make_change.py

import copy
import functools

def memoize(obj):
    cache = obj.cache = {}
    @functools.wraps(obj)
    def memoizer(*args, **kwargs):
        key = str(args) + str(kwargs)
        if key not in cache:
            cache[key] = obj(*args, **kwargs)
        return cache[key]
    return memoizer

@memoize
def make_change(rem, unit):
    if rem < 0:
	return 0

    total = 0
    if unit == 1 or rem == 0 or rem == unit:
	return 1
   
    if unit >= 5:
        total += make_change(rem - unit, 1)
	total += make_change(rem - unit, 5)
    if unit >= 10:
	total += make_change(rem - unit, 10)	
    if unit >= 25:
	total += make_change(rem - unit, 25)
    if unit == 50:
	total += make_change(rem - unit, 50)
    return total


def ways(number):
	return make_change(number, 1) + make_change(number, 5) + make_change(number, 10) + make_change(number, 25) + make_change(number, 50)