added rotate_array.py (#13336)

* added rotate_array.py

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* fixed issues

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* fixed reverse issue

* added doctests

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* changed k to steps for a descriptive name

* fixed non-pep

---------

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data_structures/arrays/rotate_array.py

@@ -0,0 +1,80 @@
+def rotate_array(arr: list[int], steps: int) -> list[int]:
+    """
+    Rotates a list to the right by steps positions.
+
+    Parameters:
+    arr (List[int]): The list of integers to rotate.
+    steps (int): Number of positions to rotate. Can be negative for left rotation.
+
+    Returns:
+    List[int]: Rotated list.
+
+    Examples:
+    >>> rotate_array([1, 2, 3, 4, 5], 2)
+    [4, 5, 1, 2, 3]
+    >>> rotate_array([1, 2, 3, 4, 5], -2)
+    [3, 4, 5, 1, 2]
+    >>> rotate_array([1, 2, 3, 4, 5], 7)
+    [4, 5, 1, 2, 3]
+    >>> rotate_array([], 3)
+    []
+    """
+
+    n = len(arr)
+    if n == 0:
+        return arr
+
+    steps = steps % n
+
+    if steps < 0:
+        steps += n
+
+    def reverse(start: int, end: int) -> None:
+        """
+        Reverses a portion of the list in place from index start to end.
+
+        Parameters:
+        start (int): Starting index of the portion to reverse.
+        end (int): Ending index of the portion to reverse.
+
+        Returns:
+        None
+
+        Examples:
+        >>> example = [1, 2, 3, 4, 5]
+        >>> def reverse_test(arr, start, end):
+        ...     while start < end:
+        ...         arr[start], arr[end] = arr[end], arr[start]
+        ...         start += 1
+        ...         end -= 1
+        >>> reverse_test(example, 0, 2)
+        >>> example
+        [3, 2, 1, 4, 5]
+        >>> reverse_test(example, 2, 4)
+        >>> example
+        [3, 2, 5, 4, 1]
+        """
+
+        while start < end:
+            arr[start], arr[end] = arr[end], arr[start]
+            start += 1
+            end -= 1
+
+    reverse(0, n - 1)
+    reverse(0, steps - 1)
+    reverse(steps, n - 1)
+
+    return arr
+
+
+if __name__ == "__main__":
+    examples = [
+        ([1, 2, 3, 4, 5], 2),
+        ([1, 2, 3, 4, 5], -2),
+        ([1, 2, 3, 4, 5], 7),
+        ([], 3),
+    ]
+
+    for arr, steps in examples:
+        rotated = rotate_array(arr.copy(), steps)
+        print(f"Rotate {arr} by {steps}: {rotated}")