使用python实现分治法中的矩阵乘法

以下是Python实现分治法中的矩阵乘法的示例代码：

def matrix_multiply(A, B):
    """
    分治法实现矩阵乘法
    :param A: 矩阵A
    :param B: 矩阵B
    :return: 矩阵C
    """
    n = len(A)
    C = [[0 for _ in range(n)] for _ in range(n)]
    if n == 1:
        C[0][0] = A[0][0] * B[0][0]
    else:
        A11, A12, A21, A22 = divide_matrix(A)
        B11, B12, B21, B22 = divide_matrix(B)
        C11 = add_matrix(matrix_multiply(A11, B11), matrix_multiply(A12, B21))
        C12 = add_matrix(matrix_multiply(A11, B12), matrix_multiply(A12, B22))
        C21 = add_matrix(matrix_multiply(A21, B11), matrix_multiply(A22, B21))
        C22 = add_matrix(matrix_multiply(A21, B12), matrix_multiply(A22, B22))
        C = merge_matrix(C11, C12, C21, C22)
    return C


def divide_matrix(A):
    """
    将矩阵A分成四个子矩阵
    :param A: 矩阵A
    :return: 四个子矩阵
    """
    n = len(A)
    m = n // 2
    A11 = [[A[i][j] for j in range(m)] for i in range(m)]
    A12 = [[A[i][j] for j in range(m, n)] for i in range(m)]
    A21 = [[A[i][j] for j in range(m)] for i in range(m, n)]
    A22 = [[A[i][j] for j in range(m, n)] for i in range(m, n)]
    return A11, A12, A21, A22


def add_matrix(A, B):
    """
    矩阵加法
    :param A: 矩阵A
    :param B: 矩阵B
    :return: 矩阵C
    """
    n = len(A)
    C = [[0 for _ in range(n)] for _ in range(n)]
    for i in range(n):
        for j in range(n):
            C[i][j] = A[i][j] + B[i][j]
    return C


def merge_matrix(A11, A12, A21, A22):
    """
    合并四个子矩阵
    :param A11: 子矩阵A11
    :param A12: 子矩阵A12
    :param A21: 子矩阵A21
    :param A22: 子矩阵A22
    :return: 矩阵A
    """
    n = len(A11)
    A = [[0 for _ in range(2 * n)] for _ in range(2 * n)]
    for i in range(n):
        for j in range(n):
            A[i][j] = A11[i][j]
            A[i][j + n] = A12[i][j]
            A[i + n][j] = A21[i][j]
            A[i + n][j + n] = A22[i][j]
    return A

在示例代码中，divide_matrix函数将矩阵A分成四个子矩阵，add_matrix函数实现矩阵加法，merge_matrix函数将四个子矩阵合并成一个矩阵。而matrix_multiply函数使用递归实现分治法的矩阵乘法，当矩阵大小为1时直接计算乘积，否则将矩阵A和矩阵B分成四个子矩阵，然后递归地计算子矩阵的乘积，并将四个子矩阵的乘积合并成一个矩阵返回。