Java 2D array diagonals

Question

I wrote a program to try to solve the 8 queens problem and one part of it required me to test all of the forward and backward diagonals to make sure there were no conflicts. I got the backwards to work perfectly but this part of the forward one was returning true while I was testing and I really can't figure out why. And help would be greatly appreciated :)

class NonAttackingQueen {
  static char [][] board = { {'X','X','X','X','X','X','X','X'}, 
                             {'X','X','X','X','X','X','X','X'},
                             {'X','X','X','X','X','X','X','X'},
                             {'X','X','X','X','X','X','X','X'},
                             {'X','X','X','X','X','X','X','X'},
                             {'X','Q','X','X','X','X','X','X'},
                             {'Q','X','X','X','X','X','X','X'},
                             {'X','X','X','X','X','X','X','X'} };
public static boolean diagonalsClear () {
    int numQueens;
    boolean clear = true;
    for (int numSpots = 1; numSpots < 9; numSpots++) {
        numQueens = 0;
        for (int row = 0; row < numSpots - 1; row++) {
            if (board[row][numSpots - 1 - row] == 'Q')
                numQueens++;
        }
        if (numQueens > 1) {
            clear = false;
            break;
        }
    }
    for (int numSpots = 7; numSpots > 0; numSpots--) {
        numQueens = 0;
        for (int row = 7; row > 7 - numSpots; row--) {
            if (board[row][15-row-numSpots] == 'Q')
                numQueens++;
        }
        if (numQueens > 1) {
            clear = false;
            break;
        }
      return clear;
    }
}

Answer 1

Little trick to solve this problem. It is obvious, that you have mistake with matrix row and column indices calculation, and your loops do not cover all cells in it. Easiest way to check it, just print it out to console. I can see, that you have problem with for (int row = 0; row < numSpots - 1; row++). Firs iteration, when numSpots=1 it skips this loop. Correct is for (int row = 0; row <= numSpots - 1; row++).

Let me give you some notes about your example. I can see that two upper and lower part of the matrix you check with opposite direction, upper one you start with row=0 and lower one - col=0. I think to do the same calculation is much better for understanding. You could decomposite you task into three simple once:

1. Check one single diagonal, starting with given row and column;
2. check upper diagonals;
3. check lower diagonals.

I think example below is more clear for reading:

private static boolean isDiagonalClear(int row, int col) {
    int total = 0;

    do {
        if (board[row--][col++] == 'Q')
            total++;
    } while (total <= 1 && row >= 0 && col < 8);

    return total <= 1;
}

public static boolean diagonalsClear() {
    for (int row = 0; row < 7; row++)
        if (!isDiagonalClear(row, 0))
            return false;

    for (int col = 0; col < 8; col++)
        if (!isDiagonalClear(7, col))
            return false;

    return true;
}