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#include <bits/stdc++.h>
using namespace std;
//https://www.geeksforgeeks.org/eulerian-path-and-circuit/
//https://www.geeksforgeeks.org/hierholzers-algorithm-directed-graph/
//Algoritmul lui Hierholzer
vector<vector<int>> citireLisAdiacenta()
{
ifstream fin("ciclueuler.in");
vector<vector<int>> lisAdiacenta;
int N, M;
fin >> N >> M;
lisAdiacenta.resize(N+1);
for (int i = 1; i <= M; ++i) {
int x, y;
fin >> x >> y;
lisAdiacenta[x].push_back(y);
}
return lisAdiacenta;
}
vector<int> circuitEuler(vector<vector<int>> &lisAdiacenta)
{
unordered_map<int, int> ctMuch; //nr de noduri adiacente unui nod
for(int i = 1; i <lisAdiacenta.size(); ++i) {
ctMuch[i] = lisAdiacenta[i].size();
}
stack<int> drumCurent;
vector<int> circuit;
//incepem din primul nod
drumCurent.push(1);
int nodCurent = 1;
while (!drumCurent.empty()) {
if (lisAdiacenta[nodCurent].size()) {
drumCurent.push(nodCurent);
int nodUrm = lisAdiacenta[nodCurent].back();
lisAdiacenta[nodCurent].pop_back();
nodCurent = nodUrm;
}
else {
circuit.push_back(nodCurent);
nodCurent = drumCurent.top();
drumCurent.pop();
}
}
return circuit;
}
int main()
{
ofstream fout("ciclueuler.out");
vector<vector<int>> lisAdiacenta;
lisAdiacenta = citireLisAdiacenta();
vector<vector<int>> copie;
copie = lisAdiacenta;
vector<int> circuit = circuitEuler(copie);
for(int i = 0; i < circuit.size(); ++i) {
fout << circuit[i] << " ";
}
/* for(int i = 0; i < copie.size(); ++i) {
for(int j = 0; j < copie[i].size(); ++j)
fout << copie[i][j] << " ";
fout << "\n";
}*/
return 0;
}