Perfectly random Android lockscreen pattern

lockscreen.py

from itertools import combinations, permutations
import re

MIN_LENGTH = 4

ILLEGAL_PATTERN_RE = re.compile('(%s)' % '|'.join(
  # Simulate negative lookbehind via negative lookahead
  # h/t https://learnbyexample.github.io/py_regular_expressions/lookarounds.html#negated-groups
  f'^(?!.*{b}.*{a}{c}).*{a}{c}' for a,b,c, in 
  ['123', '159', '147', '258', '369', '357', '321', '456', '654', '789', '741', '753', '852', '987', '951', '963']
))

PATTERNS = sorted(filter(
  lambda seq: not ILLEGAL_PATTERN_RE.match(seq),
  (seq for l in range(MIN_LENGTH, 10) for nodes in combinations('123456789', l)
      for seq in (
        ''.join(node for node in _seq)
        for _seq in permutations(nodes)
      )
  )
))


def repr_pattern(pattern):
  return '{0} {1} {2}\n{3} {4} {5}\n{6} {7} {8}'.format(*(
    ('123456789'[pattern.index(node)] if node in pattern else '-')
    for node in '123456789'
  ))


if __name__ == '__main__':
  from random import SystemRandom
  _rand = SystemRandom()
  print(repr_pattern(_rand.choice(PATTERNS)))