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

Possible improvement on the starting position in Yacoby's solution

No legal position has more than 16 pieces of each color. The number of ways to place up to 16 black and 16 white pieces on 64 squares is about 3.63e27. Log2(3.63e27)=91.55. This means you can encode the position and color of all pieces in 92 bits. This is less than the 64 bits for position + up to 32 bits for color that Yacoby's solution requires. You can save 4 bits in the worst case at the expense of considerable complexity in the encoding.

On the other hand, it increases the size for positions with 5 or more pieces missing. These positions represent only <4% of all positions, but they are probably a majority of the cases where you want to record a starting position different than the inital position.

This leads to the complete solution

1. Encode the position and color of pieces according to the method above. 92 bits.
2. To specify the type of each piece, use a Huffman Code: pawn: '0', rook: '100', knight: '101', bishop: '110', queen: '1110', king: '1111'. This requires (16*1 + 12*3 + 4*4) = 68 bits for a full set of pieces. The full board position can be encoded in 92 + 68 = 160 bits maximum.
3. Additional game state shoud be added: turn: 1 bit, which castling is possible: 4 bits, “en passant” possible: up to 4 bits (1 bit tells it is the case and 3 bits tell which one). The starting position is encoded in = 160 + 9 = 169 bits
4. For the list of moves, enumerate all possible moves for a given position and store the position of the move in the list. The list of moves includes all special cases (castling, en passant, and resigning). Use only as many bits as necessary to store the highest position. On average it shouldn't exceed 7 bits per move (16 possible pieces and 8 legal moves per piece on average). In some case, when a move is forced, it requires only 1 bit (move or resign).