Simple implementation of merge sort in Python (and time comparison with built-in sort)

mergesort.py

#!/usr/bin/python

def mergesort(arr,length):
	if length == 1:
		return arr
	else:
		cut = length/2
		left = mergesort(arr[:cut],len(arr[:cut]))
		right = mergesort(arr[cut:],len(arr[cut:]))
		return merge(left,right, length)


def merge(left, right, length):
	i = j = 0
	out = [None] * length
	right_len = len(right)
	left_len = len(left)
	for k in range(length):
		if j >= right_len or (i < left_len and left[i] < right[j]):
			out[k] = left[i]
			i += 1
		else:
			out[k] = right[j]
			j += 1
	return out

if (__name__ == '__main__'):

	import random
	import timeit
	
	# One example to visually check that sorting works

	arr = [4,9,2,1,23,4,12,84,3,5,25,33,1,345,2,4,7]
	print('Not sorted : %s' % arr)
	print('Sorted : %s' % mergesort(arr, len(arr)))

	# Comparison between this merge sort and the built-in Python sort

	big_arr = [random.random() for _ in range(10000)]
	t1 = timeit.Timer(lambda: mergesort(big_arr, len(big_arr))).timeit(number=1)
	t2 = timeit.Timer(lambda: sorted(big_arr)).timeit(number=1)
	print('Time to sort 10000 floats with mergesort : %f seconds' % t1)
	print('Time to sort 10000 floats with python built-in sort : %f seconds' % t2)
	print('Ratio : %f' % (t1/t2))

Without any optimization as it is, the built-in Python sort is usually about 25 times faster.