Gauss.java

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Scanner;

public class Gauss {

    public static void swapRows(double[][] a, double[] b, int i, int j) {
        double[] row = a[i];
        a[i] = a[j];
        a[j] = row;

        double tmp = b[i];
        b[i] = b[j];
        b[j] = tmp;
    }

    // a[j] -= a[i] * multiplier;
    private static void subtractRow(double[][] a, double[] b, int i, int j, double multiplier) {
        for (int k = 0; k < a.length; k++) {
            a[j][k] -= a[i][k] * multiplier;
        }
        b[j] -= b[i] * multiplier;
    }

    public static double[] solveLinearSystem(double[][] a, double[] b) {
        // sanity check
        int n = a.length;
        for (double[] row : a) {
            if (a.length != n)
                throw new IllegalArgumentException();
        }
        if (b.length != n)
            throw new IllegalArgumentException();

        // Gaussian elimination
        for (int i = 0; i < n; i++) {
            int maxRow = i;
            for (int j = i + 1; j < n; j++) {
                if (Math.abs(a[j][i]) > Math.abs(a[maxRow][i]))
                    maxRow = j;
            }

            swapRows(a, b, i, maxRow);

            for (int j = i + 1; j < n; j++) {
                subtractRow(a, b, i, j, a[j][i] / a[i][i]);
            }
        }

        for (int i = n - 1; i > 0; i--) {
            for (int j = i - 1; j >= 0; j--) {
                subtractRow(a, b, i, j, a[j][i] / a[i][i]);
            }
        }

        // constructing result
        double[] result = new double[n];
        for (int i = 0; i < n; i++) {
            result[i] = b[i] / a[i][i];
        }

        return result;
    }

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = sc.nextInt();
        double[][] a = new double[n][n];
        double[] b = new double[n];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                a[i][j] = sc.nextDouble();
            }

            b[i] = sc.nextDouble();
        }

        double[] result = solveLinearSystem(a, b);
        for (int i = 0; i < result.length; i++) {
            if (i > 0)
                out.print(' ');
            out.print(result[i]);
        }
        out.println();

        out.close();
    }

}