hamilton.py

class Graph():
    def __init__(self, vertices):
        self.graph = [[0 for column in range(vertices)]
                      for row in range(vertices)]
        self.V = vertices

    def isSafe(self, v, pos, path):
        # Check if current vertex and last vertex
        # in path are adjacent
        if self.graph[path[pos - 1]][v] == 0:
            return False

        # Check if current vertex not already in path
        for vertex in path:
            if vertex == v:
                return False

        return True

    def hamCycleUtil(self, path, pos):

        # base case: if all vertices are
        # included in the path
        if pos == self.V:
            # Last vertex must be adjacent to the
            # first vertex in path to make a cyle
            if self.graph[path[pos - 1]][path[0]] == 1:
                return True
            else:
                return False

        for v in range(1, self.V):

            if self.isSafe(v, pos, path) is True:

                path[pos] = v

                if self.hamCycleUtil(path, pos + 1) is True:
                    return True

                # Remove current vertex if it doesn't
                # lead to a solution
                path[pos] = -1

        return False

    def hamCycle(self):
        path = [-1] * self.V
        ''' Let us put vertex 0 as the first vertex
            in the path. If there is a Hamiltonian Cycle,
            then the path can be started from any point
            of the cycle as the graph is undirected '''
        path[0] = 0

        if self.hamCycleUtil(path, 1) is False:
            print("Solution does not exist\n")
            return False

        self.printSolution(path)
        return True

    def printSolution(self, path):
        print("Solution Exists: Following is one Hamiltonian Cycle")
        for vertex in path:
            print(vertex)
        print(path[0], "\n")


'''
Let us create the following graph
      (0)--(1)--(2)
       |   / \   |
       |  /   \  |
       | /     \ |
      (3)-------(4)
'''
g1 = Graph(5)
g1.graph = [
    [0, 1, 0, 1, 0],
    [1, 0, 1, 1, 1],
    [0, 1, 0, 0, 1],
    [1, 1, 0, 0, 1],
    [0, 1, 1, 1, 0],
]

# Print the solution
g1.hamCycle()
'''
Let us create the following graph
      (0)--(1)--(2)
       |   / \   |
       |  /   \  |
       | /     \ |
      (3)       (4)
'''
g2 = Graph(5)
g2.graph = [
    [0, 1, 0, 1, 0],
    [1, 0, 1, 1, 1],
    [0, 1, 0, 0, 1],
    [1, 1, 0, 0, 0],
    [0, 1, 1, 0, 0],
]

# Print the solution
g2.hamCycle()