#include<iostream>
#include<vector>
#define NODE 5
using namespace std;
int graph[NODE][NODE] = {{0, 1, 1, 1, 1},
{1, 0, 1, 1, 0},
{1, 1, 0, 1, 0},
{1, 1, 1, 0, 1},
{1, 0, 0, 1, 0}
};
int tempGraph[NODE][NODE];
int findStartVert(){
for(int i = 0; i<NODE; i++){
int deg = 0;
for(int j = 0; j<NODE; j++){
if(tempGraph[i][j])
deg++; //increase degree, when connected edge found
}
if(deg % 2 != 0) //when degree of vertices are odd
return i; //i is node with odd degree
}
return 0; //when all vertices have even degree, start from 0
}
bool isBridge(int u, int v){
int deg = 0;
for(int i = 0; i<NODE; i++)
if(tempGraph[v][i])
deg++;
if(deg>1){
return false; //the edge is not forming bridge
}
return true; //edge forming a bridge
}
int edgeCount(){
int count = 0;
for(int i = 0; i<NODE; i++)
for(int j = i; j<NODE; j++)
if(tempGraph[i][j])
count++;
return count; //count nunber of edges in the graph
}
void fleuryAlgorithm(int start){
static int edge = edgeCount();
for(int v = 0; v<NODE; v++){
if(tempGraph[start][v]){ //when (u,v) edge is presnt and not forming bridge
if(edge <= 1 || !isBridge(start, v)){
cout << start << "--" << v << " ";
tempGraph[start][v] = tempGraph[v][start] = 0; //remove edge from graph
edge--; //reduce edge
fleuryAlgorithm(v);
}
}
}
}
int main(){
for(int i = 0; i<NODE; i++) //copy main graph to tempGraph
for(int j = 0; j<NODE; j++)
tempGraph[i][j] = graph[i][j];
cout << "Euler Path Or Circuit: ";
fleuryAlgorithm(findStartVert());
}
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