Merge pull request #458 from shubhamgpt198/master

Added Eulerian Graph/C++/eulerian_graph.cpp

Author: probot-auto-merge[bot]

Graph Algorithms/Eulerian Graph/C++/eulerian_graph.cpp

@@ -0,0 +1,159 @@
+// 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 add_edge(int v, int w); 
+
+	// Method to check if this graph is Eulerian or not 
+	int is_eulerian(); 
+
+	// Method to check if all non-zero degree vertices are connected 
+	bool is_connected(); 
+
+	// Function to do DFS starting from v. Used in is_connected(); 
+	void get_dfs(int v, bool visited[]); 
+}; 
+
+void Graph::add_edge(int v, int w) 
+{ 
+	adj[v].push_back(w); 
+	adj[w].push_back(v); // Note: the graph is undirected 
+} 
+
+void Graph::get_dfs(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]) 
+			get_dfs(*i, visited); 
+} 
+
+// Method to check if all non-zero degree vertices are connected. 
+// It mainly does DFS traversal starting from 
+bool Graph::is_connected() 
+{ 
+	// 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 
+	get_dfs(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::is_eulerian() 
+{ 
+	// Check if all non-zero degree vertices are connected 
+	if (is_connected() == 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.is_eulerian(); 
+	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.add_edge(1, 0); 
+	g1.add_edge(0, 2); 
+	g1.add_edge(2, 1); 
+	g1.add_edge(0, 3); 
+	g1.add_edge(3, 4); 
+	test(g1); 
+
+	Graph g2(5); 
+	g2.add_edge(1, 0); 
+	g2.add_edge(0, 2); 
+	g2.add_edge(2, 1); 
+	g2.add_edge(0, 3); 
+	g2.add_edge(3, 4); 
+	g2.add_edge(4, 0); 
+	test(g2); 
+
+	Graph g3(5); 
+	g3.add_edge(1, 0); 
+	g3.add_edge(0, 2); 
+	g3.add_edge(2, 1); 
+	g3.add_edge(0, 3); 
+	g3.add_edge(3, 4); 
+	g3.add_edge(1, 3); 
+	test(g3); 
+
+	// Let us create a graph with 3 vertices 
+	// connected in the form of cycle 
+	Graph g4(3); 
+	g4.add_edge(0, 1); 
+	g4.add_edge(1, 2); 
+	g4.add_edge(2, 0); 
+	test(g4); 
+
+	// Let us create a graph with all veritces 
+	// with zero degree 
+	Graph g5(3); 
+	test(g5); 
+
+	return 0; 
+}