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。
1 import java.util.*; 2 import java.math.*; 3 4 public class Main { 5 public static BigInteger g[][] = new BigInteger[110][110]; 6 7 public static boolean Gauss(int n) { 8 BigInteger tmp, a, b; 9 int i, j, k; 10 for (i = 0; i < n; i++) { 11 for (j = i; j < n; j++) { 12 if (g[j][i].compareTo(BigInteger.ZERO) != 0) 13 break; 14 } 15 if (j >= n) 16 return false; 17 if (j != i) { 18 for (k = 0; k <= n; k++) { 19 tmp = g[i][k]; 20 g[i][k] = g[j][k]; 21 g[j][k] = tmp; 22 } 23 } 24 a = g[i][i]; 25 for (j = i + 1; j < n; j++) { 26 if (g[j][i].compareTo(BigInteger.ZERO) != 0) { 27 b = g[j][i]; 28 for (k = i; k <= n; k++) { 29 g[j][k] = g[j][k].multiply(a).subtract( 30 g[i][k].multiply(b)); 31 } 32 } 33 } 34 } 35 return true; 36 } 37 38 public static void main(String[] args) { 39 Scanner in = new Scanner(System.in); 40 BigInteger x[] = new BigInteger[110]; 41 BigInteger y[] = new BigInteger[110]; 42 BigInteger tmp, up, down; 43 int n, i, j; 44 boolean neg; 45 while (in.hasNext()) { 46 n = in.nextInt(); 47 for (i = 0; i < n; i++) { 48 for (j = 0; j <= n; j++) 49 g[i][j] = in.nextBigInteger(); 50 } 51 if (Gauss(n)) { 52 for (i = n - 1; i >= 0; i--) { 53 up = BigInteger.ZERO; 54 down = BigInteger.ONE; 55 for (j = i + 1; j < n; j++) { 56 up = y[j].multiply(up).add( 57 g[i][j].multiply(x[j].multiply(down))); 58 down = y[j].multiply(down); 59 } 60 up = g[i][n].multiply(down).subtract(up); 61 down = g[i][i].multiply(down); 62 if (up.multiply(down).compareTo(BigInteger.ZERO) < 0) 63 neg = true; 64 else 65 neg = false; 66 up = up.abs(); 67 down = down.abs(); 68 tmp = up.gcd(down); 69 x[i] = up.divide(tmp); 70 y[i] = down.divide(tmp); 71 if (neg) 72 x[i] = x[i].negate(); 73 } 74 for (i = 0; i < n; i++) { 75 if (x[i].mod(y[i]).compareTo(BigInteger.ZERO) == 0) 76 System.out.println(x[i].divide(y[i])); 77 else 78 System.out.println(x[i] + "/" + y[i]); 79 } 80 } else 81 System.out.println("No solution."); 82 System.out.println(); 83 } 84 } 85 }
