Generates every valid password for an incredibly stupid authentication system

password.py

import itertools

# Finding every single terrible password
# 
# (Password requirements from http://kottke.org/12/06/the-worlds-worst-password-requirements-list)
#
# Must be exactly 8 characters long
# Must contain at least one character from each of these sets: 
# 	['@', '#', '$'],
# 	['0', '1', '2', '3', '4', '5', '6', '7', '8', '9'],
# 	['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n',
# 	 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z', 'A', 'B',
# 	 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P',
# 	 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z']
# Must not contain '@', #', or '$' in either the first or last position
# Must not contain adjacent duplicate characters
#
# Prints every valid password to STDOUT after a very long time

def hasIdenticalAdjacents(str):
	for x in zip(str[:-1], str[1:]):
		if x[0] == x[1]:
			return True
	return False

characters = '@#$0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'
restricted = '@#$'

for x in itertools.product(characters, repeat=8):
	if x[0] not in restricted and x[-1] not in restricted:
		if not hasIdenticalAdjacents(x):
			print x

# Analysis:
#                                             ratio
# length           valid / possible       valid : possible
# ------        -------------------       ----------------
#    2              3782 / 4225              0.895
#    3            242234 / 274625            0.882
#    4          15502790 / 17850625          0.868
#    5         991359850 / 1160290625        0.854  (est)
#    6       63414165750 / 75418890625       0.841  (est)
#    7     4055346181250 / 4902227890625     0.827  (est)
#    8   259270153268750 / 318644812890625   0.814  (est)
# 
# With approximately 260 trillion passwords, a file containing all passwords
# would take up 2.0725 petabytes.