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#include <fstream>
#include <list>
#include <vector>
#include <stack>
using namespace std;
vector <list<int>> readGraph(const string& inputPath)
{
int n, m;
ifstream fin(inputPath);
fin >> n >> m;
vector<list<int>> graph(n);
int x, y;
for (int i = 0; i < m; i++)
{
fin >> x >> y;
x--; y--;
graph[x].push_back(y);
graph[y].push_back(x);
}
return graph;
}
void dfs(vector<list<int>> & graph, int source, vector<bool> & visited)
{
visited[source] = true;
for (auto y: graph[source])
if (!visited[y])
dfs(graph, y, visited);
}
bool isEulerian(vector<list<int>> & graph)
{
for (const auto& edges: graph)
if (edges.size() % 2 != 0)
return false;
vector<bool> visited(graph.size(), false);
dfs(graph, 0, visited);
for (bool v: visited)
if (!v)
return false;
return true;
}
vector<int> eulerianCycle(vector<list<int>> & graph)
{
vector<int> cycle;
if (!isEulerian(graph))
{
cycle.push_back(-1);
cycle.push_back(-1);
}
else
{
stack<int> nodes;
nodes.push(0);
int x, y;
while (!nodes.empty())
{
x = nodes.top();
if (graph[x].size() <= 0)
{
cycle.push_back(x);
nodes.pop();
}
else
{
y = graph[x].front();
graph[x].pop_front();
graph[y].remove(x);
nodes.push(y);
}
}
}
return cycle;
}
void writeCycle(const string& outPath, const vector<int>& cycle)
{
ofstream fout(outPath);
for (int i = 0;i < cycle.size() - 1; i++)
fout << cycle[i] + 1 << " ";
fout.close();
}
int main()
{
auto graph = readGraph("ciclueuler.in");
writeCycle("ciclueuler.out", eulerianCycle(graph));
return 0;
}