How do I model a chessboard when programming a computer to play chess?

Question

What data structures would you use to represent a chessboard for a computer chess program?

Answer 1

An alternative to the standard 8x8 board is the 10x12 mailbox (so-called because, uh, I guess it looks like a mailbox). This is a one-dimensional array that includes sentinels around its "borders" to assist with move generation. It looks like this:

-1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
-1, "a8", "b8", "c8", "d8", "e8", "f8", "g8", "h8", -1,
-1, "a7", "b7", "c7", "d7", "e7", "f7", "g7", "h7", -1,
-1, "a6", "b6", "c6", "d6", "e6", "f6", "g6", "h6", -1,
-1, "a5", "b5", "c5", "d5", "e5", "f5", "g5", "h5", -1,
-1, "a4", "b4", "c4", "d4", "e4", "f4", "g4", "h4", -1,
-1, "a3", "b3", "c3", "d3", "e3", "f3", "g3", "h3", -1,
-1, "a2", "b2", "c2", "d2", "e2", "f2", "g2", "h2", -1,
-1, "a1", "b1", "c1", "d1", "e1", "f1", "g1", "h1", -1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1

You can generate that array like this (in JavaScript):

function generateEmptyBoard() {
    var row = [];
    for(var i = 0; i < 120; i++) {
        row.push((i < 20 || i > 100 || !(i % 10) || i % 10 == 9) 
            ? -1 
            : i2an(i));
    }
    return row;
}

// converts an index in the mailbox into its corresponding value in algebraic notation
function i2an(i) {
    return "abcdefgh"[(i % 10) - 1] + (10 - Math.floor(i / 10));
}

Of course, in a real implementation you'd put actual piece objects where the board labels are. But you'd keep the negative ones (or something equivalent). Those locations make move generation a lot less painful because you can easily tell when you've run off the board by checking for that special value.

Let's first look at generating the legal moves for the knight (a non-sliding piece):

function knightMoves(square, board) {
    var i = an2i(square);
    var moves = [];
    [8, 12, 19, 21].forEach(function(offset) {
        [i + offset, i - offset].forEach(function(pos) {
            // make sure we're on the board
            if (board[pos] != -1) {
                // in a real implementation you'd also check whether 
                // the squares you encounter are occupied
                moves.push(board[pos]);
            }
        });
    });
    return moves;
}

// converts a position in algebraic notation into its location in the mailbox
function an2i(square) {
    return "abcdefgh".indexOf(square[0]) + 1 + (10 - square[1]) * 10;
}

We know that the valid Knight moves are a fixed distance from the piece's starting point, so we only needed to check that those locations are valid (i.e. not sentinel squares).

The sliding pieces aren't much harder. Let's look at the bishop:

function bishopMoves(square, board) {
    var oSlide = function(direction) {
        return slide(square, direction, board);
    }
    return [].concat(oSlide(11), oSlide(-11), oSlide(9), oSlide(-9)); 
}

function slide(square, direction, board) {
    var moves = [];
    for(var pos = direction + an2i(square); board[pos] != -1; pos += direction) {
        // in a real implementation you'd also check whether 
        // the squares you encounter are occupied
        moves.push(board[pos]);
    }
    return moves;
}

Here are some examples:

knightMoves("h1", generateEmptyBoard()) => ["f2", "g3"]
bishopMoves("a4", generateEmptyBoard()) => ["b3", "c2", "d1", "b5", "c6", "d7", "e8"]

Note that the slide function is a general implementation. You should be able to model the legal moves of the other sliding pieces fairly easily.