Python recursive program to prime factorize a number

Question

I wrote the following program to prime factorize a number:

import math
def prime_factorize(x,li=[]):
    until = int(math.sqrt(x))+1
    for i in xrange(2,until)         


        

Answer 1

@Anthony's correctly answered your original question about print. However, in the spirit of the several tips that were also offered, here's a simple refactorization using tail recursion removal:

def prime_factorize(x):
  li = []
  while x >= 2:
    until = int(math.sqrt(x))+1
    for i in xrange(2,until):
      if not x%i:
        li.append(i)
        break
    else:
      li.append(x)
      return li
    x //= i

This doesn't address the crucial performance issues (big-O behavior is the same as for your original solution) -- but since Python itself doesn't do tail-recursion optimization, it's important to learn to do it manually.

"Change the [non-base-case] recursive steps 'return thisfun(newargs)' into args=newargs; continue and put the whole body into a while True: loop" is the basic idea of tail-recursion optimization. Here I've also made li a non-arg (no reason for it to be an arg), put a condition on the while, and avoided the continue since the recursive step was at the end of the body anyway.

This formulation would be a good basis from which to apply further optimizing refactorings (sqrt avoidance, memoization, ...) to reach towards better performance.