Merge pull request #410 from Manasi2001/issue-409

Hamiltonian Cycle (Python)

Author: smv1999

Backtracking/Hamiltonian_Cycle.py

@@ -0,0 +1,109 @@
+'''
+Hamiltonian Path: a Hamiltonian path (or traceable path) is a path
+    in an undirected or directed graph that visits each vertex exactly
+    once. A Hamiltonian cycle (or Hamiltonian circuit) is a Hamiltonian
+    path that is a cycle.
+Aim: To determine the existance of a Hamiltonian Cycle in the provided
+        undirected graph and return the path if such path exist.
+        The nodes are numbered from 1 to N.
+
+'''
+
+from collections import defaultdict
+
+
+def Move_next_node(n, graph, pos, ans):
+    # Base Case: If all the node is visited:
+    if pos == n:
+
+        # Check wether the last node and the first node are
+        # connected in order to form a Cycle
+        if ans[0] in graph[ans[-1]]:
+            return ans + [ans[0]]
+
+        return False
+
+    current = ans[-1]
+
+    # Check for each of the adjoining vertices
+    for i in graph[current]:
+
+        # Check wether the node is already visited or not
+        if i not in ans:
+            ans += [i]
+            temp = Move_next_node(n, graph, pos + 1, ans)
+            if temp:
+                return temp
+
+            ans.pop()
+
+    return False
+
+
+def Hamiltonial_Cycle(n, graph):
+    # To keep a track of already visited node and the answer
+    # We will start exploring the graph from Vertex 1
+    answer = [1]
+
+    # Start Exploring adjoining node/vertex
+    return Move_next_node(n, graph, 1, answer)
+
+
+# ------------------------DRIVER CODE ------------------------
+if __name__ == "__main__":
+    n, m = map(int, input("Enter the number of vertex and edges: ").split())
+    print("Enter the edges: ")
+    graph = defaultdict(list)
+    for i in range(m):
+        a, b = map(int, input().split())
+        graph[a] += [b]
+        graph[b] += [a]
+    ans = Hamiltonial_Cycle(n, graph)
+    if not ans:
+        print("Hamiltonian Cycle is not possible in the Given graph")
+    else:
+        print("Hamiltonian Cycle is possible in the graph")
+        print("The path is : ", *ans)
+
+'''
+
+Sample Working:
+    
+     5----1------2
+    /\     \    /
+   /  \     \  /
+  /    \     \/
+ 3------6-----4
+Enter the number of vertex and edges: 6 8
+Enter the edges
+5 1
+1 2
+1 4
+5 6
+6 4
+4 2
+3 6
+5 3
+Hamiltonian Cycle is possible in the graph
+The path is :  1 5 3 6 4 2 1
+     5----1------2
+     \     \
+      \     \
+       \     \
+ 3------6-----4
+Enter the number of vertex and edges: 6 6
+Enter the edges:
+5 1
+3 6
+6 4
+1 2
+5 6
+1 4
+Hamiltonian Cycle is not possible in the Given graph
+
+COMPLEXITY:
+    
+     Time Complexity ->  O(2^N)
+     Space Complexity -> O(N)
+     
+'''