Row_reduced_echelon

#include <iostream>
#include <vector>

using namespace std;

void printMatrix(const vector<vector<int>>& matrix) {
    int p = matrix.size();
    int q = matrix[0].size();
    for (int i = 0; i < p; ++i) {
        for (int j = 0; j < q; ++j) {
            cout << matrix[i][j] << " ";
        }
        cout << endl;
    }
}


void rowReform(vector<vector<int>>& matrix) {
    int p = matrix.size();
    int q = matrix[0].size();
    
    int lead = 0;  

    for (int i = 0; i < p; ++i) {
        if (lead >= q) return;

        int row = i;
        while (matrix[row][lead] == 0) {
            row++;
            if (row == p) {
                row = i;
                lead++;
                if (lead >= q) return;
            }
        }

    
        if (row != i) {
            swap(matrix[row], matrix[i]);
        }

    
        int leadElement = matrix[i][lead];
        for (int j = 0; j < q; ++j) {
            matrix[i][j] /= leadElement;
        }
        for (int k = 0; k < p; ++k) {
            if (k != i) {
                int factor = matrix[k][lead];
                for (int j = 0; j < q; ++j) {
                    matrix[k][j] -= factor * matrix[i][j];
                }
            }
        }

        lead++;
    }
}

int main() {
    int p, q;
    cout << "Enter number of rows and columns: ";
    cin >> p >> q;

    vector<vector<int>> matrix(p, vector<int>(q));

    cout << "Enter matrix elements:" << endl;
    for (int i = 0; i < p; ++i) {
        for (int j = 0; j < q; ++j) {
            cin >> matrix[i][j];
        }
    }

    cout << "Original Matrix:" << endl;
    printMatrix(matrix);

    rowReform(matrix);

    cout << "Matrix after row reduction:" << endl;
    printMatrix(matrix);

    return 0;
}