def narrow_region(frontier, target, max_states=100):
''' Given a frontier to start with, run through the largest powers of BASE
until we get a decent number of starting states
>>> base = 2
>>> target = IntegerBaseFixed(1031 * 1093, None, None, base=2)
>>> num_digits = target_to_max_factor_num_digits(target, base=2, moe=0)
>>> frontier = generate_starting_products(num_digits, base=2)
>>> frontier = narrow_region(frontier, target, 5)
>>> for prod in frontier:
... print prod.num_fixed_digits_left, prod.num_fixed_digits_right, prod
1 6 10000100001x10000100001=100010000110001000001
1 6 10000000001x10001000001=100010000100001000001
1 7 10000000001x10000110001=100001100100000110001
1 7 10000010001x10000100001=100001100101000110001
1 7 10000010001x10000110001=100010000101101000001
'''
frontier = deque(frontier)
while len(frontier) < max_states:
prod = frontier.popleft()
assert prod.base == target.base
children = generate_children(prod, 'r')
for child in children:
if child.as_int == target.as_int:
return deque([child])
if has_potential_children(child, target):
frontier.append(child)
return frontier
def factorize(target, base=BASE):
''' Simple breadth first factorization algorithm
>>> factorize(143, 2)
(11, 13)
>>> factorize(169, 2)
(13, 13)
>>> factorize(289, 2)
(17, 17)
>>> factorize(323, 2)
(17, 19)
>>> factorize(309485009822787627980424653, 2)
(17592186044443L, 17592186044471L)
'''
target = IntegerBaseFixed(target, None, None, base)
num_digits = target_to_max_factor_num_digits(target, base=base, moe=0)
frontier = deque(generate_starting_products(num_digits, base))
# Now narrow starting from the right, in case we have a very low or very
# high factor
frontier = narrow_region(frontier, target, max_states=100)
if len(frontier) == 1:
prod = frontier[0]
assert prod.as_int == target.as_int
p, q = prod.p.as_int, prod.q.as_int
return order(p, q)
while len(frontier):
prod = frontier.popleft()
if prod.num_fixed_digits_left > prod.num_fixed_digits_right:
children = generate_children(prod, 'r')
else:
children = generate_children(prod, 'l')
for child in children:
if child.as_int == target.as_int:
p, q = child.p.as_int, child.q.as_int
return order(p, q)
if has_potential_children(child, target):
frontier.append(child)
print 'No factorization found!'
