
vector<int>Cost_min(Nr_noduri + 1, costuri);
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
costuri = 0;
Cost_min[1] = 0;
pq.push({ 0,1 });
while (!pq.empty()) {
int nod = pq.top().second;
int cost = pq.top().first;
pq.pop();
if (In_MST[nod] == true) {
continue;
}
costuri = costuri + cost;
nr_muchii++;
In_MST[nod] = true;
for (int i = 0; i < Lista_de_adiacenta[nod].size(); i++) {
int nod_curent = Lista_de_adiacenta[nod][i];
int cost_curent = Costuri[nod][i];
if (In_MST[nod_curent] == false && cost_curent < Cost_min[nod_curent]) {
Cost_min[nod_curent] = cost_curent;
pq.push({ Cost_min[nod_curent],nod_curent });
Vector_tati[nod_curent] = nod;
}
}
}
return Vector_tati;
}
void Graf_neorientat::APM_infoarena(int cost, ofstream& f_out) {
int nr_muchii_APM = 0;
const vector<int> rez = Arbore_partial_de_cost_minim(cost, nr_muchii_APM);
f_out << cost << endl << nr_muchii_APM - 1 << endl;
for (int i = 2; i <= Nr_noduri; i++)
{
f_out << rez[i] << " " << i << endl;
}
}
///-------------------------------------------------Paduri de multimi disjuncte----------------------------------------------
int Graf_neorientat::Gaseste_tata_arbore(int element, vector<int>& Vector_tati) {
int e = element, copie_element;
/// caut tatal arborelui
while (e != Vector_tati[e])
e = Vector_tati[e];
/// actualizez tatal arborelui in vectorul de tati
while (element != Vector_tati[element]) {
copie_element = Vector_tati[element];
Vector_tati[element] = e;
element = copie_element;
}
return e;
}
void Graf_neorientat::Reuniune_de_multimi(int M1, int M2, vector<int>& Vector_tati) {
int m1 = Gaseste_tata_arbore(M1, Vector_tati);
int m2 = Gaseste_tata_arbore(M2, Vector_tati);
Vector_tati[m2] = m1;
}
void Graf_neorientat::Pad_de_mult_dis_infoarena(ifstream& f_in, ofstream& f_out) {
int op, x, y;
vector<int>Vector_tati(Nr_noduri + 1);
for (int i = 1; i <= Nr_noduri; i++)
Vector_tati[i] = i;
for (int i = 1; i <= Nr_muchii; i++)
{
f_in >> op >> x >> y;
if (op == 1)
{
if (Gaseste_tata_arbore(x, Vector_tati) != Gaseste_tata_arbore(y, Vector_tati))
Reuniune_de_multimi(x, y, Vector_tati);
}
else {
if (Gaseste_tata_arbore(x, Vector_tati) == Gaseste_tata_arbore(y, Vector_tati))
f_out << "DA" << endl;
else
f_out << "NU" << endl;
}
}
}
///--------------------------------------------------------Dijkstra--------------------------------------------------------
void Graf_orientat::Dijkstra(int Nod_start, vector<int>& Distante) {
vector<bool>Vector_vizitati(Nr_noduri + 1, false);
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
Distante[Nod_start] = 0;
pq.push({ 0,Nod_start });
while (!pq.empty()) {
int nod_curent = pq.top().second;
pq.pop();
if (Vector_vizitati[nod_curent] == false) {
Vector_vizitati[nod_curent] = true;
///// Parcurgem vecinii
for (int i = 0; i < Lista_de_adiacenta[nod_curent].size(); i++)
{
int vecin = Lista_de_adiacenta[nod_curent][i];
int cost = Costuri[nod_curent][i];
///// Actualizez distantele de la nodul de start la nodul curent
if (Distante[nod_curent] + cost < Distante[vecin]) {
Distante[vecin] = Distante[nod_curent] + cost;
pq.push({ Distante[vecin],vecin });
}
}
}
}
}
void Graf_orientat::Dijkstra_infoarena(ifstream& f_in, ofstream& f_out) {
int Nr_noduri, Nr_muchii, nod_st, nod_dr, cost;
f_in >> Nr_noduri >> Nr_muchii;
this->Nr_noduri = Nr_noduri;
this->Nr_muchii = Nr_muchii;
this->Lista_de_adiacenta.resize(Nr_noduri + 1);
this->Costuri.resize(Nr_noduri + 1);
for (int i = 1; i <= Nr_muchii; i++) {
f_in >> nod_st >> nod_dr >> cost;
this->Lista_de_adiacenta[nod_st].push_back(nod_dr);
this->Costuri[nod_st].push_back(cost);
}
vector<int>Distante(Nr_noduri + 1, oo);
Dijkstra(1, Distante);
for (int i = 2; i < Distante.size(); i++)
if (Distante[i] == oo)
f_out << 0 << " ";
else
f_out << Distante[i] << " ";
}
///-------------------------------------------------Bellman_ford-------------------------------------
void Graf_orientat::Bellman_ford(int Nod_start, vector<int>& Distante, bool& ciclu) {
vector<int>Vector_vizitati(Nr_noduri + 1, 0);
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
Distante[Nod_start] = 0;
pq.push({ 0,Nod_start });
while (!pq.empty()) {
int nod_curent = pq.top().second;
pq.pop();
Vector_vizitati[nod_curent]++;
if (Vector_vizitati[nod_curent] < Nr_noduri - 1) {
///// Parcurgem vecinii
for (int i = 0; i < Lista_de_adiacenta[nod_curent].size(); i++)
{
int vecin = Lista_de_adiacenta[nod_curent][i];
int cost = Costuri[nod_curent][i];
///// Actualizez distantele de la nodul de start la nodul curent
if (Distante[nod_curent] + cost < Distante[vecin]) {
Distante[vecin] = Distante[nod_curent] + cost;
pq.push({ Distante[vecin],vecin });
}
}
}
else {
ciclu = true;
while (!pq.empty())
pq.pop();
}
}
}
void Graf_orientat::Bellman_ford_infoarena(ofstream& f_out) {
vector<int>Distante(Nr_noduri + 1, oo);
bool ciclu = false;
Bellman_ford(1, Distante, ciclu);
if (ciclu == true)
f_out << "Ciclu negativ!";
else
{
for (int i = 2; i < Distante.size(); i++)
f_out << Distante[i] << " ";
}
}
void Graf_neorientat::Afla_distante_dfs(int Nod_start, vector<int>& Vector_vizitati, vector<int>& Distante) {
Vector_vizitati[Nod_start] = 0; ///Marcam nodul de unde incepe dfs-ul ca vizitat
for (int i = 0; i < Lista_de_adiacenta[Nod_start].size(); i++)///parcurgem vecinii nodului
{
int nod_curent = Lista_de_adiacenta[Nod_start][i];
if (Vector_vizitati[nod_curent] == -1)
{
Distante[nod_curent] = Distante[Nod_start] + 1;
Afla_distante_dfs(nod_curent, Vector_vizitati, Distante);
}
}
}
int Graf_neorientat::Diametru_arbore() {
vector<int>Vector_vizitati(Nr_noduri + 1, -1);
vector<int> Distante(Nr_noduri + 1, 1);
Afla_distante_dfs(1, Vector_vizitati, Distante);
int maxim = -1, nod;
for (int i = 1; i <= Nr_noduri; i++)
if (Distante[i] > maxim)
{
nod = i;
maxim = Distante[i];
}
Vector_vizitati.clear();
Distante.clear();
Vector_vizitati.resize(Nr_noduri + 1, -1);
Distante.resize(Nr_noduri + 1, 1);
Afla_distante_dfs(nod, Vector_vizitati, Distante);
return *max_element(Distante.begin(), Distante.end());
}
void Graf_orientat::Roy_Floyd(vector<vector<long long>>& Matrice) {
for (int k = 0; k < Nr_noduri; k++)
for (int i = 0; i < Nr_noduri; i++)
for (int j = 0; j < Nr_noduri; j++)
if (Matrice[i][j] > Matrice[i][k] + Matrice[k][j])
Matrice[i][j] = Matrice[i][k] + Matrice[k][j];
}
int Graf_orientat::Bfs_flux(const int& Start_nod, const int& destinatie, vector<int> Vector_vizitati, const vector<vector<int>>& Vec_fluxuri, vector<int>& Vector_tati) {
deque<int>coada;
coada.push_back(Start_nod);
Vector_vizitati[Start_nod] = 0;
while (!coada.empty())
{
int primul_nod_din_coada = coada.front();
for (int i = 0; i < Lista_de_adiacenta[primul_nod_din_coada].size(); i++)
{
int nod_curent = Lista_de_adiacenta[primul_nod_din_coada][i];
if (Costuri[primul_nod_din_coada][nod_curent - 1] == Vec_fluxuri[primul_nod_din_coada][nod_curent - 1] || Vector_vizitati[nod_curent] != -1)
continue;
coada.push_back(nod_curent);
Vector_vizitati[nod_curent] = 0;
Vector_tati[nod_curent] = primul_nod_din_coada;
}
coada.pop_front();
}
return Vector_vizitati[destinatie];
}
int Graf_orientat::Flux_maxim() {
vector<int>vec(Nr_noduri + 1, 0);
vector<int>Vector_vizitati(Nr_noduri + 1, -1);
vector<vector<int>>Vector_fluxuri(Nr_noduri + 1, vector<int>(Nr_noduri, 0));
vector<int> Vector_tati(Nr_noduri + 1, -1);
int rezultat = 0;
while (Bfs_flux(1, Nr_noduri, Vector_vizitati, Vector_fluxuri, Vector_tati) == 0)
{
int f_min = oo;
for (int nod = Nr_noduri; nod > 1; nod = Vector_tati[nod])
f_min = min(f_min, Costuri[Vector_tati[nod]][nod - 1] - Vector_fluxuri[Vector_tati[nod]][nod - 1]);
rezultat += f_min;
for (int nod = Nr_noduri; nod > 1; nod = Vector_tati[nod])
{
Vector_fluxuri[Vector_tati[nod]][nod - 1] += f_min;
}
Vector_tati.resize(Nr_noduri + 1, -1);
}
return rezultat;
}
bool Graf_neorientat::Verif_cilcu_eulerian() const {
for (int i = 1; i <=Nr_noduri; i++)
if (Lista_de_adiacenta[i].size() % 2 != 0)
return false;
return true;
}
void Graf_neorientat::Ciclu_eulerian(int Start, vector<bool>& Vector_vizitati_muchii, vector<int>& Rezultat) {
while (!Lista_de_adiacenta[Start].empty())
{
int nod_curent = Lista_de_adiacenta[Start].back();
int nr_muchie = Costuri[Start].back();
Lista_de_adiacenta[Start].pop_back();
Costuri[Start].pop_back();
if (Vector_vizitati_muchii[nr_muchie] == false)
{
Vector_vizitati_muchii[nr_muchie] = true;
///Ciclu_eulerian(nod_curent, Vector_vizitati_muchii, Rezultat);
}
}
Rezultat.push_back(Start);
}
/// --------------------------Probleme infoarena-----------------------------------------
vector<int> Graf_orientat::BFS_infoarena(int Start_nod) const {
return BFS(Start_nod);
}
void BFS_infoarena_rezolvare() {///BFS - PROBLEMA INFOARENA
ifstream f_in("bfs.in");
ofstream f_out("bfs.out");
int Nr_noduri, Nr_muchii, Start_nod, Nod_st, Nod_dr;
f_in >> Nr_noduri;
f_in >> Nr_muchii;
f_in >> Start_nod;
vector<vector<int>>Lista_de_adiacenta(Nr_noduri + 1);
for (int i = 0; i < Nr_muchii; i++)
{
f_in >> Nod_st >> Nod_dr;
Lista_de_adiacenta[Nod_st].push_back(Nod_dr);
}
Graf_orientat graf(Nr_noduri, Nr_muchii, Lista_de_adiacenta);
const vector<int> Distante = graf.BFS_infoarena(Start_nod);
for (int i = 1; i < Distante.size(); i++)
f_out << Distante[i] << " ";
f_in.close();
f_out.close();
Lista_de_adiacenta.clear();
}
void DFS_infoarena_rezolvare() { ///DFS INFOARENA
ifstream f_in("dfs.in");
ofstream f_out("dfs.out");
Graf_neorientat graf;
f_in >> graf;
f_out << graf.DFS_infoarena();
f_in.close();
f_out.close();
}
void Sortare_vector_perechi(vector<vector<pair<int, int>>>& Comp_biconexe, int Numar_comp_biconexe) {
for (int i = 0; i < Numar_comp_biconexe; i++) ///Sortam perechile de muchii
{
sort(Comp_biconexe[i].begin(), Comp_biconexe[i].end());
}
}
vector<vector<pair<int, int>>> Graf_neorientat::Componente_biconexe_infoarena(int& Numar_comp_biconexe) {
return Componente_biconexe(Numar_comp_biconexe);
}
void Componente_biconexe_infoarena_rezolvare() {
ifstream f_in("biconex.in");
ofstream f_out("biconex.out");
int Numar_comp_biconexe = 0;
Graf_neorientat graf;
f_in >> graf;
vector<vector<pair<int, int>>>Componente_biconexe = graf.Componente_biconexe_infoarena(Numar_comp_biconexe);
f_out << Numar_comp_biconexe << '\n';
Sortare_vector_perechi(Componente_biconexe, Numar_comp_biconexe);///sortam perechile de muchii
for (int i = 0; i < Numar_comp_biconexe; i++)
{
vector<bool>Verifica(graf.get_nr_noduri() + 1, false);
for (int j = 0; j < Componente_biconexe[i].size(); j++) {
if (Verifica[Componente_biconexe[i][j].first] == false)
{
f_out << Componente_biconexe[i][j].first << " ";
Verifica[Componente_biconexe[i][j].first] = true;
}
if (Verifica[Componente_biconexe[i][j].second] == false)
{
f_out << Componente_biconexe[i][j].second << " ";
Verifica[Componente_biconexe[i][j].second] = true;
}
}
f_out << '\n';
}
f_in.close();
f_out.close();
}
vector<int> Graf_orientat::Sortare_topologica_infoarena() const {
return Sortare_topologica();
}
void Sortare_topologica_infoarena_rezolvare() {
ifstream f_in("sortaret.in");
ofstream f_out("sortaret.out");
Graf_orientat g;
f_in >> g;
const vector<int> Rezultat = g.Sortare_topologica_infoarena();
for (int i = 0; i < Rezultat.size(); i++)
f_out << Rezultat[i] << " ";
f_in.close();
f_out.close();
}
vector<pair<int, int>> Graf_neorientat::Afla_muchii_critice_rezolvare() {
return AMC();
}
void Afla_muchii_critice_rezolvare_problema() {
int Nr_noduri, Nr_muchii, Start_nod, Nod_st, Nod_dr;
cin >> Nr_noduri;
cin >> Nr_muchii;
vector<pair<int, int>>Vector_perechi_muchii(Nr_noduri + 1);
for (int i = 0; i < Nr_muchii; i++)
{
cin >> Nod_st;
cin >> Nod_dr;
pair<int, int>Muchii;
Muchii.first = Nod_st;
Muchii.second = Nod_dr;
Vector_perechi_muchii.push_back(Muchii);
}
vector<vector<int>>Lista_de_adiacenta(Nr_noduri + 1);
for (int i = 0; i < Vector_perechi_muchii.size(); i++)
{
Lista_de_adiacenta[Vector_perechi_muchii[i].first].push_back(Vector_perechi_muchii[i].second);
Lista_de_adiacenta[Vector_perechi_muchii[i].second].push_back(Vector_perechi_muchii[i].first);
}
Graf_neorientat graf(Nr_noduri, Nr_muchii, Lista_de_adiacenta);
vector<pair<int, int>>Muchii_critice = graf.Afla_muchii_critice_rezolvare();
vector<vector<int>>Rezultat;
for (int i = 0; i < Muchii_critice.size(); i++) {
vector<int>Vector;
Vector.push_back(Muchii_critice[i].first);
Vector.push_back(Muchii_critice[i].second);
Rezultat.push_back(Vector);
}
if (Rezultat.size() != 0)
cout << "[";
for (int i = 0; i < Muchii_critice.size(); i++)
{
cout << "[" << Muchii_critice[i].first << "," << Muchii_critice[i].second << "]";
if (i == Muchii_critice.size() - 1)
cout << "]";
else
cout << ",";
}
}
void Graf_neorientat::Havel_Hakimi_sol() {
vector<int>Secventa_de_grade;
int nr;
for (int i = 0; i < Nr_noduri; i++)
{
cin >> nr;
Secventa_de_grade.push_back(nr);
}
if (Havel_Hakimi_algoritm(Secventa_de_grade) == true)
cout << "Da, este posibil.";
else
cout << "Nu, nu este posibil.";
}
void Havel_Hakimi_rezolvare() {
int Nr_noduri;
cout << "Introduceti numarul de noduri: ";
cin >> Nr_noduri;
Graf_neorientat g(Nr_noduri);
g.Havel_Hakimi_sol();
}
void Sorteaza_muchii(vector<vector<int>>& Componente_tare_conexe) {
for (int i = 1; i < Componente_tare_conexe.size(); i++)
sort(Componente_tare_conexe[i].begin(), Componente_tare_conexe[i].end());
}
vector<vector<int>> Graf_orientat::CTC_infoarena(int& Nr_componente_tare_conexe) {
return CTC(Nr_componente_tare_conexe);
}
void Componente_tare_conexe_infoarena_rezolvare() {
ifstream f_in("ctc.in");
ofstream f_out("ctc.out");
Graf_orientat g;
f_in >> g;
int Nr_componente_tare_conexe = 0;
vector<vector<int>>Componente_tare_conexe = g.CTC_infoarena(Nr_componente_tare_conexe);
f_out << Nr_componente_tare_conexe;
Sorteaza_muchii(Componente_tare_conexe);
for (int i = 1; i < Componente_tare_conexe.size(); i++)
{
f_out << '\n';
for (int j = 0; j < Componente_tare_conexe[i].size(); j++)
f_out << Componente_tare_conexe[i][j] << " ";
}
f_in.close();
f_out.close();
}
void APM_rezolvare() {
ifstream f_in("apm.in");
ofstream f_out("apm.out");
int Nr_noduri, Nr_muchii, nod_st, nod_dr, cost;
f_in >> Nr_noduri;
f_in >> Nr_muchii;
vector<vector<int>>Lista_de_adiacenta(Nr_noduri + 1);
vector<vector<int>>Costuri(Nr_noduri + 1);
for (int i = 1; i <= Nr_muchii; i++) {
f_in >> nod_st >> nod_dr >> cost;
Lista_de_adiacenta[nod_st].push_back(nod_dr);
Lista_de_adiacenta[nod_dr].push_back(nod_st);
Costuri[nod_st].push_back(cost);
Costuri[nod_dr].push_back(cost);
}
Graf_neorientat g(Nr_noduri, Nr_muchii, Lista_de_adiacenta, Costuri);
g.APM_infoarena(oo, f_out);
}
void Padure_de_multimi_disjuncte() {
ifstream f_in("disjoint.in");
ofstream f_out("disjoint.out");
int Nr_noduri, Nr_muchii, op;
f_in >> Nr_noduri >> Nr_muchii;
Graf_neorientat graf(Nr_noduri, Nr_muchii);
graf.Pad_de_mult_dis_infoarena(f_in, f_out);
f_in.close();
f_out.close();
}
void Dijkstra_Infoarena_rezolvare() {
ifstream f_in("dijkstra.in");
ofstream f_out("dijkstra.out");
Graf_orientat graf;
graf.Dijkstra_infoarena(f_in, f_out);
f_in.close();
f_out.close();
}
void Bellman_ford_infoarena_rezolvare() {
ifstream f_in("bellmanford.in");
ofstream f_out("bellmanford.out");
int Nr_noduri, Nr_muchii, nod_st, nod_dr, cost;
f_in >> Nr_noduri;
f_in >> Nr_muchii;
vector<vector<int>>Lista_de_adiacenta(Nr_noduri + 1);
vector<vector<int>>Costuri(Nr_noduri + 1);
for (int i = 1; i <= Nr_muchii; i++) {
f_in >> nod_st >> nod_dr >> cost;
Lista_de_adiacenta[nod_st].push_back(nod_dr);
Costuri[nod_st].push_back(cost);
}
Graf_orientat g(Nr_noduri, Nr_muchii, Lista_de_adiacenta, Costuri);
g.Bellman_ford_infoarena(f_out);
f_in.close();
f_out.close();
}
void Diametru_arbore_infoarena()
{
ifstream f_in("darb.in");
ofstream f_out("darb.out");
int Nr_noduri;
f_in >> Nr_noduri;
vector<vector<int>> Lista_de_adiacenta(Nr_noduri + 1);
for (int i = 1; i <= Nr_noduri - 1; i++)
{
int nod_st, nod_dr;
f_in >> nod_st;
f_in >> nod_dr;
Lista_de_adiacenta[nod_st].push_back(nod_dr);
Lista_de_adiacenta[nod_dr].push_back(nod_st);
}
int Nr_muchii = Nr_noduri - 1;
Graf_neorientat g(Nr_noduri, Nr_muchii, Lista_de_adiacenta);
f_out << g.Diametru_arbore();
f_in.close();
f_out.close();
}
void Roy_Floyd_infoarena() {
int Nr_noduri, val;
cin >> Nr_noduri;
vector<vector<long long>>Matrice(Nr_noduri);
for (int i = 0; i < Nr_noduri; i++)
for (int j = 0; j < Nr_noduri; j++)
{
cin >> val;
if (val == 0 && i != j)
Matrice[i].push_back(oo);
else
Matrice[i].push_back(val);
}
Graf_orientat g(Nr_noduri);
g.Roy_Floyd(Matrice);
cout << '\n';
for (int i = 0; i < Nr_noduri; i++)
{
for (int j = 0; j < Nr_noduri; j++)
if (Matrice[i][j] == oo)
cout << 0 << " ";
else
cout << Matrice[i][j] << " ";
cout << '\n';
}
}
void Flux_maxim_infoarena() {
ifstream f_in("maxflow.in");
ofstream f_out("maxflow.out");
int Nr_noduri, Nr_muchii, nod_st, nod_dr, cost;
f_in >> Nr_noduri;
f_in >> Nr_muchii;
vector<vector<int>>Lista_de_adiacenta(Nr_noduri + 1);
vector<vector<int>>Costuri(Nr_noduri + 1, vector<int>(Nr_noduri, 0));
for (int i = 1; i <= Nr_muchii; i++) {
f_in >> nod_st >> nod_dr >> cost;
Lista_de_adiacenta[nod_st].push_back(nod_dr);
Costuri[nod_st][nod_dr - 1] = cost;
}
Graf_orientat g(Nr_noduri, Nr_muchii, Lista_de_adiacenta, Costuri, 1);
f_out << g.Flux_maxim();
}
void Ciclu_Eulerian_infoarena()
{
ifstream f_in("ciclueuler.in");
ofstream f_out("ciclueuler.out");
int Nr_noduri, Nr_muchii, nod_st, nod_dr;
f_in >> Nr_noduri >> Nr_muchii;
Graf_neorientat g(Nr_noduri, Nr_muchii, {}, {});
for (int i = 1; i <= Nr_muchii; i++)
{
f_in >> nod_st >> nod_dr;
g.Adauga_in_lista_de_adiacenta(nod_st, nod_dr, i);
}
if (g.Verif_cilcu_eulerian() == false)
f_out <<-1;
else
{
vector<bool>Vector_vizitati_muchii(Nr_muchii + 1, false);
vector<int>Rezultat;
g.Ciclu_eulerian(1, Vector_vizitati_muchii, Rezultat);
for (int i = 0; i < Rezultat.size(); i++)
f_out << Rezultat[i] <<" ";
}
f_in.close();
f_out.close();
}
int main()
{
///BFS_infoarena_rezolvare();
///DFS_infoarena_rezolvare();
///Componente_biconexe_infoarena_rezolvare();
///Sortare_topologica_infoarena_rezolvare();
///Afla_muchii_critice_rezolvare_problema();
///Havel_Hakimi_rezolvare();
///Componente_tare_conexe_infoarena_rezolvare();
///APM_rezolvare();
///Padure_de_multimi_disjuncte();
///Dijkstra_Infoarena_rezolvare();
///Bellman_ford_infoarena_rezolvare();
///Diametru_arbore_infoarena();
///Roy_Floyd_infoarena();
///Flux_maxim_infoarena();
Ciclu_Eulerian_infoarena();
return 0;
}