added eulerian path python code

src/main/python/algorithms/graph algorithms/eulerian path.py

@@ -0,0 +1,115 @@
+# Python program to check if a given graph is Eulerian of not using eulerian path identification
+# Complexity : O(V+E)
+
+from collections import defaultdict
+
+
+class Graph:
+    def __init__(self, vertices):
+        self.V = vertices  # No. of vertices
+        self.graph = defaultdict(list)  # default dictionary to store graph
+
+    # function to add an edge to graph
+    def addEdge(self, u, v):
+        self.graph[u].append(v)
+        self.graph[v].append(u)
+
+    # A function used by isConnected
+    def DFSUtil(self, v, visited):
+        # Mark the current node as visited
+        visited[v] = True
+
+        # Recur for all the vertices adjacent to this vertex
+        for i in self.graph[v]:
+            if visited[i] == False:
+                self.DFSUtil(i, visited)
+
+    def isConnected(self):
+
+        # Mark all the vertices as not visited
+        visited = [False] * (self.V)
+
+        #  Find a vertex with non-zero degree
+        for i in range(self.V):
+            if len(self.graph[i]) > 1:
+                break
+
+        # If there are no edges in the graph, return true
+        if i == self.V - 1:
+            return True
+
+        # Start DFS traversal from a vertex with non-zero degree
+        self.DFSUtil(i, visited)
+
+        # Check if all non-zero degree vertices are visited
+        for i in range(self.V):
+            if visited[i] == False and len(self.graph[i]) > 0:
+                return False
+
+        return True
+
+    def isEulerian(self):
+        # Check if all non-zero degree vertices are connected
+        if self.isConnected() == False:
+            return 0
+        else:
+            # Count vertices with odd degree
+            odd = 0
+            for i in range(self.V):
+                if len(self.graph[i]) % 2 != 0:
+                    odd += 1
+            if odd == 0:
+                return 2
+            elif odd == 2:
+                return 1
+            elif odd > 2:
+                return 0
+
+    # Function to run test cases
+    def test(self):
+        res = self.isEulerian()
+        if res == 0:
+            print("graph is not Eulerian")
+        elif res == 1:
+            print("graph has a Euler path")
+        else:
+            print("graph has a Euler cycle")
+
+
+# Creating an example graph for implementation
+g1 = Graph(5)
+g1.addEdge(1, 0)
+g1.addEdge(0, 2)
+g1.addEdge(2, 1)
+g1.addEdge(0, 3)
+g1.addEdge(3, 4)
+g1.test()
+
+g2 = Graph(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)
+g2.test()
+
+g3 = Graph(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)
+g3.test()
+
+
+g4 = Graph(3)
+g4.addEdge(0, 1)
+g4.addEdge(1, 2)
+g4.addEdge(2, 0)
+g4.test()
+
+
+g5 = Graph(3)
+g5.test()