How can I find a Hamiltonian path in a graph using Python?

How can I find a Hamiltonian path in a graph using Python?

To find a Hamiltonian path in a graph using Python, you can use backtracking. Would you like a code example?

Yes, please provide a code example.

Here's a simple implementation:

def is_valid(v, pos, path, graph):
    if graph[path[pos-1]][v] == 0:
        return False
    if v in path:
        return False
    return True

def hamiltonian_util(graph, path, pos):
    if pos == len(graph):
        return True
    for v in range(1, len(graph)):
        if is_valid(v, pos, path, graph):
            path[pos] = v
            if hamiltonian_util(graph, path, pos + 1):
                return True
            path[pos] = -1
    return False

def hamiltonian_path(graph):
    path = [-1] * len(graph)
    path[0] = 0
    if not hamiltonian_util(graph, path, 1):
        return None
    return path

This function checks for a Hamiltonian path in a given graph represented as an adjacency matrix.

What kind of graphs can this algorithm handle?

This algorithm can handle undirected graphs represented as adjacency matrices. However, it may not be efficient for large graphs due to its exponential time complexity.