8皇后问题——回溯法、递归解决
最近工作上不太顺，虽然做大数据，但是部门拉胯，现在已经成为了CRUD工程师，唉。
开始重温Java了，学习韩顺平老大的Java培训课，总不能就这样拉跨下去吧。
看到了8皇后问题，这个很经典的问题。
八皇后问题是一个古老而又著名的问题，是学习回溯算法的一个经典案例。之前应该练习过，今天我们就一起来探究一下吧！
时间退回到1848年，国际西洋棋棋手马克斯·贝瑟尔提出了这样的一个问题，
在8×8格的国际象棋上摆放八个皇后，使其不能互相攻击，即任意两个皇后都不能处于同一行、同一列或同一斜线上，问一共有多少种摆法。
用Java写了一个，解法在下面：
public class EgihtQueue {
public static void main(String[] args) {
int num = 8;
int[][] map = new int[num][num];
// 给原始地图赋值为全0
for(int i = 0; i < map.length; i++){
for(int j = 0; j < map[i].length; j++){
map[i][j] = 0;
}
}
// 开始
MyTool myTool = new MyTool();
myTool.putQueue(map, 0);
}
}
class MyTool{
// 在类内设置一个全局变量用来做计数器
int count = 0;
public void showQueue(int[][] map){
count++;
System.out.println("Situation :" + count);
for(int i = 0; i < map.length; i++){
for(int j = 0; j < map[i].length; j++){
System.out.print(map[i][j] + " ");
}
System.out.println();
}
}
// 判断是否可以为皇后放置的位置
public boolean checkQueue(int[][] map, int row, int column){
// 判断列上是否有其他皇后，其他皇后只可能出现在该行的前面
for(int i = row - 1; i >= 0; i--){
if(map[i][column] == 1){
return false;
}
}
// 一行只会有一个皇后，对于行来说不需要判断
// 判断当前皇后摆放的左上部分是否存在其他皇后，行和列都要减小
for(int i = row - 1, j = column - 1; i >= 0 && j >= 0; i--, j--){
if(map[i][j] == 1){
return false;
}
}
// 判断当前皇后摆放的右上角是否存在其他皇后，行要减小但是列要增加
for(int i = row - 1, j = column + 1; i >= 0 && j < map[i].length; i--, j++){
if(map[i][j] == 1){
return false;
}
}
return true;
}
// 开始进行回溯来寻找放置皇后的位置
public void putQueue(int[][] map, int row){
// 从每个行开始，遍历每一个列，行已经 给了，列指针走动就好
for(int j = 0; j < map[row].length; j++){
if(checkQueue(map, row, j)){
// 如果当前位置可以为皇后放置的位置则置为1
map[row][j] = 1;
// 递归终止条件为行数到达最大，也就是找到了最后一个皇后
if(row == map.length - 1){
// 此时得到了一个8皇后的结果
showQueue(map);
}else{
// 如果行数没有达到最大，则进行递归，进行行增大
putQueue(map, row + 1);
}
// 如果当前位置不可以为皇后放置的位置则置为0，开始回溯，在对应行开始重新放置
map[row][j] = 0;
}
}
}
}
结果：
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