Example: Standard Matrix Multiplication in C++

// Standard Matrix Multiplication
#include <iostream>
#include <vector>

// Function to print a matrix
void printMatrix(const std::vector<std::vector<int>>& matrix) {
    for (const auto& row : matrix) {
        for (int val : row) {
            std::cout << val << " ";
        }
        std::cout << std::endl;
    }
}

// Function for standard matrix multiplication
std::vector<std::vector<int>> standardMultiply(
    const std::vector<std::vector<int>>& A,
    const std::vector<std::vector<int>>& B) {

    int rowsA = A.size();
    int colsA = A[0].size();
    int rowsB = B.size();
    int colsB = B[0].size();

    if (colsA != rowsB) {
        std::cerr << "Error: Matrices dimensions are not compatible for multiplication." << std::endl;
        return {}; // Return empty matrix
    }

    std::vector<std::vector<int>> C(rowsA, std::vector<int>(colsB, 0));

    // Step 1: Iterate through rows of matrix A
    for (int i = 0; i < rowsA; ++i) {
        // Step 2: Iterate through columns of matrix B
        for (int j = 0; j < colsB; ++j) {
            // Step 3: Iterate through columns of A (or rows of B)
            for (int k = 0; k < colsA; ++k) {
                C[i][j] += A[i][k] * B[k][j];
            }
        }
    }
    return C;
}

int main() {
    std::vector<std::vector<int>> A = {{1, 2}, {3, 4}};
    std::vector<std::vector<int>> B = {{5, 6}, {7, 8}};

    std::cout << "Matrix A:" << std::endl;
    printMatrix(A);
    std::cout << "\nMatrix B:" << std::endl;
    printMatrix(B);

    std::vector<std::vector<int>> C = standardMultiply(A, B);

    std::cout << "\nResult of Standard Multiplication (C = A * B):" << std::endl;
    printMatrix(C);

    return 0;
}