adding a matrix equalization algorithm (#11360)

* adding a matrix equalization algorithm

* Adding url for more details

* Implementing suggestions

matrix/matrix_equalization.py

@@ -0,0 +1,55 @@
+from sys import maxsize
+
+
+def array_equalization(vector: list[int], step_size: int) -> int:
+    """
+    This algorithm equalizes all elements of the input vector
+    to a common value, by making the minimal number of
+    "updates" under the constraint of a step size (step_size).
+
+    >>> array_equalization([1, 1, 6, 2, 4, 6, 5, 1, 7, 2, 2, 1, 7, 2, 2], 4)
+    4
+    >>> array_equalization([22, 81, 88, 71, 22, 81, 632, 81, 81, 22, 92], 2)
+    5
+    >>> array_equalization([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 5)
+    0
+    >>> array_equalization([22, 22, 22, 33, 33, 33], 2)
+    2
+    >>> array_equalization([1, 2, 3], 0)
+    Traceback (most recent call last):
+    ValueError: Step size must be positive and non-zero.
+    >>> array_equalization([1, 2, 3], -1)
+    Traceback (most recent call last):
+    ValueError: Step size must be positive and non-zero.
+    >>> array_equalization([1, 2, 3], 0.5)
+    Traceback (most recent call last):
+    ValueError: Step size must be an integer.
+    >>> array_equalization([1, 2, 3], maxsize)
+    1
+    """
+    if step_size <= 0:
+        raise ValueError("Step size must be positive and non-zero.")
+    if not isinstance(step_size, int):
+        raise ValueError("Step size must be an integer.")
+
+    unique_elements = set(vector)
+    min_updates = maxsize
+
+    for element in unique_elements:
+        elem_index = 0
+        updates = 0
+        while elem_index < len(vector):
+            if vector[elem_index] != element:
+                updates += 1
+                elem_index += step_size
+            else:
+                elem_index += 1
+        min_updates = min(min_updates, updates)
+
+    return min_updates
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()