EulerianPath.cpp

#include<iostream>
#include<vector>
#define NODE 5
using namespace std;
int graph[NODE][NODE] = {{0, 1, 1, 1, 0},
   {1, 0, 1, 0, 0},
   {1, 1, 0, 0, 0},
   {1, 0, 0, 0, 1},
   {0, 0, 0, 1, 0}};
/*int graph[NODE][NODE] = {{0, 1, 1, 1, 1},
   {1, 0, 1, 0, 0},
   {1, 1, 0, 0, 0},
   {1, 0, 0, 0, 1},
   {1, 0, 0, 1, 0}};*/ //uncomment to check Euler Circuit as well as path
/*int graph[NODE][NODE] = {{0, 1, 1, 1, 0},
   {1, 0, 1, 1, 0},
   {1, 1, 0, 0, 0},
   {1, 1, 0, 0, 1},
   {0, 0, 0, 1, 0}};*/ //Uncomment to check Non Eulerian Graph
void traverse(int u, bool visited[]) {
   visited[u] = true; //mark v as visited
   for(int v = 0; v<NODE; v++) {
      if(graph[u][v]) {
         if(!visited[v])
            traverse(v, visited);
      }
   }
}
bool isConnected() {
   bool *vis = new bool[NODE];
   //for all vertex u as start point, check whether all nodes are visible or not
   for(int u; u < NODE; u++) {
      for(int i = 0; i<NODE; i++)
         vis[i] = false; //initialize as no node is visited
         traverse(u, vis);
         for(int i = 0; i<NODE; i++){
            if(!vis[i]) //if there is a node, not visited by traversal, graph is not connected
               return false;
         }
   }
   return true;
}
int isEulerian() {
   if(isConnected() == false) //when graph is not connected
   return 0;
   vector<int> degree(NODE, 0);
   int oddDegree = 0;
   for(int i = 0; i<NODE; i++) {
      for(int j = 0; j<NODE; j++) {
         if(graph[i][j])
            degree[i]++; //increase degree, when connected edge found
      }
      if(degree[i] % 2 != 0) //when degree of vertices are odd
         oddDegree++; //count odd degree vertices
   }
   if(oddDegree > 2) //when vertices with odd degree greater than 2
      return 0;
   return 1; //when oddDegree is 0, it is Euler circuit, and when 2, it is Euler path
}
int main() {
   if(isEulerian() != 0) {
      cout << "The graph has Eulerian path." << endl;
   } else {
      cout << "The graph has No Eulerian path." << endl;
   }
}