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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