C++ Programming Code Examples
C++ > Computer Graphics Code Examples
Check Whether an Undirected Graph Contains a Eulerian Path
/* Check Whether an Undirected Graph Contains a Eulerian Path
This is a C++ Program to check whether an undirected graph contains Eulerian Path. The criteran Euler suggested,
1. If graph has no odd degree vertex, there is at least one Eulerian Circuit.
2. If graph as two vertices with odd degree, there is no Eulerian Circuit but at least one Eulerian Path.
3. If graph has more than two vertices with odd degree, there is no Eulerian Circuit or Eulerian Path. */
// A C++ program to check if a given graph is Eulerian or not
#include<iostream>
#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;
} // To avoid memory leak
// function to add an edge to graph
void addEdge(int v, int w);
// Method to check if this graph is Eulerian or not
int isEulerian();
// Method to check if all non-zero degree vertices are connected
bool isConnected();
// Function to do DFS starting from v. Used in isConnected();
void DFSUtil(int v, bool visited[]);
};
void Graph::addEdge(int v, int w)
{
adj[v].push_back(w);
adj[w].push_back(v); // Note: the graph is undirected
}
void Graph::DFSUtil(int v, bool visited[])
{
// Mark the current node as visited and print it
visited[v] = true;
// Recur for all the vertices adjacent to this vertex
list<int>::iterator i;
for (i = adj[v].begin(); i != adj[v].end(); ++i)
if (!visited[*i])
DFSUtil(*i, visited);
}
// Method to check if all non-zero degree vertices are connected.
// It mainly does DFS traversal starting from
bool Graph::isConnected()
{
// Mark all the vertices as not visited
bool visited[V];
int i;
for (i = 0; i < V; i++)
visited[i] = false;
// Find a vertex with non-zero degree
for (i = 0; i < V; i++)
if (adj[i].size() != 0)
break;
// If there are no edges in the graph, return true
if (i == V)
return true;
// Start DFS traversal from a vertex with non-zero degree
DFSUtil(i, visited);
// Check if all non-zero degree vertices are visited
for (i = 0; i < V; i++)
if (visited[i] == false && adj[i].size() > 0)
return false;
return true;
}
/* The function returns one of the following values
0 --> If grpah is not Eulerian
1 --> If graph has an Euler path (Semi-Eulerian)
2 --> If graph has an Euler Circuit (Eulerian) */
int Graph::isEulerian()
{
// Check if all non-zero degree vertices are connected
if (isConnected() == false)
return 0;
// Count vertices with odd degree
int odd = 0;
for (int i = 0; i < V; i++)
if (adj[i].size() & 1)
odd++;
// If count is more than 2, then graph is not Eulerian
if (odd > 2)
return 0;
// If odd count is 2, then semi-eulerian.
// If odd count is 0, then eulerian
// Note that odd count can never be 1 for undirected graph
return (odd) ? 1 : 2;
}
// Function to run test cases
void test(Graph &g)
{
int res = g.isEulerian();
if (res == 0)
cout << "Graph is not Eulerian\n";
else if (res == 1)
cout << "Graph has a Euler path\n";
else
cout << "Graph has a Euler cycle\n";
}
// Driver program to test above function
int main()
{
// Let us create and test graphs shown in above figures
Graph g1(5);
g1.addEdge(1, 0);
g1.addEdge(0, 2);
g1.addEdge(2, 1);
g1.addEdge(0, 3);
g1.addEdge(3, 4);
cout<<"Result for Graph 1: ";
test(g1);
Graph g2(5);
g2.addEdge(1, 0);
g2.addEdge(0, 2);
g2.addEdge(2, 1);
g2.addEdge(0, 3);
g2.addEdge(3, 4);
g2.addEdge(4, 0);
cout<<"Result for Graph 2: ";
test(g2);
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(1, 3);
cout<<"Result for Graph 3: ";
test(g3);
// Let us create a graph with 3 vertices
// connected in the form of cycle
Graph g4(3);
g4.addEdge(0, 1);
g4.addEdge(1, 2);
g4.addEdge(2, 0);
cout<<"Result for Graph 4: ";
test(g4);
// Let us create a graph with all veritces
// with zero degree
Graph g5(3);
cout<<"Result for Graph 5: ";
test(g5);
return 0;
}
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