# Merge Sort Algorithm Python

I started implementing algorithms to learn them in order to get better at programming. Here is a merge sort one and criticisms / optimizations are welcome.

import unittest
import random

def mergeSort(list):
"""Sorts a mutable list.

Args:
list: An unordered list

Returns:
The sorted list.
"""
if len(list) > 1:
middle = len(list) // 2
left_sorted = mergeSort(list[:middle])
right_sorted = mergeSort(list[middle:])
i,j,k = 0, 0, 0
merged_list = []
while (k < len(list) and len(left_sorted) != i and len(right_sorted) != j):
if left_sorted[i] < right_sorted[j]:
merged_list.append(left_sorted[i])
i+=1
else:
merged_list.append(right_sorted[j])
j+=1
k+=1
# Handle remaining items in the list.
if len(left_sorted) == i:
merged_list += right_sorted[j:]
elif len(right_sorted) == j:
merged_list += left_sorted[i:]
return merged_list
else:
return list

class test_mergeSort(unittest.TestCase):
def test_mergeSort(self):
random_list = [random.randrange(0, 1000) for _ in range(500)]
self.assertEqual(mergeSort(random_list), sorted(random_list))

if __name__ == '__main__':
unittest.main()


### Reduce nesting

If you invert the condition if len(list) > 1: near the beginning and use an early return, you can reduce the level of nesting, making the code slightly easier to read:

if len(list) <= 1:
return list

middle = len(list) // 2
left_sorted = mergeSort(list[:middle])
right_sorted = mergeSort(list[middle:])
# ...


### Eliminate k

The variable k is unnecessary, as it will never reach len(list). You can delete it and all its uses.

### Style

The implementation doesn't follow recommended conventions of naming and formatting. I suggest to read and follow PEP8.

### The good

It's really great that you included unit tests, it made the review easier :-)