add: hamiltonian cycle in py

README.md

@@ -604,8 +604,8 @@ In order to achieve greater coverage and encourage more people to contribute to
                 </a>
             </td>
             <td> <!-- Python -->
-                <a href="./CONTRIBUTING.md">
-                    <img align="center" height="25" src="./logos/github.svg" />
+                <a href="./src/python/hamiltonian_cycle.py">
+                    <img align="center" height="25" src="./logos/python.svg" />
                 </a>
             </td>
             <td> <!-- Go -->

src/python/hamiltonian_cycle.py

@@ -0,0 +1,107 @@
+# Hamiltonian Cycle is a path in a graph that visits each vertex exactly once and returns to the starting vertex.
+
+# (A)---------------(B)-------------(E)---------------(F)
+#  |                 |               |                 |
+#  |                 |               |                 |
+#  |                 |               |                 | 
+# (C)---------------(D)---------------                 |
+#                    |                                 |
+#                    -----------------------------------
+
+# 6 Vertices
+# 9 Edges
+
+class Vertex:
+    def __init__(self, id):
+        self.id = id
+        self.neighbors = []
+        self.visited = False
+
+def connect_vertices(v1, v2):
+    v1.neighbors.append(v2)
+    v2.neighbors.append(v1)
+
+def hamiltonian_cycle_helper(graph, path, pos):
+    # If all vertices are included in the path
+    if pos == len(graph):
+        # Check if last vertex is connected to first vertex
+        if path[-1] in path[0].neighbors:
+            return True
+        return False
+
+    # Try different vertices as next candidate
+    for vertex in graph:
+        if can_add_to_path(vertex, path, pos):
+            path[pos] = vertex
+            vertex.visited = True
+
+            if hamiltonian_cycle_helper(graph, path, pos + 1):
+                return True
+
+            # Backtrack
+            vertex.visited = False
+            path[pos] = None
+
+    return False
+
+def can_add_to_path(vertex, path, pos):
+    # If vertex is already visited, skip it
+    if vertex.visited:
+        return False
+
+    # For first vertex, any unvisited vertex is valid
+    if pos == 0:
+        return True
+
+    # Check if current vertex is connected to the previous vertex in path
+    if vertex not in path[pos-1].neighbors:
+        return False
+
+    return True
+
+def find_hamiltonian_cycle(graph):
+    # Initialize the path
+    path = [None] * len(graph)
+
+    # Reset all vertices to unvisited
+    for vertex in graph:
+        vertex.visited = False
+
+    if hamiltonian_cycle_helper(graph, path, 0):
+        # Add the first vertex at the end to complete the cycle
+        return path + [path[0]]
+    return None
+
+def main():
+    # Create graph vertices
+    graph = [
+        Vertex('A'),  # 0
+        Vertex('B'),  # 1
+        Vertex('C'),  # 2
+        Vertex('D'),  # 3
+        Vertex('E'),  # 4
+        Vertex('F')   # 5
+    ]
+
+    # Connect vertices according to the graph diagram
+    connect_vertices(graph[0], graph[1])  # A - B
+    connect_vertices(graph[0], graph[2])  # A - C
+    connect_vertices(graph[1], graph[3])  # B - D
+    connect_vertices(graph[2], graph[3])  # C - D
+    connect_vertices(graph[1], graph[4])  # B - E
+    connect_vertices(graph[3], graph[4])  # D - E
+    connect_vertices(graph[4], graph[5])  # E - F
+    connect_vertices(graph[3], graph[5])  # D - F
+    connect_vertices(graph[1], graph[5])  # B - F
+
+    # Find Hamiltonian cycle
+    cycle = find_hamiltonian_cycle(graph)
+
+    if cycle:
+        print("Hamiltonian Cycle found:")
+        print(" -> ".join(vertex.id for vertex in cycle))
+    else:
+        print("No Hamiltonian Cycle exists")
+
+if __name__ == "__main__":
+    main()