Iterative merge sort implementation

sorts/iterative_merge_sort.py

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+"""
+This is pure implementation of iterative merge sort in python
+Author: Aman Gupta
+
+For doctests run following command:
+python -m doctest -v shell_sort.py
+or
+python3 -m doctest -v shell_sort.py
+
+For manual testing run:
+python shell_sort.py
+"""
+
+from typing import List
+
+
+def merge(low: int, mid: int, high: int, inputlist: List) -> List:
+    """
+    sorting left-half and right-half individually
+    then merging them into result
+    """
+    result = []
+    left, right = inputlist[low:mid], inputlist[mid : high + 1]
+    while left and right:
+        result.append((left if left[0] <= right[0] else right).pop(0))
+    inputlist[low : high + 1] = result + left + right
+    return inputlist
+
+
+# iteration over the unsorted list
+def iter_merge_sort(inputlist: List) -> List:
+    """
+    Returns sorted list of the input numbers list
+
+    Examples
+
+    >>> iter_merge_sort([5,9,8,1,2,7])
+    [1, 2, 5, 7, 8, 9]
+
+    >>> iter_merge_sort([6])
+    [6]
+
+    >>> iter_merge_sort([-2,-9,-1,-4])
+    [-9, -4, -2, -1]
+
+    """
+
+    if len(inputlist) <= 1:
+        return inputlist
+
+    # iteration for two-way merging
+    p = 2
+    while p < len(inputlist):
+        # getting low, high and middle value for merge-sort of single list
+        for i in range(0, len(inputlist), p):
+            low = i
+            high = i + p - 1
+            mid = (low + high + 1) // 2
+            inputlist = merge(low, mid, high, inputlist)
+        # final merge of last two parts
+        if p * 2 >= len(inputlist):
+            mid = i
+            inputlist = merge(0, mid, len(inputlist) - 1, inputlist)
+
+        p *= 2
+
+    return inputlist
+
+
+if __name__ == "__main__":
+    user_input = input("Enter numbers separated by a comma:\n").strip()
+    unsorted = [int(item) for item in user_input.split(",")]
+    print(*iter_merge_sort(unsorted), sep=",")