【HDU】2449 Gauss Elimination

题意：给出n个未知数的方程组，求未知数。不是正数的用分数表示。

赤裸裸的Java暴力，消元的时候用乘法相消，避免除法。

import java.util.*;
import java.math.*;

public class Main {
    public static BigInteger g[][] = new BigInteger[110][110];

    public static boolean Gauss(int n) {
        BigInteger tmp, a, b;
        int i, j, k;
        for (i = 0; i < n; i++) {
            for (j = i; j < n; j++) {
                if (g[j][i].compareTo(BigInteger.ZERO) != 0)
                    break;
            }
            if (j >= n)
                return false;
            if (j != i) {
                for (k = 0; k <= n; k++) {
                    tmp = g[i][k];
                    g[i][k] = g[j][k];
                    g[j][k] = tmp;
                }
            }
            a = g[i][i];
            for (j = i + 1; j < n; j++) {
                if (g[j][i].compareTo(BigInteger.ZERO) != 0) {
                    b = g[j][i];
                    for (k = i; k <= n; k++) {
                        g[j][k] = g[j][k].multiply(a).subtract(
                                g[i][k].multiply(b));
                    }
                }
            }
        }
        return true;
    }

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        BigInteger x[] = new BigInteger[110];
        BigInteger y[] = new BigInteger[110];
        BigInteger tmp, up, down;
        int n, i, j;
        boolean neg;
        while (in.hasNext()) {
            n = in.nextInt();
            for (i = 0; i < n; i++) {
                for (j = 0; j <= n; j++)
                    g[i][j] = in.nextBigInteger();
            }
            if (Gauss(n)) {
                for (i = n - 1; i >= 0; i--) {
                    up = BigInteger.ZERO;
                    down = BigInteger.ONE;
                    for (j = i + 1; j < n; j++) {
                        up = y[j].multiply(up).add(
                                g[i][j].multiply(x[j].multiply(down)));
                        down = y[j].multiply(down);
                    }
                    up = g[i][n].multiply(down).subtract(up);
                    down = g[i][i].multiply(down);
                    if (up.multiply(down).compareTo(BigInteger.ZERO) < 0)
                        neg = true;
                    else
                        neg = false;
                    up = up.abs();
                    down = down.abs();
                    tmp = up.gcd(down);
                    x[i] = up.divide(tmp);
                    y[i] = down.divide(tmp);
                    if (neg)
                        x[i] = x[i].negate();
                }
                for (i = 0; i < n; i++) {
                    if (x[i].mod(y[i]).compareTo(BigInteger.ZERO) == 0)
                        System.out.println(x[i].divide(y[i]));
                    else
                        System.out.println(x[i] + "/" + y[i]);
                }
            } else
                System.out.println("No solution.");
            System.out.println();
        }
    }
}