递归算法生成数独
/**
*
* 递归方法生成数独
*
* @author tiger
* @date 2010-5-28 完成于公司
*
* 复杂度有点高，有空优化。
*/
public class sodu {
private int[][] sodu = null;
private int[] tai = null;
/**
* 构造方法
* 因为每执行一次递归都会把数组tai元素全置为-1.
* 所以在执行一次递归后需要重新给tai赋值。
*/
public sodu(){
do{
this.init();
tai = getMixArray();
tiger(0,0,0,0); //upleft
tai = getMixArray();
tiger(0,3,0,3); //up
tai = getMixArray();
tiger(0,6,0,6); //upright
tai = getMixArray();
tiger(3,0,3,0); //left
tai = getMixArray();
tiger(3,6,3,6); //right
tai = getMixArray();
tiger(6,0,6,0); //downleft
tai = getMixArray();
tiger(6,3,6,3); //down
tai = getMixArray();
tiger(6,6,6,6); //downright
}while(this.isHaveZero());
}
/**
* 得到一个随机数组(元素1到9无重复)
* @param array
*/
private int[] getMixArray()
{
int[] array = {1,2,3,4,5,6,7,8,9};
for (int i = 0; i < array.length; i++)
{
int rand = (int) (Math.random() * 9);
int middle = array[i];
array[i] = array[rand];
array[rand] = middle;
}
return array;
}
/**
* 初始化数独数组
* 会初始化正中间的3*3矩阵
*/
private void init()
{
sodu = new int[9][9];
int[] array = this.getMixArray();
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
sodu[3+i][3+j] = array[i * 3 + j];
}
}
}
/**
* 打印
*/
public void print(){
for (int i = 0; i < sodu.length; i++) {
for (int j = 0; j < sodu[i].length; j++) {
System.out.print(sodu[i][j] + " , ");
}
System.out.println();
}
}
/**
* 递归方法
*
* 生成(i,j)处的值
*
* xi和xj 分别是初始调用该方法时的i和j
* @return
*/
private boolean tiger(int i, int j, int xi, int xj)
{
if(i - xi == 3)return true;
for (int j2 = 0; j2 < tai.length; j2++) {
if(tai[j2] != -1 && isGood(i,j,tai[j2]))
{
sodu[i][j] = tai[j2];
tai[j2] = -1;
if(j-xj < 2){
if(tiger(i,j+1,xi,xj))
{
return true;
}else{
tai[j2] = sodu[i][j];
sodu[i][j] = 0;
continue;
}
}else{
if(tiger(i+1,xj,xi,xj))
{
return true;
}else{
tai[j2] = sodu[i][j];
sodu[i][j] = 0;
continue;
}
}
}
}
return false;
}
/**
* 判断数字number是否可以用在坐标(x,y)处
*/
private boolean isGood(int i, int j, int number) {
for (int m = 0; m < 9; m++) {
if (sodu[i][m] == number) {
return false;
}
}
for (int n = 0; n < 9; n++) {
if (sodu[n][j] == number) {
return false;
}
}
return true;
}
/**
* 判断数独数组中是否有0
*/
private boolean isHaveZero()
{
for (int i = 0; i < sodu.length; i++) {
for (int j = 0; j < sodu[i].length; j++) {
if(sodu[i][j] == 0)
{
return true;
}
}
}
return false;
}
/**
* 程序入口
* @param args
*/
public static void main(String[] args) {
new sodu().print();
}
}
/**
* 打印结果如下：
3 , 9 , 7 , 8 , 4 , 1 , 2 , 6 , 5 ,
6 , 1 , 4 , 2 , 5 , 3 , 7 , 8 , 9 ,
5 , 8 , 2 , 9 , 7 , 6 , 3 , 4 , 1 ,
7 , 5 , 6 , 4 , 8 , 2 , 9 , 1 , 3 ,
9 , 4 , 1 , 3 , 6 , 5 , 8 , 2 , 7 ,
8 , 2 , 3 , 1 , 9 , 7 , 6 , 5 , 4 ,
1 , 3 , 8 , 5 , 2 , 9 , 4 , 7 , 6 ,
4 , 7 , 5 , 6 , 3 , 8 , 1 , 9 , 2 ,
2 , 6 , 9 , 7 , 1 , 4 , 5 , 3 , 8 ,
*/
