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#! /usr/bin/env python
# Factorize numbers.
# The algorithm is not efficient, but easy to understand.
# If there are large factors, it will take forever to find them,
# because we try all odd numbers between 3 and sqrt(n)...
import sys
from math import sqrt
error = 'fact.error' # exception
def fact(n):
if n < 1: raise error # fact() argument should be >= 1
if n == 1: return [] # special case
res = []
# Treat even factors special, so we can use i = i+2 later
while n%2 == 0:
res.append(2)
n = n/2
# Try odd numbers up to sqrt(n)
limit = sqrt(float(n+1))
i = 3
while i <= limit:
if n%i == 0:
res.append(i)
n = n/i
limit = sqrt(n+1)
else:
i = i+2
if n != 1:
res.append(n)
return res
def main():
if len(sys.argv) > 1:
for arg in sys.argv[1:]:
n = eval(arg)
print n, fact(n)
else:
try:
while 1:
n = input()
print n, fact(n)
except EOFError:
pass
main()
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