There are numerous implementations of merge sort I've seen, however, I'm trying to write one which translates literally from the algorithmic definition of merge sort:

• Split the arrays till you've 1 element left
• Merge them together.

However I'm a little stuck. This is my code till now,

class MergeSort:
    def __init__(self):
        bucket = []

    def _sort(self, arr):
        if len(arr) == 1:
            pass

        mid = len(arr) //2
        self._sort(arr[:mid])
        self._sort(arr[mid:])

    def _merge(self, arr1, arr2, arr):
        i, j = 0, 0
        while i < len(arr1) and j < len(arr2):
            if arr1[i] < arr2[j]:
                arr.append(arr1[i])
                i += 1
            else:
                arr.append(arr2[j])
                j += 1

The code will be called in this manner.

merge_sort = MergeSort()
merge_sort._sort([1,9,3,2,5])

Can someone help me stitch these two methods together to get the merge sort someway. Just to reiterate I'm not looking at a new approach. Thanks.