使用python实现分治法中的矩阵乘法

以下是使用Python实现分治法中的矩阵乘法的代码：

def matrix_multiply(A, B):
    n = len(A)
    C = [[0 for j in range(n)] for i in range(n)]
    if n == 1:
        C[0][0] = A[0][0] * B[0][0]
    else:
        # 分割矩阵
        A11, A12, A21, A22 = sub_matrix(A)
        B11, B12, B21, B22 = sub_matrix(B)
        # 递归计算
        C11 = matrix_add(matrix_multiply(A11, B11), matrix_multiply(A12, B21))
        C12 = matrix_add(matrix_multiply(A11, B12), matrix_multiply(A12, B22))
        C21 = matrix_add(matrix_multiply(A21, B11), matrix_multiply(A22, B21))
        C22 = matrix_add(matrix_multiply(A21, B12), matrix_multiply(A22, B22))
        # 合并子矩阵
        merge_matrix(C, C11, C12, C21, C22)
    return C

def sub_matrix(A):
    n = len(A)
    m = n//2
    A11 = [[0 for j in range(m)] for i in range(m)]
    A12 = [[0 for j in range(m)] for i in range(m)]
    A21 = [[0 for j in range(m)] for i in range(m)]
    A22 = [[0 for j in range(m)] for i in range(m)]
    for i in range(m):
        for j in range(m):
            A11[i][j] = A[i][j]
            A12[i][j] = A[i][j+m]
            A21[i][j] = A[i+m][j]
            A22[i][j] = A[i+m][j+m]
    return A11, A12, A21, A22

def matrix_add(A, B):
    n = len(A)
    C = [[0 for j in range(n)] for i 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(C, C11, C12, C21, C22):
    n = len(C)
    m = n//2
    for i in range(m):
        for j in range(m):
            C[i][j] = C11[i][j]
            C[i][j+m] = C12[i][j]
            C[i+m][j] = C21[i][j]
            C[i+m][j+m] = C22[i][j]

在上面的代码中，我们定义了四个函数：`matrix_multiply`、`sub_matrix`、`matrix_add`和`merge_matrix`。

`sub_matrix`函数用于将一个矩阵分成四个子矩阵，即A11、A12、A21和A22。

`matrix_add`函数用于将两个矩阵相加。

`merge_matrix`函数用于将四个子矩阵合并成一个矩阵。

`matrix_multiply`函数是我们的主函数，它用于计算两个矩阵的乘积。如果矩阵的大小为1x1，则直接计算乘积。否则，我们将矩阵分成四个子矩阵，并递归地计算它们的乘积。最后，我们将四个子矩阵的乘积合并成一个矩阵。

下面是一个示例，演示如何使用上面的代码计算两个矩阵的乘积：

A = [[1, 2], [3, 4]]
B = [[5, 6], [7, 8]]
C = matrix_multiply(A, B)
print(C)

输出结果为：

[[19, 22], [43, 50]]

这个结果与直接计算AB的结果相同。