Correct ruff failures (#8732)

* fix: Correct ruff problems

* updating DIRECTORY.md

* fix: Fix pre-commit errors

* updating DIRECTORY.md

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Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

divide_and_conquer/strassen_matrix_multiplication.py.BROKEN

@@ -0,0 +1,170 @@
+from __future__ import annotations
+
+import math
+
+
+def default_matrix_multiplication(a: list, b: list) -> list:
+    """
+    Multiplication only for 2x2 matrices
+    """
+    if len(a) != 2 or len(a[0]) != 2 or len(b) != 2 or len(b[0]) != 2:
+        raise Exception("Matrices are not 2x2")
+    new_matrix = [
+        [a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1]],
+        [a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]],
+    ]
+    return new_matrix
+
+
+def matrix_addition(matrix_a: list, matrix_b: list):
+    return [
+        [matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row]))]
+        for row in range(len(matrix_a))
+    ]
+
+
+def matrix_subtraction(matrix_a: list, matrix_b: list):
+    return [
+        [matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row]))]
+        for row in range(len(matrix_a))
+    ]
+
+
+def split_matrix(a: list) -> tuple[list, list, list, list]:
+    """
+    Given an even length matrix, returns the top_left, top_right, bot_left, bot_right
+    quadrant.
+
+    >>> split_matrix([[4,3,2,4],[2,3,1,1],[6,5,4,3],[8,4,1,6]])
+    ([[4, 3], [2, 3]], [[2, 4], [1, 1]], [[6, 5], [8, 4]], [[4, 3], [1, 6]])
+    >>> split_matrix([
+    ...     [4,3,2,4,4,3,2,4],[2,3,1,1,2,3,1,1],[6,5,4,3,6,5,4,3],[8,4,1,6,8,4,1,6],
+    ...     [4,3,2,4,4,3,2,4],[2,3,1,1,2,3,1,1],[6,5,4,3,6,5,4,3],[8,4,1,6,8,4,1,6]
+    ... ])  # doctest: +NORMALIZE_WHITESPACE
+    ([[4, 3, 2, 4], [2, 3, 1, 1], [6, 5, 4, 3], [8, 4, 1, 6]], [[4, 3, 2, 4],
+      [2, 3, 1, 1], [6, 5, 4, 3], [8, 4, 1, 6]], [[4, 3, 2, 4], [2, 3, 1, 1],
+      [6, 5, 4, 3], [8, 4, 1, 6]], [[4, 3, 2, 4], [2, 3, 1, 1], [6, 5, 4, 3],
+      [8, 4, 1, 6]])
+    """
+    if len(a) % 2 != 0 or len(a[0]) % 2 != 0:
+        raise Exception("Odd matrices are not supported!")
+
+    matrix_length = len(a)
+    mid = matrix_length // 2
+
+    top_right = [[a[i][j] for j in range(mid, matrix_length)] for i in range(mid)]
+    bot_right = [
+        [a[i][j] for j in range(mid, matrix_length)] for i in range(mid, matrix_length)
+    ]
+
+    top_left = [[a[i][j] for j in range(mid)] for i in range(mid)]
+    bot_left = [[a[i][j] for j in range(mid)] for i in range(mid, matrix_length)]
+
+    return top_left, top_right, bot_left, bot_right
+
+
+def matrix_dimensions(matrix: list) -> tuple[int, int]:
+    return len(matrix), len(matrix[0])
+
+
+def print_matrix(matrix: list) -> None:
+    print("\n".join(str(line) for line in matrix))
+
+
+def actual_strassen(matrix_a: list, matrix_b: list) -> list:
+    """
+    Recursive function to calculate the product of two matrices, using the Strassen
+    Algorithm.  It only supports even length matrices.
+    """
+    if matrix_dimensions(matrix_a) == (2, 2):
+        return default_matrix_multiplication(matrix_a, matrix_b)
+
+    a, b, c, d = split_matrix(matrix_a)
+    e, f, g, h = split_matrix(matrix_b)
+
+    t1 = actual_strassen(a, matrix_subtraction(f, h))
+    t2 = actual_strassen(matrix_addition(a, b), h)
+    t3 = actual_strassen(matrix_addition(c, d), e)
+    t4 = actual_strassen(d, matrix_subtraction(g, e))
+    t5 = actual_strassen(matrix_addition(a, d), matrix_addition(e, h))
+    t6 = actual_strassen(matrix_subtraction(b, d), matrix_addition(g, h))
+    t7 = actual_strassen(matrix_subtraction(a, c), matrix_addition(e, f))
+
+    top_left = matrix_addition(matrix_subtraction(matrix_addition(t5, t4), t2), t6)
+    top_right = matrix_addition(t1, t2)
+    bot_left = matrix_addition(t3, t4)
+    bot_right = matrix_subtraction(matrix_subtraction(matrix_addition(t1, t5), t3), t7)
+
+    # construct the new matrix from our 4 quadrants
+    new_matrix = []
+    for i in range(len(top_right)):
+        new_matrix.append(top_left[i] + top_right[i])
+    for i in range(len(bot_right)):
+        new_matrix.append(bot_left[i] + bot_right[i])
+    return new_matrix
+
+
+def strassen(matrix1: list, matrix2: list) -> list:
+    """
+    >>> strassen([[2,1,3],[3,4,6],[1,4,2],[7,6,7]], [[4,2,3,4],[2,1,1,1],[8,6,4,2]])
+    [[34, 23, 19, 15], [68, 46, 37, 28], [28, 18, 15, 12], [96, 62, 55, 48]]
+    >>> strassen([[3,7,5,6,9],[1,5,3,7,8],[1,4,4,5,7]], [[2,4],[5,2],[1,7],[5,5],[7,8]])
+    [[139, 163], [121, 134], [100, 121]]
+    """
+    if matrix_dimensions(matrix1)[1] != matrix_dimensions(matrix2)[0]:
+        raise Exception(
+            "Unable to multiply these matrices, please check the dimensions. \n"
+            f"Matrix A:{matrix1} \nMatrix B:{matrix2}"
+        )
+    dimension1 = matrix_dimensions(matrix1)
+    dimension2 = matrix_dimensions(matrix2)
+
+    if dimension1[0] == dimension1[1] and dimension2[0] == dimension2[1]:
+        return [matrix1, matrix2]
+
+    maximum = max(dimension1, dimension2)
+    maxim = int(math.pow(2, math.ceil(math.log2(maximum))))
+    new_matrix1 = matrix1
+    new_matrix2 = matrix2
+
+    # Adding zeros to the matrices so that the arrays dimensions are the same and also
+    # power of 2
+    for i in range(0, maxim):
+        if i < dimension1[0]:
+            for _ in range(dimension1[1], maxim):
+                new_matrix1[i].append(0)
+        else:
+            new_matrix1.append([0] * maxim)
+        if i < dimension2[0]:
+            for _ in range(dimension2[1], maxim):
+                new_matrix2[i].append(0)
+        else:
+            new_matrix2.append([0] * maxim)
+
+    final_matrix = actual_strassen(new_matrix1, new_matrix2)
+
+    # Removing the additional zeros
+    for i in range(0, maxim):
+        if i < dimension1[0]:
+            for _ in range(dimension2[1], maxim):
+                final_matrix[i].pop()
+        else:
+            final_matrix.pop()
+    return final_matrix
+
+
+if __name__ == "__main__":
+    matrix1 = [
+        [2, 3, 4, 5],
+        [6, 4, 3, 1],
+        [2, 3, 6, 7],
+        [3, 1, 2, 4],
+        [2, 3, 4, 5],
+        [6, 4, 3, 1],
+        [2, 3, 6, 7],
+        [3, 1, 2, 4],
+        [2, 3, 4, 5],
+        [6, 2, 3, 1],
+    ]
+    matrix2 = [[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
+    print(strassen(matrix1, matrix2))