Programmer Puzzle: Encoding a chess board state throughout a game

Question

Not strictly a question, more of a puzzle...

Over the years, I\'ve been involved in a few technical interviews of new employees. Other than asking the standard \"do you

Answer 1

A board has 64 squares, and can be represented by 64 bits showing if a square is empty or not. We only need piece information if a square has a piece. Since the player + piece takes 4 bits (as shown earlier) we can get the current state in 64 + 4 * 32 = 192 bits. Throw in the current turn and you have 193 bits.

However, we also need to encode the legal moves for each piece. First, we calculate the number of legal moves for each piece, and append that many bits after the piece identifier of a full square. I calculated as follows:

Pawn: Forward, first turn two forward, en passant * 2, promotion = 7 bits. You can combine the first turn forward and promotion into a single bit since they cannot happen from the same position, so you have 6. Rook: 7 vertical squares, 7 horizontal squares = 14 bits Knight: 8 squares = 8 bits Bishop: 2 diagonals * 7 = 14 bits Queen: 7 vertical, 7 horizontal, 7 diagonal, 7 diagonal = 28 bits King: 8 surrounding squares

This still means you would need to map the targeted squares based on the current position, but it (should be) a simple calculation.

Since we have 16 pawns, 4 rooks/knights/bishops, and 2 queens/kings, this is 16 * 6 + 4 * 14 + 4 * 8 + 4 * 14 + 2 * 28 + 2 * 8 = 312 more bits, bringing the total to 505 bits overall.

As for the number of bits required per piece for possible moves, some optimisations could be added to that and the number of bits probably reduced, I just used easy numbers to work with. For example, for sliding pieces you could store how far away they could move, but this would require extra calculations.

Long story short: Only store extra data (piece, etc) when a square is occupied, and only store the minimum number of bits for each piece to represent its legal moves.

EDIT1: Forgot about castling and pawn promotion to any piece. This could bring the total with explicit positions to 557 moves (3 more bits for pawns, 2 for kings)