八皇后回溯 Java版

　　

 

?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

public class Queen {   protected int num = 8;  // the number of queens   // chessboard索引表示行,即第几个queen,chessboard[i]=value,表示第i+1个queen,位于value+1列   int[] chessboard = new int[num];   private static int count = 0;  // 记录多少种摆法     public void lay(int n) {  // n表示放置第几个queen,从0开始     /*     n==8时,8个queen已就绪,lay返回,回溯到第8个queen(即第8行),往第八行的下一列继续放置     当for(int i = 0; i< num; ++i)结束时,表明第8行所有列已经(此时n==7)尝试完毕,继续回溯至n==6,     即第7行,往第7行的下一列继续尝试(for循环),继续进入n==7的所有i遍历,直至回溯到n==0(第一行)      */     if (n == num) {       print();       return;     }     for (int i = 0; i < num; ++i) {       chessboard[n] = i; // 将第n+1行的queen至于第i+1列       if (feasible(n)) {  // feasible会引用当前queen的列数,即chessboard[n]的值         lay(n + 1); // 当前queen与前面的queen不冲突       }     }   }     /**    * diagonal有双向,Math.abs(行差) == Math.abs(列差)即diagonal,行差即chessboard索引差,列差即    * chessboard对应的值差    *    * @param n n+1行的queen    * @return boolean    */   public boolean feasible(int n) {  // n 第n+1行queen     for (int i = 0; i < n; ++i) {       if (chessboard[i] == chessboard[n] || (n - i) == Math.abs(chessboard[n] - chessboard[i])) {         return false;       }     }     return true;   }     /**    * 找到一种摆法,打印,counter++    */   public void print() {     count++;     for(int i=0;i<num;++i){       System.out.print(chessboard[i]+" ");     }     System.out.println();   }     public static void main(String[] args){     Queen queen=new Queen();     queen.lay(0);  // 从第1行放置queen     System.out.println("count: "+count);   } }

　　

 

class Queen {
    private int counter;
    private static final int[] chessboard = new int[8];

    protected void lay(int row) {
        if (row == 8) {
            print();
            return;
        }
        for (int i = 0; i < 8; i++) {
            chessboard[row] = i;
            if (feasible(row)) {
                lay(row + 1);
            }
        }
    }

    private boolean feasible(int row) {
        for (int i = 0; i < row; ++i) {
            if (chessboard[i] == chessboard[row] || row - i == Math.abs(chessboard[row] - chessboard[i])) {
                return false;
            }
        }
        return true;
    }

    private void print() {
        counter++;
        System.out.println("Solution = " + counter);
        for (int i : chessboard) {
            for (int v = 0; v < 8; ++v) {
                System.out.print(v == i ? '$' : '*');
            }
            System.out.println();
        }
    }
}