/**
 * \file
 * \brief [Gaussian elimination
 * method](https://en.wikipedia.org/wiki/Gaussian_elimination)
 */
package Maths;
import java.util.*;

/** Main function */
public class Gaussian {

  public static void main(String[] args) {
    int mat_size, i, j, step;
    Scanner sc = new Scanner(System.in);
    
    System.out.println("Matrix Size : ");
    mat_size = sc.nextInt();

    double [][] mat = new double[mat_size+1][mat_size+1];
    double [][] x = new double[mat_size][mat_size+1];

    System.out.println("Enter value of the matrix");
    System.out.println(' ');
    for (i = 0; i < mat_size; i++) {
        for (j = 0; j <= mat_size; j++) {
            mat[i][j] = sc.nextInt();
        }
    }

    // perform Gaussian elimination
    for (step = 0; step < mat_size - 1; step++) {
        for (i = step; i < mat_size - 1; i++) {
            double a = (mat[i + 1][step] / mat[step][step]);

            for (j = step; j <= mat_size; j++)
                mat[i + 1][j] = mat[i + 1][j] - (a * mat[step][j]);
        }
    }
    
    System.out.println("Matrix using Gaussian Elimination method: ");
    System.out.println(" ");
    for (i = 0; i < mat_size; i++) {
        for (j = 0; j <= mat_size; j++) {
            x[i][j] = mat[i][j];
            System.out.print(mat[i][j] + " ");
        }
        System.out.println();
    }
    System.out.println( "Value of the Gaussian Elimination method: ");
    System.out.println(" ");
    
    for (i = mat_size - 1; i >= 0; i--) {
        double sum = 0;
        for (j = mat_size - 1; j > i; j--) {
            x[i][j] = x[j][j] * x[i][j];
            sum = x[i][j] + sum;
        }
        if (x[i][i] == 0){
            x[i][i] = 0;
        }
        else{
            x[i][i] = (x[i][mat_size] - sum) / (x[i][i]);
        }
        System.out.print("x" + i + "=" + x[i][i]);
        System.out.println(" ");
    }
  }
}