如何使用递归回溯解决8皇后问题？

Question

更新代码：我的最后一个问题是我如何得到它以便我的程序打印 8x8 板的所有 92 个解决方案，而没有任何 Queens 互相攻击？到目前为止，我的代码只打印 1 个解决方案。例如，当我将其更改为 4x4 板时，我只有 1 个解决方案，而我认为应该有 2 个。

public class Queen{

   public static void display(int[] board){
      int n = board.length;
      for(int column = 0; column < n; column++){
         for(int row = 0; row < n; row++){
            if(board[column] == row)
               System.out.print('Q');
       else 
         System.out.print('x');



         }
         System.out.print('\n');
      }
   }

    public static int[] solveQueens(int n){
        int board[] = new int[n];
        placeQueen(board,0);
        return board;
    }
    private static boolean placeQueen(int[] board, int column){
        int n = board.length;
        if (n == column){
            return true;
        }else{
            for (int row = 0; row < n; row++){
                int i; //remove
                for (i = 0; i < column; i++){  //for (int i)
                    if (board[i] == row || i - column == board[i] - row || column - i == board[i] - row){
                        break;
                    }
                }
                if (i == column){ 
                    board[column] = row;
                    if (placeQueen(board, column + 1))
                        return true;
                }
            }
        }
        return false;
    }
    public static void main(String args[]){
        int finished[] = solveQueens(8);
        display(finished);
        }
    }

现在我的程序returns:

Qxxxxxxx
xxxxQxxx
xxxxxxxQ
xxxxxQxx
xxQxxxxx
xxxxxxQx
xQxxxxxx
xxxQxxxx

旧代码：我需要使用递归回溯来解决 8 皇后区问题。 n 皇后问题是一个难题，需要将 n 个国际象棋皇后放在 n × n 的棋盘上，以便 none 个皇后互相攻击。

我需要写一个public solveQueens(int n)方法来解决nxn板的问题

我还需要编写一个私有递归 placeQueen(board, column) 方法来尝试在指定列中放置一个皇后。

到目前为止，这是我的代码：

public class Queen{

    public static int[] solveQueens(int n){
      int board[] = new int[n];
       int finished[] = placeQueen(board,0);
       return finished;

    }
    private static int[] placeQueen(int[] board, int column){
       int n = board.length;
       int row = column;
       if (n == column){
          return board;
       }else{ 
          for (row = n; row < n; row++){
            board[column] = row;
             if (board[n] == 0 && board[n-1] == 0 && board[n+1] == 0){
               board[n] = 1;
                placeQueen(board, column+1);
             }
          }
         for (row = n; row < n; row++){
             board[row] = column; 
            if (board[n] == 0 && board[n-1] == 0 && board[n+1] == 0){
                board[n] = 1;
                placeQueen(board, column+1);
             }
          }
       }
       return board;
    }
    public static void main(String args[]){
       int finished[] = solveQueens(8);
       for (int item: finished){
          System.out.print(item);
       }
    }
}

每当我运行我的程序时，它 returns 就是

----jGRASP exec: java Queen
00000000

是否有任何关于如何设置我的 8x8 板以及如何放置皇后以使它们不会互相攻击的说明？

Answer 1

我对 solveQueens 和 placeQueen 做了一些改动：

public class Queen{

    public static int[] solveQueens(int n){
        int board[] = new int[n];
        placeQueen(board,0);  //it fills the board
        return board;
    }
    private static boolean placeQueen(int[] board, int column){
        int n = board.length;
        int row;
        if (n == column){
            return true;
        }else{
            for (row = 0; row < n; row++){
                int c;
                for (c=0; c<column; c++){
                    if (board[c]==row || c-column==board[c]-row || column-c==board[c]-row){
                        //check if it is safe position (we know 2 queens couldn't place in a same column or row or diameter
                        break;
                    }
                }
                if (c==column){   //if previous loop didn't break...=> it is safe position
                    board[column]=row;
                    if (placeQueen(board, column+1))   //if it is possible to fill the rest of board //else: test the next row
                        return true;
                }
            }
        }
        return false;
    }
    public static void main(String args[]){
        int finished[] = solveQueens(8);
        for (int item: finished){
            System.out.print(item);
        }
    }
}

如何使用递归回溯解决8皇后问题？

How to use recursive backtracking to solve 8 queens?

java

arrays

recursion

stack

call