Create adaptive_merge_sort.py

sorts/adaptive_merge_sort.py

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+"""
+Adaptive Merge Sort Algorithm
+@see https://www.tutorialspoint.com/adaptive-merging-and-sorting-in-data-structure
+"""
+
+def adaptive_merge_sort(sequence: list) -> list:
+    """
+    Sorts a list using the Adaptive Merge Sort algorithm.
+
+    :param sequence: list of elements to be sorted
+    :return: sorted list
+
+    >>> adaptive_merge_sort([12, 11, 13, 5, 6, 7])
+    [5, 6, 7, 11, 12, 13]
+
+    >>> adaptive_merge_sort([5, 4, 3, 2, 1])
+    [1, 2, 3, 4, 5]
+
+    >>> adaptive_merge_sort(['zebra', 'apple', 'mango', 'banana'])
+    ['apple', 'banana', 'mango', 'zebra']
+    """
+    if len(sequence) < 2:
+        return sequence
+
+    aux = sequence[:]
+    adaptive_merge_sort_helper(sequence, aux, 0, len(sequence) - 1)
+    return sequence
+
+
+def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int):
+    if high <= low:
+        return
+
+    mid = (low + high) // 2
+
+    adaptive_merge_sort_helper(aux, array, low, mid)
+    adaptive_merge_sort_helper(aux, array, mid + 1, high)
+
+    if array[mid] <= array[mid + 1]:
+        array[low:high + 1] = aux[low:high + 1]
+        return
+
+    merge(array, aux, low, mid, high)
+
+
+def merge(array: list, aux: list, low: int, mid: int, high: int):
+    i, j = low, mid + 1
+
+    for k in range(low, high + 1):
+        if i > mid:
+            aux[k] = array[j]
+            j += 1
+        elif j > high:
+            aux[k] = array[i]
+            i += 1
+        elif array[j] < array[i]:
+            aux[k] = array[j]
+            j += 1
+        else:
+            aux[k] = array[i]
+            i += 1