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# based on this:
# https://stackoverflow.com/questions/28518369/build-all-hamiltonian-paths-from-an-edge-list
 
graph = {
#   node: [list of allowed followers]
    1: [2, 3, 6, 8, 9, 10],   # Lost In The Brain
    2: [3, 5, 10],   # Afraid Of The Dark
    3: [2, 4, 6, 8],         # Total Annihilation
    4: [3, 8, 9, 10],   # Humps
    5: [2, 3, 6, 7, 8, 10],       # U Break My Heart
    6: [1, 2, 3, 4, 5, 8, 10 ],   # Walking Home
    7: [1, 3, 4, 5, 8],      # Hey Last Night
    8: [1, 3, 9],         # Mellow Vibes
    9: [3, 5, 8, 10],   # O Oh
    10: [1, 3, 5, 9],      # Strawberry Wine
}
 
# allowed starting nodes
starts = [2]
 
 
 
def find_all_paths(graph, start, totallen, path=[]):
    path = path + [start]
    if len(path) == totallen:
        return [path]
    if not graph.has_key(start):
        return []
    paths = []
    for node in graph[start]:
        if node not in path:
            newpaths = find_all_paths(graph, node, totallen, path)
            for newpath in newpaths:
                paths.append(newpath)
    return paths
 
cycles = []
 
for start in starts:
    print "Non-cyclic paths starting with", start
    paths = find_all_paths(graph, start, len(graph), [])
    for path in paths:
        first = path[0]
        last = path[-1]
        if first in graph[last]:
            cycles.append(path)
        else:
            print path
 
print "Cycles (duplicated for each start song):"
for cycle in cycles:
    print cycle

Success #stdin #stdout 0.1s 65700KB

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Standard input is empty

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Non-cyclic paths starting with 2
[2, 3, 4, 8, 1, 6, 10, 9, 5, 7]
[2, 3, 4, 8, 9, 5, 7, 1, 6, 10]
[2, 3, 4, 8, 9, 10, 1, 6, 5, 7]
[2, 3, 4, 9, 5, 7, 8, 1, 6, 10]
[2, 3, 4, 9, 8, 1, 6, 10, 5, 7]
[2, 3, 4, 9, 10, 1, 6, 5, 7, 8]
[2, 3, 4, 9, 10, 5, 7, 1, 6, 8]
[2, 3, 4, 10, 1, 6, 5, 7, 8, 9]
[2, 3, 4, 10, 1, 6, 8, 9, 5, 7]
[2, 3, 4, 10, 5, 7, 1, 6, 8, 9]
[2, 3, 4, 10, 9, 5, 7, 1, 6, 8]
[2, 3, 4, 10, 9, 8, 1, 6, 5, 7]
[2, 3, 6, 1, 8, 9, 5, 7, 4, 10]
[2, 3, 6, 1, 8, 9, 10, 5, 7, 4]
[2, 3, 6, 1, 9, 10, 5, 7, 4, 8]
[2, 3, 6, 1, 10, 5, 7, 4, 8, 9]
[2, 3, 6, 1, 10, 5, 7, 4, 9, 8]
[2, 3, 6, 1, 10, 9, 5, 7, 4, 8]
[2, 3, 6, 4, 8, 1, 9, 10, 5, 7]
[2, 3, 6, 4, 8, 1, 10, 9, 5, 7]
[2, 3, 6, 4, 8, 9, 5, 7, 1, 10]
[2, 3, 6, 4, 9, 5, 7, 8, 1, 10]
[2, 3, 6, 4, 9, 8, 1, 10, 5, 7]
[2, 3, 6, 4, 9, 10, 5, 7, 1, 8]
[2, 3, 6, 4, 10, 1, 8, 9, 5, 7]
[2, 3, 6, 4, 10, 1, 9, 5, 7, 8]
[2, 3, 6, 4, 10, 5, 7, 1, 8, 9]
[2, 3, 6, 4, 10, 5, 7, 1, 9, 8]
[2, 3, 6, 4, 10, 5, 7, 8, 1, 9]
[2, 3, 6, 4, 10, 9, 5, 7, 1, 8]
[2, 3, 6, 5, 7, 4, 8, 1, 9, 10]
[2, 3, 6, 5, 7, 4, 8, 1, 10, 9]
[2, 3, 6, 5, 7, 4, 9, 8, 1, 10]
[2, 3, 6, 5, 7, 4, 9, 10, 1, 8]
[2, 3, 6, 5, 7, 4, 10, 1, 8, 9]
[2, 3, 6, 5, 7, 4, 10, 1, 9, 8]
[2, 3, 6, 8, 1, 9, 5, 7, 4, 10]
[2, 3, 6, 8, 1, 9, 10, 5, 7, 4]
[2, 3, 6, 8, 1, 10, 5, 7, 4, 9]
[2, 3, 6, 8, 1, 10, 9, 5, 7, 4]
[2, 3, 6, 10, 1, 8, 9, 5, 7, 4]
[2, 3, 6, 10, 1, 9, 5, 7, 4, 8]
[2, 3, 6, 10, 5, 7, 4, 8, 1, 9]
[2, 3, 8, 1, 6, 4, 9, 10, 5, 7]
[2, 3, 8, 1, 6, 4, 10, 9, 5, 7]
[2, 3, 8, 1, 6, 5, 7, 4, 9, 10]
[2, 3, 8, 1, 6, 5, 7, 4, 10, 9]
[2, 3, 8, 1, 6, 10, 5, 7, 4, 9]
[2, 3, 8, 1, 6, 10, 9, 5, 7, 4]
[2, 3, 8, 9, 5, 7, 1, 6, 4, 10]
[2, 3, 8, 9, 10, 1, 6, 5, 7, 4]
[2, 3, 8, 9, 10, 5, 7, 1, 6, 4]
[2, 5, 7, 1, 3, 6, 4, 8, 9, 10]
[2, 5, 7, 1, 3, 6, 4, 10, 9, 8]
[2, 5, 7, 1, 6, 3, 4, 8, 9, 10]
[2, 5, 7, 1, 6, 3, 4, 10, 9, 8]
[2, 5, 7, 1, 6, 4, 3, 8, 9, 10]
[2, 5, 7, 1, 6, 4, 9, 10, 3, 8]
[2, 5, 7, 1, 6, 4, 10, 3, 8, 9]
[2, 5, 7, 1, 6, 4, 10, 9, 3, 8]
[2, 5, 7, 1, 6, 8, 3, 4, 9, 10]
[2, 5, 7, 1, 6, 8, 3, 4, 10, 9]
[2, 5, 7, 1, 6, 8, 9, 3, 4, 10]
[2, 5, 7, 1, 6, 8, 9, 10, 3, 4]
[2, 5, 7, 1, 6, 10, 3, 4, 8, 9]
[2, 5, 7, 1, 6, 10, 3, 4, 9, 8]
[2, 5, 7, 1, 6, 10, 9, 3, 4, 8]
[2, 5, 7, 1, 6, 10, 9, 8, 3, 4]
[2, 5, 7, 1, 8, 3, 6, 4, 9, 10]
[2, 5, 7, 1, 8, 3, 6, 4, 10, 9]
[2, 5, 7, 1, 8, 9, 3, 6, 4, 10]
[2, 5, 7, 1, 8, 9, 10, 3, 6, 4]
[2, 5, 7, 1, 9, 8, 3, 6, 4, 10]
[2, 5, 7, 1, 9, 10, 3, 6, 4, 8]
[2, 5, 7, 1, 10, 3, 6, 4, 8, 9]
[2, 5, 7, 1, 10, 3, 6, 4, 9, 8]
[2, 5, 7, 1, 10, 9, 3, 6, 4, 8]
[2, 5, 7, 1, 10, 9, 8, 3, 6, 4]
[2, 5, 7, 3, 4, 8, 1, 6, 10, 9]
[2, 5, 7, 3, 4, 9, 8, 1, 6, 10]
[2, 5, 7, 3, 4, 9, 10, 1, 6, 8]
[2, 5, 7, 3, 4, 10, 1, 6, 8, 9]
[2, 5, 7, 3, 6, 4, 8, 1, 9, 10]
[2, 5, 7, 3, 6, 4, 8, 1, 10, 9]
[2, 5, 7, 3, 6, 4, 9, 8, 1, 10]
[2, 5, 7, 3, 6, 4, 9, 10, 1, 8]
[2, 5, 7, 3, 6, 4, 10, 1, 8, 9]
[2, 5, 7, 3, 6, 4, 10, 1, 9, 8]
[2, 5, 7, 3, 8, 1, 6, 4, 9, 10]
[2, 5, 7, 3, 8, 1, 6, 4, 10, 9]
[2, 5, 7, 3, 8, 9, 10, 1, 6, 4]
[2, 5, 7, 4, 3, 6, 1, 8, 9, 10]
[2, 5, 7, 4, 3, 6, 1, 10, 9, 8]
[2, 5, 7, 4, 3, 6, 8, 1, 9, 10]
[2, 5, 7, 4, 3, 6, 8, 1, 10, 9]
[2, 5, 7, 4, 3, 6, 10, 1, 8, 9]
[2, 5, 7, 4, 3, 6, 10, 1, 9, 8]
[2, 5, 7, 4, 3, 8, 1, 6, 10, 9]
[2, 5, 7, 4, 8, 1, 3, 6, 10, 9]
[2, 5, 7, 4, 8, 1, 9, 3, 6, 10]
[2, 5, 7, 4, 8, 3, 6, 1, 9, 10]
[2, 5, 7, 4, 8, 3, 6, 1, 10, 9]
[2, 5, 7, 4, 8, 3, 6, 10, 1, 9]
[2, 5, 7, 4, 8, 9, 3, 6, 1, 10]
[2, 5, 7, 4, 9, 3, 6, 8, 1, 10]
[2, 5, 7, 4, 9, 3, 6, 10, 1, 8]
[2, 5, 7, 4, 9, 3, 8, 1, 6, 10]
[2, 5, 7, 4, 9, 8, 1, 3, 6, 10]
[2, 5, 7, 4, 9, 8, 3, 6, 1, 10]
[2, 5, 7, 4, 9, 10, 1, 3, 6, 8]
[2, 5, 7, 4, 9, 10, 1, 6, 3, 8]
[2, 5, 7, 4, 9, 10, 3, 6, 1, 8]
[2, 5, 7, 4, 10, 1, 3, 6, 8, 9]
[2, 5, 7, 4, 10, 1, 6, 3, 8, 9]
[2, 5, 7, 4, 10, 1, 9, 3, 6, 8]
[2, 5, 7, 4, 10, 3, 6, 1, 8, 9]
[2, 5, 7, 4, 10, 3, 6, 1, 9, 8]
[2, 5, 7, 4, 10, 3, 6, 8, 1, 9]
[2, 5, 7, 4, 10, 9, 3, 6, 1, 8]
[2, 5, 7, 8, 1, 3, 6, 4, 9, 10]
[2, 5, 7, 8, 1, 3, 6, 4, 10, 9]
[2, 5, 7, 8, 1, 6, 3, 4, 9, 10]
[2, 5, 7, 8, 1, 6, 3, 4, 10, 9]
[2, 5, 7, 8, 1, 6, 10, 3, 4, 9]
[2, 5, 7, 8, 1, 6, 10, 9, 3, 4]
[2, 5, 7, 8, 1, 9, 3, 6, 4, 10]
[2, 5, 7, 8, 1, 9, 10, 3, 6, 4]
[2, 5, 7, 8, 1, 10, 3, 6, 4, 9]
[2, 5, 7, 8, 1, 10, 9, 3, 6, 4]
[2, 5, 7, 8, 3, 6, 4, 10, 1, 9]
[2, 5, 7, 8, 9, 10, 1, 3, 6, 4]
[2, 5, 7, 8, 9, 10, 1, 6, 3, 4]
[2, 10, 1, 3, 6, 4, 8, 9, 5, 7]
[2, 10, 1, 3, 6, 4, 9, 5, 7, 8]
[2, 10, 1, 3, 6, 5, 7, 4, 8, 9]
[2, 10, 1, 3, 6, 5, 7, 4, 9, 8]
[2, 10, 1, 3, 6, 8, 9, 5, 7, 4]
[2, 10, 1, 6, 3, 4, 8, 9, 5, 7]
[2, 10, 1, 6, 3, 4, 9, 5, 7, 8]
[2, 10, 1, 6, 3, 8, 9, 5, 7, 4]
[2, 10, 1, 6, 4, 3, 8, 9, 5, 7]
[2, 10, 1, 6, 4, 9, 5, 7, 3, 8]
[2, 10, 1, 6, 5, 7, 3, 4, 8, 9]
[2, 10, 1, 6, 5, 7, 3, 4, 9, 8]
[2, 10, 1, 6, 5, 7, 4, 3, 8, 9]
[2, 10, 1, 6, 5, 7, 4, 9, 3, 8]
[2, 10, 1, 6, 5, 7, 8, 3, 4, 9]
[2, 10, 1, 6, 5, 7, 8, 9, 3, 4]
[2, 10, 1, 6, 8, 3, 4, 9, 5, 7]
[2, 10, 1, 6, 8, 9, 5, 7, 3, 4]
[2, 10, 1, 8, 3, 6, 4, 9, 5, 7]
[2, 10, 1, 8, 3, 6, 5, 7, 4, 9]
[2, 10, 1, 8, 9, 3, 6, 5, 7, 4]
[2, 10, 1, 8, 9, 5, 7, 3, 6, 4]
[2, 10, 1, 9, 3, 6, 5, 7, 4, 8]
[2, 10, 1, 9, 5, 7, 3, 6, 4, 8]
[2, 10, 1, 9, 5, 7, 4, 3, 6, 8]
[2, 10, 1, 9, 5, 7, 8, 3, 6, 4]
[2, 10, 1, 9, 8, 3, 6, 5, 7, 4]
[2, 10, 3, 4, 9, 5, 7, 1, 6, 8]
[2, 10, 3, 4, 9, 8, 1, 6, 5, 7]
[2, 10, 3, 6, 1, 8, 9, 5, 7, 4]
[2, 10, 3, 6, 1, 9, 5, 7, 4, 8]
[2, 10, 3, 6, 4, 8, 1, 9, 5, 7]
[2, 10, 3, 6, 4, 9, 5, 7, 1, 8]
[2, 10, 3, 6, 5, 7, 4, 8, 1, 9]
[2, 10, 3, 6, 8, 1, 9, 5, 7, 4]
[2, 10, 3, 8, 1, 6, 4, 9, 5, 7]
[2, 10, 3, 8, 1, 6, 5, 7, 4, 9]
[2, 10, 3, 8, 9, 5, 7, 1, 6, 4]
[2, 10, 5, 7, 1, 3, 6, 4, 8, 9]
[2, 10, 5, 7, 1, 3, 6, 4, 9, 8]
[2, 10, 5, 7, 1, 6, 3, 4, 8, 9]
[2, 10, 5, 7, 1, 6, 3, 4, 9, 8]
[2, 10, 5, 7, 1, 6, 4, 3, 8, 9]
[2, 10, 5, 7, 1, 6, 4, 9, 3, 8]
[2, 10, 5, 7, 1, 6, 8, 3, 4, 9]
[2, 10, 5, 7, 1, 6, 8, 9, 3, 4]
[2, 10, 5, 7, 1, 8, 3, 6, 4, 9]
[2, 10, 5, 7, 1, 8, 9, 3, 6, 4]
[2, 10, 5, 7, 1, 9, 3, 6, 4, 8]
[2, 10, 5, 7, 1, 9, 8, 3, 6, 4]
[2, 10, 5, 7, 3, 6, 4, 8, 1, 9]
[2, 10, 5, 7, 3, 8, 1, 6, 4, 9]
[2, 10, 5, 7, 4, 3, 6, 1, 8, 9]
[2, 10, 5, 7, 4, 3, 6, 1, 9, 8]
[2, 10, 5, 7, 4, 3, 6, 8, 1, 9]
[2, 10, 5, 7, 4, 8, 3, 6, 1, 9]
[2, 10, 5, 7, 4, 9, 3, 6, 1, 8]
[2, 10, 5, 7, 8, 1, 3, 6, 4, 9]
[2, 10, 5, 7, 8, 1, 6, 3, 4, 9]
[2, 10, 5, 7, 8, 1, 9, 3, 6, 4]
[2, 10, 9, 3, 4, 8, 1, 6, 5, 7]
[2, 10, 9, 3, 8, 1, 6, 5, 7, 4]
[2, 10, 9, 5, 7, 1, 3, 6, 4, 8]
[2, 10, 9, 5, 7, 1, 6, 3, 4, 8]
[2, 10, 9, 5, 7, 1, 6, 4, 3, 8]
[2, 10, 9, 5, 7, 1, 6, 8, 3, 4]
[2, 10, 9, 5, 7, 1, 8, 3, 6, 4]
[2, 10, 9, 5, 7, 3, 8, 1, 6, 4]
[2, 10, 9, 5, 7, 4, 3, 6, 1, 8]
[2, 10, 9, 5, 7, 8, 1, 3, 6, 4]
[2, 10, 9, 5, 7, 8, 1, 6, 3, 4]
[2, 10, 9, 8, 1, 3, 6, 5, 7, 4]
[2, 10, 9, 8, 1, 6, 5, 7, 3, 4]
Cycles (duplicated for each start song):
[2, 3, 4, 8, 9, 10, 5, 7, 1, 6]
[2, 3, 4, 9, 10, 5, 7, 8, 1, 6]
[2, 3, 4, 10, 9, 5, 7, 8, 1, 6]
[2, 3, 6, 4, 8, 9, 10, 5, 7, 1]
[2, 3, 6, 4, 9, 10, 5, 7, 8, 1]
[2, 3, 6, 4, 10, 9, 5, 7, 8, 1]
[2, 3, 6, 5, 7, 4, 8, 9, 10, 1]
[2, 3, 6, 5, 7, 4, 10, 9, 8, 1]
[2, 3, 6, 8, 9, 5, 7, 4, 10, 1]
[2, 3, 6, 10, 5, 7, 4, 9, 8, 1]
[2, 3, 6, 10, 9, 5, 7, 4, 8, 1]
[2, 3, 8, 9, 5, 7, 4, 10, 1, 6]
[2, 5, 7, 1, 6, 4, 8, 9, 10, 3]
[2, 5, 7, 1, 6, 4, 10, 9, 8, 3]
[2, 5, 7, 3, 4, 8, 9, 10, 1, 6]
[2, 5, 7, 3, 4, 10, 9, 8, 1, 6]
[2, 5, 7, 3, 6, 4, 8, 9, 10, 1]
[2, 5, 7, 3, 6, 4, 10, 9, 8, 1]
[2, 5, 7, 4, 3, 6, 8, 9, 10, 1]
[2, 5, 7, 4, 3, 6, 10, 9, 8, 1]
[2, 5, 7, 4, 3, 8, 9, 10, 1, 6]
[2, 5, 7, 4, 8, 1, 6, 10, 9, 3]
[2, 5, 7, 4, 8, 1, 9, 10, 3, 6]
[2, 5, 7, 4, 8, 1, 10, 9, 3, 6]
[2, 5, 7, 4, 8, 9, 3, 6, 10, 1]
[2, 5, 7, 4, 8, 9, 10, 1, 3, 6]
[2, 5, 7, 4, 8, 9, 10, 1, 6, 3]
[2, 5, 7, 4, 8, 9, 10, 3, 6, 1]
[2, 5, 7, 4, 9, 8, 1, 6, 10, 3]
[2, 5, 7, 4, 9, 8, 1, 10, 3, 6]
[2, 5, 7, 4, 9, 8, 3, 6, 10, 1]
[2, 5, 7, 4, 9, 10, 1, 6, 8, 3]
[2, 5, 7, 4, 9, 10, 1, 8, 3, 6]
[2, 5, 7, 4, 9, 10, 3, 6, 8, 1]
[2, 5, 7, 4, 9, 10, 3, 8, 1, 6]
[2, 5, 7, 4, 10, 1, 6, 8, 9, 3]
[2, 5, 7, 4, 10, 1, 8, 9, 3, 6]
[2, 5, 7, 4, 10, 1, 9, 8, 3, 6]
[2, 5, 7, 4, 10, 9, 3, 6, 8, 1]
[2, 5, 7, 4, 10, 9, 3, 8, 1, 6]
[2, 5, 7, 4, 10, 9, 8, 1, 3, 6]
[2, 5, 7, 4, 10, 9, 8, 1, 6, 3]
[2, 5, 7, 4, 10, 9, 8, 3, 6, 1]
[2, 5, 7, 8, 1, 6, 4, 9, 10, 3]
[2, 5, 7, 8, 1, 6, 4, 10, 9, 3]
[2, 5, 7, 8, 3, 4, 9, 10, 1, 6]
[2, 5, 7, 8, 3, 6, 4, 9, 10, 1]
[2, 5, 7, 8, 9, 3, 4, 10, 1, 6]
[2, 5, 7, 8, 9, 3, 6, 4, 10, 1]
[2, 5, 7, 8, 9, 10, 1, 6, 4, 3]
[2, 10, 1, 6, 4, 8, 9, 5, 7, 3]
[2, 10, 1, 6, 4, 9, 5, 7, 8, 3]
[2, 10, 1, 6, 5, 7, 4, 8, 9, 3]
[2, 10, 1, 6, 5, 7, 4, 9, 8, 3]
[2, 10, 1, 6, 8, 9, 5, 7, 4, 3]
[2, 10, 1, 8, 9, 5, 7, 4, 3, 6]
[2, 10, 1, 9, 5, 7, 4, 8, 3, 6]
[2, 10, 3, 4, 8, 9, 5, 7, 1, 6]
[2, 10, 3, 4, 9, 5, 7, 8, 1, 6]
[2, 10, 3, 6, 4, 8, 9, 5, 7, 1]
[2, 10, 3, 6, 4, 9, 5, 7, 8, 1]
[2, 10, 3, 6, 5, 7, 4, 9, 8, 1]
[2, 10, 5, 7, 1, 6, 4, 8, 9, 3]
[2, 10, 5, 7, 1, 6, 4, 9, 8, 3]
[2, 10, 5, 7, 3, 4, 9, 8, 1, 6]
[2, 10, 5, 7, 3, 6, 4, 9, 8, 1]
[2, 10, 5, 7, 4, 8, 1, 9, 3, 6]
[2, 10, 5, 7, 4, 8, 9, 3, 6, 1]
[2, 10, 5, 7, 4, 9, 3, 6, 8, 1]
[2, 10, 5, 7, 4, 9, 3, 8, 1, 6]
[2, 10, 5, 7, 4, 9, 8, 1, 3, 6]
[2, 10, 5, 7, 4, 9, 8, 1, 6, 3]
[2, 10, 5, 7, 4, 9, 8, 3, 6, 1]
[2, 10, 5, 7, 8, 1, 6, 4, 9, 3]
[2, 10, 9, 3, 6, 5, 7, 4, 8, 1]
[2, 10, 9, 5, 7, 1, 6, 4, 8, 3]
[2, 10, 9, 5, 7, 3, 4, 8, 1, 6]
[2, 10, 9, 5, 7, 3, 6, 4, 8, 1]
[2, 10, 9, 5, 7, 4, 3, 6, 8, 1]
[2, 10, 9, 5, 7, 4, 3, 8, 1, 6]
[2, 10, 9, 5, 7, 4, 8, 1, 3, 6]
[2, 10, 9, 5, 7, 4, 8, 1, 6, 3]
[2, 10, 9, 5, 7, 4, 8, 3, 6, 1]
[2, 10, 9, 5, 7, 8, 1, 6, 4, 3]
[2, 10, 9, 8, 1, 6, 5, 7, 4, 3]

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