Iterative merge sort implementation

sorts/iterative_merge_sort.py

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+"""
+Implementation of iterative merge sort in Python
+Author: Aman Gupta
+
+For doctests run following command:
+python3 -m doctest -v iterative_merge_sort.py
+
+For manual testing run:
+python3 iterative_merge_sort.py
+"""
+
+from typing import List
+
+
+def merge(input_list: List, low: int, mid: int, high: int) -> List:
+    """
+    sorting left-half and right-half individually
+    then merging them into result
+    """
+    result = []
+    left, right = input_list[low:mid], input_list[mid : high + 1]
+    while left and right:
+        result.append((left if left[0] <= right[0] else right).pop(0))
+    input_list[low : high + 1] = result + left + right
+    return input_list
+
+
+# iteration over the unsorted list
+def iter_merge_sort(input_list: List) -> List:
+    """
+    Return a sorted copy of the input list
+
+    >>> iter_merge_sort([5, 9, 8, 7, 1, 2, 7])
+    [1, 2, 5, 7, 7, 8, 9]
+    >>> iter_merge_sort([6])
+    [6]
+    >>> iter_merge_sort([])
+    []
+    >>> iter_merge_sort([-2, -9, -1, -4])
+    [-9, -4, -2, -1]
+    >>> iter_merge_sort([1.1, 1, 0.0, -1, -1.1])
+    [-1.1, -1, 0.0, 1, 1.1]
+    >>> iter_merge_sort(['c', 'b', 'a'])
+    ['a', 'b', 'c']
+    >>> iter_merge_sort('cba')
+    ['a', 'b', 'c']
+    """
+    if len(input_list) <= 1:
+        return input_list
+    input_list = list(input_list)
+
+    # iteration for two-way merging
+    p = 2
+    while p < len(input_list):
+        # getting low, high and middle value for merge-sort of single list
+        for i in range(0, len(input_list), p):
+            low = i
+            high = i + p - 1
+            mid = (low + high + 1) // 2
+            input_list = merge(input_list, low, mid, high)
+        # final merge of last two parts
+        if p * 2 >= len(input_list):
+            mid = i
+            input_list = merge(input_list, 0, mid, len(input_list) - 1)
+        p *= 2
+
+    return input_list
+
+
+if __name__ == "__main__":
+    user_input = input("Enter numbers separated by a comma:\n").strip()
+    unsorted = [int(item.strip()) for item in user_input.split(",")]
+    print(iter_merge_sort(unsorted))