Example: Matrix Multiplication in C++

// Matrix Multiplication
#include <iostream> // For input/output operations
#include <vector>   // For using std::vector to represent matrices

// Function to get matrix dimensions and elements from the user
void getMatrixInput(int& rows, int& cols, std::vector<std::vector<int>>& matrix) {
    std::cout << "Enter number of rows: ";
    std::cin >> rows;
    std::cout << "Enter number of columns: ";
    std::cin >> cols;

    matrix.resize(rows, std::vector<int>(cols)); // Resize matrix to given dimensions

    std::cout << "Enter matrix elements (" << rows << "x" << cols << "):\n";
    for (int i = 0; i < rows; ++i) {
        for (int j = 0; j < cols; ++j) {
            std::cout << "Enter element [" << i << "][" << j << "]: ";
            std::cin >> matrix[i][j];
        }
    }
}

// Function to display a matrix
void displayMatrix(const std::vector<std::vector<int>>& matrix) {
    for (const auto& row : matrix) {
        for (int element : row) {
            std::cout << element << "\t";
        }
        std::cout << "\n";
    }
}

int main() {
    // Step 1: Declare variables for matrix dimensions and the matrices themselves
    int rows1, cols1, rows2, cols2;
    std::vector<std::vector<int>> matrix1;
    std::vector<std::vector<int>> matrix2;
    std::vector<std::vector<int>> resultMatrix;

    // Step 2: Get input for the first matrix
    std::cout << "--- Enter details for Matrix 1 ---\n";
    getMatrixInput(rows1, cols1, matrix1);

    // Step 3: Get input for the second matrix
    std::cout << "\n--- Enter details for Matrix 2 ---\n";
    getMatrixInput(rows2, cols2, matrix2);

    // Step 4: Check for matrix compatibility
    // For multiplication, columns of matrix1 must equal rows of matrix2
    if (cols1 != rows2) {
        std::cout << "\nError: Matrices are not compatible for multiplication.\n";
        std::cout << "Number of columns in Matrix 1 (" << cols1 << ") must be equal to number of rows in Matrix 2 (" << rows2 << ").\n";
        return 1; // Indicate an error
    }

    // Step 5: Initialize the result matrix dimensions
    // The result matrix will have rows1 rows and cols2 columns
    resultMatrix.resize(rows1, std::vector<int>(cols2, 0)); // Initialize all elements to 0

    // Step 6: Perform matrix multiplication
    // The core logic for matrix multiplication uses three nested loops
    for (int i = 0; i < rows1; ++i) { // Iterate through rows of matrix1
        for (int j = 0; j < cols2; ++j) { // Iterate through columns of matrix2
            for (int k = 0; k < cols1; ++k) { // Iterate through columns of matrix1 (or rows of matrix2)
                resultMatrix[i][j] += matrix1[i][k] * matrix2[k][j];
            }
        }
    }

    // Step 7: Display the input matrices
    std::cout << "\n--- Matrix 1 ---\n";
    displayMatrix(matrix1);
    std::cout << "\n--- Matrix 2 ---\n";
    displayMatrix(matrix2);

    // Step 8: Display the result matrix
    std::cout << "\n--- Product Matrix ---\n";
    displayMatrix(resultMatrix);

    return 0; // Indicate successful execution
}