pattern-security

#!/usr/bin/python3
import argparse
import sys

helper_tab = [
    ('start', 'Pattern starting digit'),
    ('end', 'Pattern ending digit'),
    ('length', 'Pattern length'),
  ]

bridges = {
    1: {3: 2, 7: 4, 9: 5},
    2: {8: 5},
    3: {1: 2, 7: 5, 9: 6},
    4: {6: 5},
    5: {},
    6: {4: 5},
    7: {1: 4, 3: 5, 9: 8},
    8: {2: 5},
    9: {1: 5, 3: 6, 7: 8},
}

def is_allowed(a, b, paths):
  if (a == b or b not in paths): return False
  bridge = bridges[a].get(b, None)
  if (bridge and bridge in paths):
    return False
  return True

def find_paths(a, b, l, paths):
  if (l == 0 and a == b):
    return 1
  if ((l == 0 and a != b) or len(paths) == 0):
    return 0
  res = 0
  for path in paths:
    if is_allowed(a, path, paths):
      tmp_paths = paths.copy()
      tmp_paths.remove(path)
      res += find_paths(path, b, l - 1, tmp_paths)
  return (res)

def compute(a, b, l):
  if (a == b):
    print('Start and End digit can not be equal', file=sys.stderr)
    return 0
  paths = list(range(1, 10))
  paths.remove(a)
  res = find_paths(a, b, l - 1, paths)
  return (res)

if __name__ == '__main__':
  parser = argparse.ArgumentParser(description='Android pattern security')
  for name, desc in helper_tab:
    parser.add_argument(
        name, metavar='{} [1-9]'.format(name),
        choices=range(1, 10), type=int, help=desc)
  args = vars(parser.parse_args()).values()
  print(compute(*args))