Print Euler Path, C++ (gcc)

Print Euler Path

// A C++ program print Eulerian Trail in a given Eulerian or Semi-Eulerian Graph 
#include <iostream> 
#include <string.h> 
#include <algorithm> 
#include <list> 
using namespace std; 
  
// A class that represents an undirected graph 
class Graph 
{ 
  int V;    // No. of vertices 
  list<int> *adj;    // A dynamic array of adjacency lists 
public: 
    // Constructor and destructor 
  Graph(int V)  { this->V = V;  adj = new list<int>[V];  } 
  ~Graph()      { delete [] adj;  } 
  
  // functions to add and remove edge 
  void addEdge(int u, int v) {  adj[u].push_back(v); adj[v].push_back(u); } 
  void rmvEdge(int u, int v); 
  
  // Methods to print Eulerian tour 
  void printEulerTour(); 
  void printEulerUtil(int s); 
  
  // This function returns count of vertices reachable from v. It does DFS 
  int DFSCount(int v, bool visited[]); 
  
  // Utility function to check if edge u-v is a valid next edge in 
  // Eulerian trail or circuit 
  bool isValidNextEdge(int u, int v); 
}; 
  
/* The main function that print Eulerian Trail. It first finds an odd 
   degree vertex (if there is any) and then calls printEulerUtil() 
   to print the path */
void Graph::printEulerTour() 
{ 
  // Find a vertex with odd degree 
  int u = 0; 
  for (int i = 0; i < V; i++) 
      if (adj[i].size() & 1) 
        {   u = i; break;  } 
  
  // Print tour starting from oddv 
  printEulerUtil(u); 
  cout << endl; 
} 
  
// Print Euler tour starting from vertex u 
void Graph::printEulerUtil(int u) 
{ 
  // Recur for all the vertices adjacent to this vertex 
  list<int>::iterator i; 
  for (i = adj[u].begin(); i != adj[u].end(); ++i) 
  { 
      int v = *i; 
  
      // If edge u-v is not removed and it's a a valid next edge 
      if (v != -1 && isValidNextEdge(u, v)) 
      { 
          cout << u << "-" << v << "  "; 
          rmvEdge(u, v); 
          printEulerUtil(v); 
      } 
  } 
} 
  
// The function to check if edge u-v can be considered as next edge in 
// Euler Tout 
bool Graph::isValidNextEdge(int u, int v) 
{ 
  // The edge u-v is valid in one of the following two cases: 
  
  // 1) If v is the only adjacent vertex of u 
  int count = 0;  // To store count of adjacent vertices 
  list<int>::iterator i; 
  for (i = adj[u].begin(); i != adj[u].end(); ++i) 
     if (*i != -1) 
        count++; 
  if (count == 1) 
    return true; 
  
  
  // 2) If there are multiple adjacents, then u-v is not a bridge 
  // Do following steps to check if u-v is a bridge 
  
  // 2.a) count of vertices reachable from u 
  bool visited[V]; 
  memset(visited, false, V); 
  int count1 = DFSCount(u, visited); 
  
  // 2.b) Remove edge (u, v) and after removing the edge, count 
  // vertices reachable from u 
  rmvEdge(u, v); 
  memset(visited, false, V); 
  int count2 = DFSCount(u, visited); 
  
  // 2.c) Add the edge back to the graph 
  addEdge(u, v); 
  
  // 2.d) If count1 is greater, then edge (u, v) is a bridge 
  return (count1 > count2)? false: true; 
} 
  
// This function removes edge u-v from graph.  It removes the edge by 
// replacing adjcent vertex value with -1. 
void Graph::rmvEdge(int u, int v) 
{ 
  // Find v in adjacency list of u and replace it with -1 
  list<int>::iterator iv = find(adj[u].begin(), adj[u].end(), v); 
  *iv = -1; 
  
  // Find u in adjacency list of v and replace it with -1 
  list<int>::iterator iu = find(adj[v].begin(), adj[v].end(), u); 
  *iu = -1; 
} 
  
// A DFS based function to count reachable vertices from v 
int Graph::DFSCount(int v, bool visited[]) 
{ 
  // Mark the current node as visited 
  visited[v] = true; 
  int count = 1; 
  
  // Recur for all vertices adjacent to this vertex 
  list<int>::iterator i; 
  for (i = adj[v].begin(); i != adj[v].end(); ++i) 
      if (*i != -1 && !visited[*i]) 
          count += DFSCount(*i, visited); 
  
  return count; 
} 
  
// Driver program to test above function 
int main() 
{ 
  // Let us first create and test graphs shown in above figure 
  Graph g1(4); 
  g1.addEdge(0, 1); 
  g1.addEdge(0, 2); 
  g1.addEdge(1, 2); 
  g1.addEdge(2, 3); 
  g1.printEulerTour(); 
  
  Graph g2(3); 
  g2.addEdge(0, 1); 
  g2.addEdge(1, 2); 
  g2.addEdge(2, 0); 
  g2.printEulerTour(); 
  
  Graph g3(5); 
  g3.addEdge(1, 0); 
  g3.addEdge(0, 2); 
  g3.addEdge(2, 1); 
  g3.addEdge(0, 3); 
  g3.addEdge(3, 4); 
  g3.addEdge(3, 2); 
  g3.addEdge(3, 1); 
  g3.addEdge(2, 4); 
  g3.printEulerTour(); 
  
  return 0; 
}


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