fleury_algorithm.cpp

/*Fleury’s Algorithm is used to display the Euler path or Euler circuit from a given graph. In this algorithm, starting from one edge, it tries to move other adjacent vertices by removing the previous vertices. Using this trick, the graph becomes simpler in each step to find the Euler path or circuit.*/
//Euler Path Or Circuit: 0--1 1--2 2--3 3--1 1--4 4--5 5--6 6--4 4--7 7--5 5--2 2--0

#include<iostream>
#include<vector>
#include<cmath>
#define NODE 8

using namespace std;
int graph[NODE][NODE] = {
   {0,1,1,0,0,0,0,0},
   {1,0,1,1,1,0,0,0},
   {1,1,0,1,0,1,0,0},
   {0,1,1,0,0,0,0,0},
   {0,1,0,0,0,1,1,1},
   {0,0,1,0,1,0,1,1},
   {0,0,0,0,1,1,0,0},
   {0,0,0,0,1,1,0,0}
};
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
}
int dfs(int prev, int start, bool visited[]){
   int count = 1;
   visited[start] = true;
   for(int u = 0; u<NODE; u++){
      if(prev != u){
         if(!visited[u]){
            if(tempGraph[start][u]){
               count += dfs(start, u, visited);
            }
         }
      }
   }
   return count;
}
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;
}
void fleuryAlgorithm(int start) {
   static int edge = edgeCount();
   static int v_count = NODE;
   for(int v = 0; v<NODE; v++) {
      if(tempGraph[start][v]) {
         bool visited[NODE] = {false};
         if(isBridge(start, v)){
            v_count--;
         }
         int cnt = dfs(start, v, visited);
         if(abs(v_count-cnt) <= 2){
            cout << start << "--" << v << " ";
            if(isBridge(v, start)){
               v_count--;
            }
            tempGraph[start][v] = tempGraph[v][start] = 0; //remove edge from graph
            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());
}