请用c++实现strassen算法,并在主函数中调用此算法计算两个8阶方阵的乘积。代码

Strassen矩阵乘法是一种优化的分治算法，用于快速地计算两个大矩阵的乘积。以下是C++实现Strassen算法的一个基本版本，它计算两个8x8的矩阵。请注意，实际使用时需要处理边界条件并可能需要一些辅助函数来完成递归过程。

#include <iostream>
#include <vector>

// 辅助函数，用于拆分和组合矩阵
std::vector<std::vector<int>> split(const std::vector<std::vector<int>>& matrix, int n) {
    std::vector<std::vector<int>> result(n * n);
    for (int i = 0; i < n; ++i)
        for (int j = 0; j < n; ++j)
            result[i][j] = matrix[i / n][j / n];
    return result;
}

std::vector<std::vector<int>> combine(const std::vector<std::vector<int>>& a, const std::vector<std::vector<int>>& b, int n) {
    std::vector<std::vector<int>> result(n / 2, std::vector<int>(n / 2));
    for (int i = 0; i < n / 2; ++i)
        for (int j = 0; j < n / 2; ++j) {
            result[i][j] = a[i][j] + b[i][j];
            result[i][j + n / 2] = a[i][j + n / 2] + b[i][j + n / 2];
            result[i + n / 2][j] = a[i + n / 2][j] + b[i + n / 2][j];
            result[i + n / 2][j + n / 2] = a[i + n / 2][j + n / 2] - b[i][j];
        }
    return result;
}

// Strassen's Matrix Multiplication function
std::vector<std::vector<int>> strassen(std::vector<std::vector<int>>& a, std::vector<std::vector<int>>& b) {
    // Base case: when matrices are of size 1
    if (a.size() == 1)
        return a;

    int n = a.size();
    std::vector<std::vector<int>> mat[7]; // 创建存储中间结果的数组

    // Split matrices into submatrices
    mat[0] = split(a, n); // P1 = A[0..n/2, 0..n/2]
    mat[1] = split(b, n); // Q1 = B[0..n/2, 0..n/2]
    mat[2] = split(a, n); // P2 = A[0..n/2, n/2..n]
    mat[3] = split(b, n); // Q2 = B[0..n/2, n/2..n]
    mat[4] = split(a, n); // P3 = A[n/2..n, 0..n/2]
    mat[5] = split(b, n); // Q3 = B[n/2..n, 0..n/2]
    mat[6] = split(a, n); // P4 = A[n/2..n, n/2..n]

    // Perform recursive calls and compute intermediate results
    mat[1] = strassen(combine(mat[0], mat[4], n), combine(mat[2], mat[6], n)); // R1 = P1 + P3
    mat[2] = strassen(combine(mat[0], mat[5], n), n);          // R2 = P1 + P4
    mat[3] = strassen(mat[1], mat[3], n);                     // R3 = Q1 - R2
    mat[4] = strassen(mat[2], mat[4], n);                     // R4 = P2 - R1
    mat[5] = strassen(combine(mat[1], mat[3], n), n);          // R5 = Q1 + Q3
    mat[6] = strassen(combine(mat[4], mat[5], n), n);          // R6 = 2 * (P2 + P4)

    // Combine the results to get the final product
    return combine(combine(combine(mat[0], mat[2], n), mat[3], n), n), // C = (R1 + R3) * (Q2 + R6)
           combine(mat[1], mat[5], n),                            // D = (R2 - R4) * (Q1 + R5)
           n);
}

int main() {
    // 初始化两个8x8的示例矩阵
    std::vector<std::vector<int>> matrixA = {{...}, {...}, {...}, {...}}; // 填充矩阵值
    std::vector<std::vector<int>> matrixB = {{...}, {...}, {...}, {...}}; // 填充矩阵值

    // 调用Strassen算法计算乘积
    std::vector<std::vector<int>> result = strassen(matrixA, matrixB);

    // 打印结果矩阵
    for (const auto& row : result)
        for (const auto& elem : row)
            std::cout << elem << ' ';
        std::cout << '\n';