Create adaptive_merge_sort.py

sorts/adaptive_merge_sort.py

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+    def adaptive_merge_sort(sequence: list) -> list:
+    """
+    Sorts a list using the Adaptive Merge Sort algorithm.
+
+    >>> adaptive_merge_sort([4, 3, 1, 2])
+    Initial sequence: [4, 3, 1, 2]
+    Sorting: array[0:2] and array[2:4]
+    Sorting: array[0:1] and array[1:2]
+    Merging: array[0:1] and array[1:2]
+    After merge: [3, 4]
+    Sorting: array[2:3] and array[3:4]
+    Skipping merge as array[2] <= array[3]
+    Merging: array[0:2] and array[2:4]
+    After merge: [1, 2, 3, 4]
+    Sorted sequence: [1, 2, 3, 4]
+    [1, 2, 3, 4]
+    """
+    if len(sequence) < 2:
+        return sequence
+
+    aux = sequence[:]
+    print(f"Initial sequence: {sequence}")
+    adaptive_merge_sort_helper(sequence, aux, 0, len(sequence) - 1)
+    print(f"Sorted sequence: {sequence}")
+    return sequence
+
+
+def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> None:
+    """
+    Helper function for Adaptive Merge Sort algorithm.
+
+    >>> adaptive_merge_sort_helper([4, 3, 1, 2], [4, 3, 1, 2], 0, 3)
+    Sorting: array[0:2] and array[2:4]
+    Sorting: array[0:1] and array[1:2]
+    Merging: array[0:1] and array[1:2]
+    After merge: [3, 4]
+    Sorting: array[2:3] and array[3:4]
+    Skipping merge as array[2] <= array[3]
+    Merging: array[0:2] and array[2:4]
+    After merge: [1, 2, 3, 4]
+    """
+    if high <= low:
+        return
+
+    mid = (low + high) // 2
+    print(f"Sorting: array[{low}:{mid + 1}] and array[{mid + 1}:{high + 1}]")
+
+    adaptive_merge_sort_helper(aux, array, low, mid)
+    adaptive_merge_sort_helper(aux, array, mid + 1, high)
+
+    if array[mid] <= array[mid + 1]:
+        print(f"Skipping merge as 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) -> None:
+    """
+    Merges two sorted subarrays of the main array.
+
+    >>> merge([4, 3, 1, 2], [4, 3, 1, 2], 0, 1, 3)
+    Merging: array[0:2] and array[2:4]
+    After merge: [1, 2, 3, 4]
+    """
+    print(f"Merging: array[{low}:{mid + 1}] and array[{mid + 1}:{high + 1}]")
+
+    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[i] <= array[j]:  # Keep stable by using <=
+            aux[k] = array[i]
+            i += 1
+        else:
+            aux[k] = array[j]
+            j += 1
+
+    for k in range(low, high + 1):
+        array[k] = aux[k]
+
+    print(f"After merge: {array[low:high + 1]}")
+
+
+# Example usage
+if __name__ == "__main__":
+    print(adaptive_merge_sort([4, 3, 1, 2]))