hack.py

import copy

paths = [ ('A', 'F', 0.58), ('D', 'F', 0.27), ('C', 'E', 0.3),
          ('E', 'F', 0.22), ('B', 'E', 0.59), ('A', 'B', 1.27),
          ('B', 'C', 0.61), ('C', 'D', 1.08), ('A', 'D', 0.72)
          ]

bi_paths = copy.copy(paths)
for path in paths:
    bi_paths.append( (path[1], path[0], path[2]) )
print bi_paths

def find_all_from(paths, node):
    exits = []
    for path in paths:
        if path[0] == node:
            exits.append(path)
    return exits

def remove_path(paths, path_to_remove):
    new_paths = []
    for path in paths:
        if path != path_to_remove:
            new_paths.append(path)
    return new_paths
    
def search(paths, node, nodes_so_far, end_node, accum, good_paths):
    exits = find_all_from(paths, node)
    for exit in exits:
        nodes = copy.copy(nodes_so_far)
        accum_dist = copy.copy(accum)
        if exit[1] == end_node and len (nodes) > 1:
            nodes.append(end_node)
            accum_dist = accum_dist + exit[2]
            good_paths.append( (nodes, accum_dist) )
            continue
            
        exit_to = None
        if exit[0] == node:
            nodes.append(exit[1])
            exit_to = exit[1]
            
        new_paths = remove_path(paths, exit)
        if exit_to:
            accum_dist = exit[2] + accum_dist
            search(new_paths, exit_to, nodes, end_node, accum_dist, good_paths)

paths = []
search(bi_paths, 'F', ['F'], 'F', 0.0, paths)
dd = {}
for path in paths:
    ss = ''.join(path[0])
    if not dd.has_key(ss) and not dd.has_key(ss[::-1]):
        dd[ss] = path[1]  
print len(paths), len(dd)

print dd

output

[('A', 'F', 0.58), ('D', 'F', 0.27), ('C', 'E', 0.3), ('E', 'F', 0.22), ('B', 'E', 0.59), ('A', 'B', 1.27), ('B', 'C', 0.61), ('C', 'D', 1.08), ('A', 'D', 0.72), ('F', 'A', 0.58), ('F', 'D', 0.27), ('E', 'C', 0.3), ('F', 'E', 0.22), ('E', 'B', 0.59), ('B', 'A', 1.27), ('C', 'B', 0.61), ('D', 'C', 1.08), ('D', 'A', 0.72)]

1489 778

{'FABADAF': 5.14,
 'FABADCBCDAF': 8.52,
 'FABADCBCDF': 7.49,
 'FABADCBCEBECDAF': 10.3,
 'FABADCBCEBECDF': 9.27,
 'FABADCBCEBEF': 7.84,
 'FABADCBCECDAF': 9.120000000000001,
 'FABADCBCECDF': 8.09,
 'FABADCBCEF': 6.66,
 'FABADCBEBCDAF': 9.700000000000001,
 'FABADCBEBCDF': 8.67,
 'FABADCBEBCECDAF': 10.3,
 'FABADCBEBCECDF': 9.27,
 'FABADCBEBCEF': 7.84,
 'FABADCBECDAF': 8.8,
 'FABADCBECDF': 7.77,
 'FABADCBECEBCDAF': 10.3,
 'FABADCBECEBCDF': 9.27,
 'FABADCBECEF': 6.9399999999999995,
 'FABADCBEF': 6.34,
 'FABADCDAF': 7.3,
 'FABADCDF': 6.27,
 'FABADCEBCBECDAF': 10.3,
 'FABADCEBCBECDF': 9.27,
 'FABADCEBCBEF': 7.84,
 'FABADCEBCDAF': 8.8,
 'FABADCEBCDF': 7.77,
 'FABADCEBECBCDAF': 10.3,
 'FABADCEBECBCDF': 9.27,
 'FABADCEBECDAF': 9.08,
 'FABADCEBECDF': 8.049999999999999,
 'FABADCEBEF': 6.619999999999999,
 'FABADCECBCDAF': 9.120000000000001,
 'FABADCECBCDF': 8.09,
 'FABADCECBEBCDAF': 10.3,
 'FABADCECBEBCDF': 9.27,
 'FABADCECBEF': 6.9399999999999995,
 'FABADCECDAF': 7.8999999999999995,
 'FABADCECDF': 6.869999999999999,
 'FABADCEF': 5.4399999999999995,
 'FABADF': 4.109999999999999,
 'FABAF': 3.7,
 'FABCBADAF': 6.359999999999999,
 'FABCBADCDAF': 8.52,
 'FABCBADCDF': 7.49,
 'FABCBADCEBECDAF': 10.3,
 'FABCBADCEBECDF': 9.27,
 'FABCBADCEBEF': 7.839999999999999,
 'FABCBADCECDAF': 9.12,
 'FABCBADCECDF': 8.09,
 'FABCBADCEF': 6.659999999999999,
 'FABCBADF': 5.33,
 'FABCBAF': 4.92,
 'FABCBEBADAF': 7.539999999999999,
 'FABCBEBADCDAF': 9.7,
 'FABCBEBADCDF': 8.669999999999998,
 'FABCBEBADCECDAF': 10.3,
 'FABCBEBADCECDF': 9.27,
 'FABCBEBADCEF': 7.839999999999999,
 'FABCBEBADF': 6.51,
 'FABCBECDADCEF': 8.079999999999998,
 'FABCBECDADF': 6.749999999999998,
 'FABCBECDAF': 6.339999999999999,
 'FABCBECDCEBADAF': 10.3,
 'FABCBECDCEBADF': 9.27,
 'FABCBECDCEF': 6.639999999999999,
 'FABCBECDF': 5.309999999999999,
 'FABCBECEBADAF': 8.139999999999999,
 'FABCBECEBADCDAF': 10.3,
 'FABCBECEBADCDF': 9.27,
 'FABCBECEBADF': 7.109999999999999,
 'FABCBECEF': 4.4799999999999995,
 'FABCBEF': 3.88,
 'FABCDADCBAF': 8.52,
 'FABCDADCBECEF': 8.08,
 'FABCDADCBEF': 7.4799999999999995,
 'FABCDADCEBEF': 7.759999999999999,
 'FABCDADCECBEF': 8.08,
 'FABCDADCEF': 6.579999999999999,
 'FABCDADF': 5.25,
 'FABCDAF': 4.84,
 'FABCDCBADAF': 8.52,
 'FABCDCBADF': 7.49,
 'FABCDCBAF': 7.08,
 'FABCDCBEBADAF': 9.700000000000001,
 'FABCDCBEBADF': 8.67,
 'FABCDCBECEBADAF': 10.3,
 'FABCDCBECEBADF': 9.27,
 'FABCDCBECEF': 6.64,
 'FABCDCBEF': 6.04,
 'FABCDCEBADAF': 8.799999999999999,
 'FABCDCEBADF': 7.77,
 'FABCDCEBECBADAF': 10.3,
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 'FABCDCEBEF': 6.319999999999999,
 'FABCDCECBADAF': 9.12,
 'FABCDCECBADF': 8.09,
 'FABCDCECBEBADAF': 10.3,
 'FABCDCECBEBADF': 9.27,
 'FABCDCECBEF': 6.64,
 'FABCDCEF': 5.14,
 'FABCDF': 3.81,
 'FABCEBADAF': 6.639999999999999,
 'FABCEBADCBECDAF': 10.3,
 'FABCEBADCBECDF': 9.27,
 'FABCEBADCBEF': 7.839999999999999,
 'FABCEBADCDAF': 8.799999999999999,
 'FABCEBADCDF': 7.77,
 'FABCEBADF': 5.609999999999999,
 'FABCEBECBADAF': 8.139999999999999,
 'FABCEBECBADCDAF': 10.3,
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 'FABCEBECBADF': 7.109999999999999,
 'FABCEBECBAF': 6.699999999999999,
 'FABCEBECDADCBAF': 10.299999999999999,
 'FABCEBECDADF': 7.029999999999999,
 'FABCEBECDAF': 6.619999999999999,
 'FABCEBECDCBADAF': 10.3,
 'FABCEBECDCBADF': 9.27,
 'FABCEBECDCBAF': 8.86,
 'FABCEBECDF': 5.59,
 'FABCEBEF': 4.159999999999999,
 'FABCECBADAF': 6.959999999999999,
 'FABCECBADCDAF': 9.12,
 'FABCECBADCDF': 8.09,
 'FABCECBADF': 5.93,
 'FABCECBAF': 5.52,
 'FABCECBEBADAF': 8.139999999999999,
 'FABCECBEBADCDAF': 10.3,
 'FABCECBEBADCDF': 9.27,
 'FABCECBEBADF': 7.109999999999999,
 'FABCECBEF': 4.4799999999999995,
 'FABCECDADCBAF': 9.12,
 'FABCECDADCBEF': 8.08,
 'FABCECDADF': 5.85,
 'FABCECDAF': 5.4399999999999995,
 'FABCECDCBADAF': 9.12,
 'FABCECDCBADF': 8.09,
 'FABCECDCBAF': 7.68,
 'FABCECDCBEBADAF': 10.3,
 'FABCECDCBEBADF': 9.27,
 'FABCECDCBEF': 6.64,
 'FABCECDF': 4.41,
 'FABCEF': 2.98,
 'FABEBADAF': 6.319999999999999,
 'FABEBADCBCDAF': 9.700000000000001,
 'FABEBADCBCDF': 8.67,
 'FABEBADCBCECDAF': 10.3,
 'FABEBADCBCECDF': 9.27,
 'FABEBADCBCEF': 7.84,
 'FABEBADCDAF': 8.479999999999999,
 'FABEBADCDF': 7.449999999999999,
 'FABEBADCECBCDAF': 10.3,
 'FABEBADCECBCDF': 9.27,
 'FABEBADCECDAF': 9.08,
 'FABEBADCECDF': 8.049999999999999,
 'FABEBADCEF': 6.619999999999999,
 'FABEBADF': 5.289999999999999,
 'FABEBAF': 4.88,
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 'FABEBCBADCDAF': 9.7,
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 'FABEBCBADCEF': 7.839999999999999,
 'FABEBCBADF': 6.51,
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 'FABEBCDF': 4.99,
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 'FABEBCECBADF': 7.109999999999999,
 'FABEBCECBAF': 6.699999999999999,
 'FABEBCECDADCBAF': 10.299999999999999,
 'FABEBCECDADF': 7.029999999999999,
 'FABEBCECDAF': 6.619999999999999,
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 'FABEBCEF': 4.159999999999999,
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 'FABECBADCEF': 6.939999999999999,
 'FABECBADF': 5.609999999999999,
 'FABECBAF': 5.199999999999999,
 'FABECBCDADCEF': 8.079999999999998,
 'FABECBCDADF': 6.749999999999998,
 'FABECBCDAF': 6.339999999999999,
 'FABECBCDCEBADAF': 10.3,
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 'FABECBCDCEF': 6.639999999999999,
 'FABECBCDF': 5.309999999999999,
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 'FABECBCEBADF': 7.109999999999999,
 'FABECBCEBAF': 6.699999999999999,
 'FABECBCEF': 4.4799999999999995,
 'FABECDADCBAF': 8.8,
 'FABECDADCBCEBAF': 10.3,
 'FABECDADCBCEF': 8.08,
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 'FABECDADCEBCBAF': 10.299999999999999,
 'FABECDADCEF': 6.859999999999999,
 'FABECDADF': 5.529999999999999,
 'FABECDAF': 5.12,
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 'FABECDCEBCBAF': 8.860000000000001,
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 'FADABEBCEF': 5.6,
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 'FADABECDCEF': 6.859999999999999,
 'FADABECDF': 5.529999999999999,
 'FADABECEBCDF': 7.029999999999999,
 'FADABECEF': 4.699999999999999,
 'FADABEF': 4.1,
 'FADAF': 2.5999999999999996,
 'FADCBABCDAF': 8.52,
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 'FADCBABECDF': 7.77,
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 'FADCBABECEF': 6.939999999999999,
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 'FADCBCDABEF': 7.4799999999999995,
 'FADCBCDAF': 5.9799999999999995,
 'FADCBCDF': 4.949999999999999,
 'FADCBCEBABECDF': 9.27,
 'FADCBCEBABEF': 7.839999999999999,
 'FADCBCEBECDF': 6.729999999999999,
 'FADCBCEBEF': 5.299999999999999,
 'FADCBCECDABEF': 8.08,
 'FADCBCECDF': 5.549999999999999,
 'FADCBCEF': 4.119999999999999,
 'FADCBEBABCDAF': 9.7,
 'FADCBEBABCDF': 8.669999999999998,
 'FADCBEBABCECDF': 9.27,
 'FADCBEBABCEF': 7.839999999999999,
 'FADCBEBCDAF': 7.16,
 'FADCBEBCDF': 6.130000000000001,
 'FADCBEBCECDF': 6.73,
 'FADCBEBCEF': 5.3,
 'FADCBECDABCEF': 8.08,
 'FADCBECDF': 5.229999999999999,
 'FADCBECEBABCDAF': 10.3,
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 'FADCBECEF': 4.3999999999999995,
 'FADCBEF': 3.8,
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 'FADCDABECBCEF': 8.08,
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 'FADCDABEF': 6.259999999999999,
 'FADCDAF': 4.76,
 'FADCDF': 3.73,
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 'FADCEBCBABECDAF': 10.3,
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 'FADCECDF': 4.33,
 'FADCEF': 2.9,
 'FADF': 1.5699999999999998,
 'FAF': 1.16,
 'FDABADCBCEBEF': 8.250000000000002,
 'FDABADCBCEF': 7.07,
 'FDABADCBEBCEF': 8.250000000000002,
 'FDABADCBECEF': 7.35,
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 'FDABADCEBCBEF': 8.250000000000002,
 'FDABADCEBEF': 7.029999999999999,
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 'FDABADCEF': 5.85,
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 'FDABCBECDCEF': 7.049999999999999,
 'FDABCBECEF': 4.889999999999999,
 'FDABCBEF': 4.289999999999999,
 'FDABCDCBADF': 7.9,
 'FDABCDCBECEF': 7.049999999999999,
 'FDABCDCBEF': 6.449999999999999,
 'FDABCDCEBEF': 6.729999999999999,
 'FDABCDCECBEF': 7.049999999999999,
 'FDABCDCEF': 5.549999999999999,
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 'FDABCEBECDCBADF': 9.68,
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 'FDABCECBADF': 6.34,
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 'FDABCECDCBADF': 8.5,
 'FDABCECDCBEF': 7.049999999999999,
 'FDABCEF': 3.3899999999999997,
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 'FDABEBADF': 5.699999999999999,
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 'FDABEBCBADF': 6.92,
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 'FDABECBCEF': 4.889999999999999,
 'FDABECDCBADF': 8.18,
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 'FDABECDCBCEF': 7.05,
 'FDABECDCEBADF': 8.459999999999999,
 'FDABECDCEBCBADF': 9.68,
 'FDABECDCEF': 5.829999999999999,
 'FDABECEBADF': 6.299999999999999,
 'FDABECEBCBADF': 7.52,
 'FDABECEBCDCBADF': 9.68,
 'FDABECEF': 3.6699999999999995,
 'FDABEF': 3.07,
 'FDADCBABCEBEF': 8.25,
 'FDADCBABCEF': 7.069999999999999,
 'FDADCBABEBCEF': 8.25,
 'FDADCBABECEF': 7.349999999999999,
 'FDADCBABEF': 6.749999999999999,
 'FDADCBCEBABEF': 8.25,
 'FDADCBCEBEF': 5.709999999999999,
 'FDADCBCEF': 4.529999999999999,
 'FDADCBEBABCEF': 8.25,
 'FDADCBEBCEF': 5.71,
 'FDADCBECEF': 4.81,
 'FDADCBEF': 4.21,
 'FDADCEBABCBEF': 8.25,
 'FDADCEBABEF': 7.0299999999999985,
 'FDADCEBCBABEF': 8.25,
 'FDADCEBCBEF': 5.71,
 'FDADCEBEF': 4.489999999999999,
 'FDADCECBABEF': 7.349999999999999,
 'FDADCECBEF': 4.81,
 'FDADCEF': 3.31,
 'FDADF': 1.98,
 'FDCBABCDADF': 7.9,
 'FDCBABCDF': 6.460000000000001,
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