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。

Strassen矩阵乘法是一种分治策略的应用，用于提高矩阵乘法的效率，它将大矩阵分解成小块并递归地进行计算。以下是C++实现Strassen算法的一个简化版示例，主要用于理解基本思路，实际应用中需要处理边界条件、数组大小等问题：

#include <iostream>
#include <vector>

// Strassen's Submatrix Calculation
std::vector<std::vector<int>> subMatrixMultiply(std::vector<std::vector<int>>& A, std::vector<std::vector<int>>& B, int m, int n, int p) {
    if (p <= 1) return {{A[m * p + n] * B[0][0], A[m * p + n] * B[0][1]}, {A[m * p + n + 1] * B[1][0], A[m * p + n + 1] * B[1][1]}};

    // Divide matrices into four quadrants
    std::vector<std::vector<int>> P1 = subMatrixMultiply(A, B, m, n / 2, p / 2);
    std::vector<std::vector<int>> P2 = subMatrixMultiply(A, B, m, n / 2, p / 2) + P1;
    std::vector<std::vector<int>> P3 = subMatrixMultiply(A, B + m / 2, m / 2, n, p / 2);
    std::vector<std::vector<int>> P4 = subMatrixMultiply(A + m / 2, B, m / 2, n, p / 2);
    std::vector<std::vector<int>> P5 = subMatrixMultiply(P1, P2 - P4, p / 2, n / 2, p / 2);
    std::vector<std::vector<int>> P6 = subMatrixMultiply(P3 + P4, P2, m / 2, n / 2, p / 2);
    std::vector<std::vector<int>> P7 = subMatrixMultiply(P3, P1 - P2, m / 2, n / 2, p / 2);

    // Construct result matrix
    std::vector<std::vector<int>> C(2 * p, std::vector<int>(2 * p));
    C[0][0] = P5[0][0] + P6[0][0] - P2[0][0] + P7[0][0];
    C[0][1] = P5[0][1] + P2[0][1];
    C[1][0] = P4[1][0] + P7[0][0];
    C[1][1] = P1[1][1] + P6[0][1] - P5[1][1] - P3[1][1];

    return C;
}

// Main function to calculate the product of two matrices using Strassen's algorithm
void strassenMultiplication(int m, int n, std::vector<std::vector<int>>& A, std::vector<std::vector<int>>& B) {
    if (m <= 1 || n <= 1) return; // Base case: single element or identity matrix

    // Divide matrices into quarters
    int p = std::max(m, n) / 2;
    std::vector<std::vector<int>> A1, A2, B1, B2;
    for (int i = 0; i < p; ++i)
        for (int j = 0; j < p; ++j) {
            A1.push_back({A[i * 2][j * 2], A[i * 2][j * 2 + 1]});
            A2.push_back({A[i * 2 + 1][j * 2], A[i * 2 + 1][j * 2 + 1]});
            B1.push_back({B[i * 2][j * 2], B[i * 2][j * 2 + 1]});
            B2.push_back({B[i * 2 + 1][j * 2], B[i * 2 + 1][j * 2 + 1]});
        }

    // Recursive calls and combining results
    std::vector<std::vector<int>> C1 = subMatrixMultiply(A1, B1, p, p, p);
    std::vector<std::vector<int>> C2 = subMatrixMultiply(A2, B2, p, p, p);
    std::vector<std::vector<int>> C3 = subMatrixMultiply(A1, B2, p, p, p);
    std::vector<std::vector<int>> C4 = subMatrixMultiply(A2, B1, p, p, p);

    std::vector<std::vector<int>> D1 = subMatrixMultiply(C1, C2, m, n, p);
    std::vector<std::vector<int>> D2 = subMatrixMultiply(C3, C4, m, n, p);
    std::vector<std::vector<int>> D3 = subMatrixMultiply(C2, C4, m, n, p);
    std::vector<std::vector<int>> D4 = subMatrixMultiply(C1, C3, m, n, p);

    for (int i = 0; i < p; ++i)
        for (int j = 0; j < p; ++j) {
            A[i * 2][j * 2] = D1[i][j];
            A[i * 2][j * 2 + 1] = D2[i][j];
            A[i * 2 + 1][j * 2] = D4[i][j];
            A[i * 2 + 1][j * 2 + 1] = D3[i][j] - D2[i][j] - D4[i][j] + D1[i][j];
        }
}

// Example usage in main function
int main() {
    const int N = 8;
    std::vector<std::vector<int>> A(N, std::vector<int>(N)), B(N, std::vector<int>(N)); // Initialize your matrices here
    strassenMultiplication(N, N, A, B); // Call the function with input matrices

    // Print the resulting matrix
    for (const auto& row : A) {
        for (const auto& elem : row)
            std::cout << elem << " ";
        std::cout << "\n";
    }