Demo/scripts/fact.py

#! /usr/local/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()