六角幻方

把 1 2 3 ... 19 共19个整数排列成六角形状，如下：    * * *   * * * *  * * * * *   * * * *     * * *    要求每个直线上的数字之和必须相等。共有15条直线哦！    再给点线索吧！我们预先填好了2个数字，第一行的头两个数字是：15 13，参见图【p1.png】，黄色一行为所求。    请你填写出中间一行的5个数字。数字间用空格分开。    这是一行用空格分开的整数，请通过浏览器提交答案，不要填写任何多余的内容（比如说明性的文字等）

<img src="http://img.blog.csdn.net/20150315202424193?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvU3Ryb25nTWFuVHdv/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/Center" alt="" />public class A {int[][] am = new int[15][19];int[] bm = new int[15];int[] col = new int[19];int[][] line = { { 0, 1, 2 }, { 3, 4, 5, 6 }, { 7, 8, 9, 10, 11 },{ 12, 13, 14, 15 }, { 16, 17, 18 }, { 0, 3, 7 }, { 1, 4, 8, 12 },{ 2, 5, 9, 13, 16 }, { 6, 10, 14, 17 }, { 11, 15, 18 },{ 2, 6, 11 }, { 1, 5, 10, 15 }, { 0, 4, 9, 14, 18 },{ 3, 8, 13, 17 }, { 7, 12, 16 } };void init() {for (int i = 0; i < line.length; i++) {for (int j = 0; j < line[i].length; j++) {am[i][line[i][j]] = 1;}}for (int i = 0; i < bm.length; i++)bm[i] = 38;for (int i = 0; i < col.length; i++)col[i] = i;}void switch_row(int a, int b) {if (a == b)return;for (int j = 0; j < am[a].length; j++) {int tmp = am[a][j];am[a][j] = am[b][j];am[b][j] = tmp;}int tmp = bm[a];bm[a] = bm[b];bm[b] = tmp;}int gcd(int a, int b) {if (b == 0)return a;return gcd(b, a % b);}// k列，用k行消i行void xiao_yuan(int k, int i) {int u = am[k][k];int v = am[i][k];if (u == 0 || v == 0)return;int g = gcd(Math.abs(u), Math.abs(v));for (int j = 0; j < am[i].length; j++)am[i][j] = am[i][j] * u / g - am[k][j] * v / g;bm[i] = bm[i] * u / g - bm[k] * v / g;}void try_switch_col(int k) {int w = k;for (int j = k; j < am[k].length; j++) {if (am[k][j] != 0) {w = j;break;}}if (w == k)return;for (int i = 0; i < am.length; i++) {int tmp = am[i][k];am[i][k] = am[i][w];am[i][w] = tmp;tmp = col[k];col[k] = col[w];col[w] = tmp;}}void gauss() {for (int j = 0; j < am.length; j++) {for (int i = j; i < am.length; i++) {if (am[i][j] != 0) {switch_row(i, j);break;}}try_switch_col(j);for (int k = 0; k < am.length; k++) {if (k != j)xiao_yuan(j, k);}}}void show() {for (int i = 0; i < am.length; i++) {for (int j = 0; j < am[i].length; j++)System.out.print(String.format("%3d", am[i][j]));System.out.print(String.format("%6d", bm[i]));System.out.println();}System.out.println("----");for (int i = 0; i < 19; i++)System.out.print(col[i] + " ");System.out.println();}void test(int[] x) {for (int k = 11; k >= 0; k--) {int t1 = 0;for (int i = 12; i < 19; i++)t1 += am[k][i] * x[i];int t = (bm[k] - t1) / am[k][k];if (t < 1 || t > 19)return; // 非法值for (int i = k + 1; i < 19; i++)if (t == x[i])return; // 重复值x[k] = t;}System.out.println("find: ");int[] y = new int[19];for (int i = 0; i < 19; i++)y[col[i]] = x[i];for (int i = 0; i < 19; i++)System.out.print(y[i] + " ");// for(int i=0; i<19; i++) System.out.print(x[i] + " ");System.out.println();}// k: 当前要填充的位置void f(int[] x, int k) {if (k < 12) {test(x);return;}L1: for (int n = 1; n <= 19; n++) {for (int i = k + 1; i < 19; i++)if (x[i] == n)continue L1;x[k] = n;f(x, k - 1);if (k == 18)System.out.println(".. " + n);}}void search() {int[] x = new int[19];f(x, 18);}public static void main(String[] args) {A a = new A();a.init();a.gauss();a.show();a.search();}}