Competitive Programming

/**
 * Author: Dean
 * License: CC0
 * Description: returns de eulerian cycle/tour starting at u. If its a tour it must start at a vertex with odd degree. It is common to add edges between odd vertex to find a pseudo euler tour. Start and end in same vertex and visit each edge exactly once. All vertex degree must be even.
 * Time: O(E)
 * Status: Undirected Tested, Directed tested: http://codeforces.com/contest/508/problem/D
 * Usage: adj should contain index of edge in the vector<edge>, if undirected add index to both rows of adj list. If directed make sure if it needs to be connected, difference between in/out edges. If it is a tour then u must be a vertex with odd degree, else it can be any edge.
 */
#pragma once

struct edge{
	int u, v;
	bool used;
};

void Eulerdfs(int u, vi &nxt, vi &Euler, vector<edge> &E, const vector<vi> &adj) {
	while(nxt[u] < adj[u].size()){
		int go = adj[u][nxt[u]++];
		if(!E[go].used){
			E[go].used = 1;
			int to = (E[go].u ^ E[go].v ^ u);
			Eulerdfs(to, nxt, Euler, E, adj);
		}
	}
	Euler.push_back(u);
}

vi Eulerian(int u, vector<edge> &E, const vector<vi> &adj) {
	vi nxt (adj.size(), 0); vi Euler;
	Eulerdfs(u, nxt, Euler, E, adj);
	reverse(Euler.begin(), Euler.end());
	return Euler;
}


int main()
{
    int cases,ca=1;
    scanf("%d",&cases);
    while(cases--)
    {
        int n; scanf("%d",&n);
        vector<edge> E;
        vector<vector<int>> adj(51);
        vector<int> degree(51);
        for(int i=0; i<n;i++)
        {
            int x,y; scanf("%d%d",&x,&y);
            E.push_back({x,y,false});
            adj[x].push_back(E.size()-1);
            adj[y].push_back(E.size()-1);
            degree[x - 1]++;
            degree[y - 1]++;
        }
        printf("Case #%d\n",ca++);
        bool good = true;
        int start = -1;
        for (int i = 0; i < 50; i++) {
            if (degree[i] % 2) { //All degree must be even 
                good = false;
                break;
            }
            else if (degree[i] && start == -1)
                start = i;
        }
        if(!good) printf("some beads may be lost\n");
        else{
        vector<int> res = Eulerian(start+1,E,adj);
        for(int i=0; i<sz(res)-1;i++) printf("%d %d\n",res[i],res[(i+1)%sz(res)]);
        }
        printf("\n");
    }
    return 0;
}