Example: Matrix Operations (Addition, Subtraction, Trace) in C++

// Matrix Operations (Addition, Subtraction, Trace)
#include <iostream>
#include <vector> // Using std::vector for dynamic matrices

using namespace std;

// Function to get matrix dimensions from user
void getMatrixDimensions(int& rows, int& cols) {
    cout << "Enter number of rows: ";
    cin >> rows;
    cout << "Enter number of columns: ";
    cin >> cols;
}

// Function to get matrix elements from user
void getMatrixInput(vector<vector<int>>& matrix, int rows, int cols, const string& name) {
    cout << "Enter elements for " << name << " (" << rows << "x" << cols << "):\n";
    matrix.resize(rows, vector<int>(cols)); // Resize vector to match dimensions
    for (int i = 0; i < rows; ++i) {
        for (int j = 0; j < cols; ++j) {
            cout << name << "[" << i << "][" << j << "]: ";
            cin >> matrix[i][j];
        }
    }
}

// Function to print a matrix
void printMatrix(const vector<vector<int>>& matrix, const string& name) {
    cout << "\n" << name << ":\n";
    for (int i = 0; i < matrix.size(); ++i) {
        for (int j = 0; j < matrix[0].size(); ++j) {
            cout << matrix[i][j] << "\t";
        }
        cout << "\n";
    }
}

// Function to add two matrices
vector<vector<int>> addMatrices(const vector<vector<int>>& mat1, const vector<vector<int>>& mat2, int rows, int cols) {
    vector<vector<int>> result(rows, vector<int>(cols));
    for (int i = 0; i < rows; ++i) {
        for (int j = 0; j < cols; ++j) {
            result[i][j] = mat1[i][j] + mat2[i][j];
        }
    }
    return result;
}

// Function to subtract two matrices
vector<vector<int>> subtractMatrices(const vector<vector<int>>& mat1, const vector<vector<int>>& mat2, int rows, int cols) {
    vector<vector<int>> result(rows, vector<int>(cols));
    for (int i = 0; i < rows; ++i) {
        for (int j = 0; j < cols; ++j) {
            result[i][j] = mat1[i][j] - mat2[i][j];
        }
    }
    return result;
}

// Function to calculate the trace of a matrix
int calculateTrace(const vector<vector<int>>& matrix, int rows) {
    int trace = 0;
    for (int i = 0; i < rows; ++i) {
        trace += matrix[i][i]; // Sum main diagonal elements
    }
    return trace;
}

int main() {
    // Step 1: Declare variables for matrix dimensions and matrices
    int rowsA, colsA;
    int rowsB, colsB;
    vector<vector<int>> matrixA;
    vector<vector<int>> matrixB;
    int choice;

    // Step 2: Get dimensions and elements for Matrix A
    cout << "--- Enter details for Matrix A ---\n";
    getMatrixDimensions(rowsA, colsA);
    getMatrixInput(matrixA, rowsA, colsA, "Matrix A");
    printMatrix(matrixA, "Matrix A");

    // Step 3: Get dimensions and elements for Matrix B
    cout << "\n--- Enter details for Matrix B ---\n";
    getMatrixDimensions(rowsB, colsB);
    getMatrixInput(matrixB, rowsB, colsB, "Matrix B");
    printMatrix(matrixB, "Matrix B");

    // Step 4: Display operation menu and get user choice
    cout << "\n--- Choose an operation ---\n";
    cout << "1. Add Matrices (A + B)\n";
    cout << "2. Subtract Matrices (A - B)\n";
    cout << "3. Calculate Trace of Matrix A\n";
    cout << "Enter your choice (1-3): ";
    cin >> choice;

    // Step 5: Perform the chosen operation based on user input
    switch (choice) {
        case 1: // Addition
            if (rowsA == rowsB && colsA == colsB) {
                vector<vector<int>> sumMatrix = addMatrices(matrixA, matrixB, rowsA, colsA);
                printMatrix(sumMatrix, "Sum (A + B)");
            } else {
                cout << "Error: Matrices must have the same dimensions for addition.\n";
            }
            break;
        case 2: // Subtraction
            if (rowsA == rowsB && colsA == colsB) {
                vector<vector<int>> diffMatrix = subtractMatrices(matrixA, matrixB, rowsA, colsA);
                printMatrix(diffMatrix, "Difference (A - B)");
            } else {
                cout << "Error: Matrices must have the same dimensions for subtraction.\n";
            }
            break;
        case 3: // Trace
            if (rowsA == colsA) {
                int traceA = calculateTrace(matrixA, rowsA);
                cout << "\nTrace of Matrix A: " << traceA << "\n";
            } else {
                cout << "Error: Matrix A must be a square matrix to calculate its trace.\n";
            }
            break;
        default:
            cout << "Invalid choice. Please enter a number between 1 and 3.\n";
            break;
    }

    return 0;
}