TSP brute-force solution

optimal_tsp.py

"""
    Author: Simon Westphahl <westphahl@gmail.com>
    Description: Brute-force implementation for solving the TSP.
    http://en.wikipedia.org/wiki/Travelling_salesman_problem
"""

routes = []


def find_paths(node, cities, path, distance):
    # Add way point
    path.append(node)

    # Calculate path length from current to last node
    if len(path) > 1:
        distance += cities[path[-2]][node]

    # If path contains all cities and is not a dead end,
    # add path from last to first city and return.
    if (len(cities) == len(path)) and (cities[path[-1]].has_key(path[0])):
        global routes
        path.append(path[0])
        distance += cities[path[-2]][path[0]]
        print path, distance
        routes.append([distance, path])
        return

    # Fork paths for all possible cities not yet used
    for city in cities:
        if (city not in path) and (cities[city].has_key(node)):
            find_paths(city, dict(cities), list(path), distance)


if __name__ == '__main__':
    cities = {
        'RV': {'S': 195, 'UL': 86, 'M': 178, 'BA': 180, 'Z': 91},
        'UL': {'RV': 86, 'S': 107, 'N': 171, 'M': 123},
        'M': {'RV': 178, 'UL': 123, 'N': 170},
        'S': {'RV': 195, 'UL': 107, 'N': 210, 'F': 210, 'MA': 135, 'KA': 64},
        'N': {'S': 210, 'UL': 171, 'M': 170, 'MA': 230, 'F': 230},
        'F': {'N': 230, 'S': 210, 'MA': 85},
        'MA': {'F': 85, 'N': 230, 'S': 135, 'KA': 67},
        'KA': {'MA': 67, 'S': 64, 'BA': 191},
        'BA': {'KA': 191, 'RV': 180, 'Z': 85, 'BE': 91},
        'BE': {'BA': 91, 'Z': 120},
        'Z': {'BA': 120, 'BE': 85, 'RV': 91}
    }

    print "Start: RAVENSBURG"
    find_paths('RV', cities, [], 0)
    print "\n"
    routes.sort()
    if len(routes) != 0:
        print "Shortest route: %s" % routes[0]
    else:
        print "FAIL!"

what is the time complexity of this algorithm?