Java: обобщенная 8 королева для работы в любом начальном состоянии с использованием поиска в глубину

Я пытаюсь решить проблему с 8 ферзями для любого начального состояния (поместить 8 ферзей в любое место на доске), но это дает мне исключение stackoverflow.

вот мой код:

import java.io.IOException;

public class depth {
public static void main(String[] args) {

   //we create a board
   int[][] board = new int[8][8];
   board [0][0]=1;
   board [1][1]=1;
   board [2][2]=1;
   board [3][3]=1;
   board [4][4]=1;
   board [5][5]=1;
   board [6][6]=1;
   board [7][7]=1;

 IOException e = null;
   eightQueen(8, board, 0, 0, false);
   System.out.println("the solution as pair");
   for(int i=0;i<board.length;i++){
       for(int j=0;j<board.length;j++)
           if(board[i][j]!=0)

           System.out.println("  ("+i+" ,"+j +")");

   System.out.println("the number of node stored in memory "+count1);

   }

   e.printStackTrace();

   }

   public static int count1=0;
   public static void eightQueen(int N, int[][] board, int i, int j, boolean found) {

   long startTime = System.nanoTime();//time start

   if (!found) {
    if (IsValid(board, i, j)) {//check if the position is valid
        board[i][j] = 1;

        System.out.println("[Queen added at (" + i + "," + j + ")");
        count1++;
        PrintBoard(board);

        if (i == N - 1) {//check if its the last queen
            found = true;
            PrintBoard(board);
            double endTime = System.nanoTime();//end the method time

            double duration = (endTime - startTime)*Math.pow(10.0, -9.0);
            System.out.print("total Time"+"= "+duration+"\n");
        }
        //call the next step
        eightQueen(N, board, i + 1, 0, found);
    } else {

        //if the position is not valid & if reach the last row we backtracking
        while (j >= N - 1) {
            int[] a = Backmethod(board, i, j);
            i = a[0];
            j = a[1];

            System.out.println("back at (" + i + "," + j + ")");
            PrintBoard(board);
        }
        //we do the next call
        eightQueen(N, board, i, j + 1, false);
    }
    }

   }

  public static int[] Backmethod(int[][] board, int i, int j) {
  int[] a = new int[2];
  for (int x = i; x >= 0; x--) {
    for (int y = j; y >= 0; y--) {
        //search for the last queen
        if (board[x][y] != 0) {
            //deletes the last queen and returns the position
            board[x][y] = 0;
            a[0] = x;
            a[1] = y;
            return a;
        }
    }
  }
  return a;
}

public static boolean IsValid(int[][] board, int i, int j) {

int x;
//check the queens in column
for (x = 0; x < board.length; x++) {
    if (board[i][x] != 0) {
        return false;
    }
}
//check the queens in row
for (x = 0; x < board.length; x++) {
    if (board[x][j] != 0) {
        return false;
    }
}
//check the queens in the diagonals
if (!SafeDiag(board, i, j)) {
    return false;
}
return true;
}

public static boolean SafeDiag(int[][] board, int i, int j) {

int xx = i;
int yy = j;
while (yy >= 0 && xx >= 0 && xx < board.length && yy < board.length) {
    if (board[xx][yy] != 0) {
        return false;
    }
    yy++;
    xx++;
}
xx = i;
yy = j;
while (yy >= 0 && xx >= 0 && xx < board.length && yy < board.length) {
    if (board[xx][yy] != 0) {
        return false;
    }
    yy--;
    xx--;
}
xx = i;
yy = j;
while (yy >= 0 && xx >= 0 && xx < board.length && yy < board.length) {
    if (board[xx][yy] != 0) {
        return false;
    }
    yy--;
    xx++;
}
xx = i;
yy = j;
while (yy >= 0 && xx >= 0 && xx < board.length && yy < board.length) {
    if (board[xx][yy] != 0) {
        return false;
    }
    yy++;
    xx--;
   }
   return true;
 }
 public static void PrintBoard(int[][] board) {
System.out.print(" ");
for (int j = 0; j < board.length; j++) {
    System.out.print(j);
}
System.out.print("\n");
for (int i = 0; i < board.length; i++) {
    System.out.print(i);
    for (int j = 0; j < board.length; j++) {
        if (board[i][j] == 0) {
            System.out.print(" ");
        } else {
            System.out.print("Q");
        }
    }
    System.out.print("\n");
   }
  }

  }

и вывод:

at sun.nio.cs.StreamEncoder.write(Unknown Source)
at java.io.OutputStreamWriter.write(Unknown Source)
at java.io.BufferedWriter.flushBuffer(Unknown Source)
at java.io.PrintStream.write(Unknown Source)
at java.io.PrintStream.print(Unknown Source)
at java.io.PrintStream.println(Unknown Source)
at depth.eightQueen(depth.java:68)

странно, что это работает для следующего начального состояния:

   board [0][0]=1;
   board [1][1]=1;
   board [2][2]=1;
   board [3][3]=1;
   board [4][4]=1;
   board [5][5]=1;
   board [6][6]=1;
   board [7][1]=1;