count of automorphism for CSC3001 Assignment 3

automorphism.py

#!/usr/bin/env python3

from itertools import permutations
'''
for a permutation to be valid
A - B
A - C
A - D
B - E
B - G
C - I
C - J
D - F
D - H
E - F
E - J
F - I
G - H
G - I
H - J

ABCDEFGHIJ
0123456789

For the reshuffled 'reduced', the original points now sit in the new location.
We need to verify the new shape has the same topology with the previous one.
For example, if we have the reshuffle:

    [(0, 4, 6),...]

We want to make sure that the (0, 4, 6) at new '0' position does connect to
that he is required to connect, i.e. it connect to ...
'''

if __name__ == '__main__':
    count = 0
    automorphism_count = 0
    raw_ind = [(1, 2, 3), (0, 4, 6), (0, 8, 9), (0, 5, 7), (1, 5, 9),
               (3, 4, 8), (1, 7, 8), (3, 6, 9), (2, 5, 6), (2, 4, 7)]
    raw = [('A', 'BCD'), ('B', 'AEG'), ('C', 'AIJ'), ('D', 'AFH'), (
        'E', 'BFJ'), ('F', 'DEI'), ('G', 'BIH'), ('H', 'GJD'), ('I', 'CFG'),
           ('J', 'CEH')]
    # [for i in raw]
    for test in permutations(raw, 10):
        value = True
        for i, v in enumerate(raw_ind):
            for j in v:
                if test[j][0] not in test[i][1]:
                    value = False
        # originally this need to connect to position[v]
        # we need to check if the new item satisfy the requirement
        if value:
            automorphism_count += 1
        count += 1
        if not (count % 100000):
            print('# of iteration: ', count, ', # of founded:',
                  automorphism_count)
    # we don't count itself
    automorphism_count -= 1
    print('# of automorphisms: ', automorphism_count)