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    <p>Attacking a subproblem of encoding the steps after an initial position has been encoded. The approach is to create a "linked list" of steps. </p> <p>Each step in the game is encoded as the "old position->new position" pair. You know the initial position in the beginning of the chess game; by traversing the linked list of steps, you can get to the state after X moves. </p> <p>For encoding each step, you need 64 values to encode the starting position (6 bits for 64 squares on the board - 8x8 squares), and 6 bits for the end position. 16 bits for 1 move of each side. </p> <p>Amount of space that encoding a given game would take is then proportionate to the number of moves: </p> <p>10 x (number of white moves + number of black moves) bits. </p> <p>UPDATE: potential complication with promoted pawns. Need to be able to state what the pawn is promoted to - may need special bits (would use gray code for this to save space, as pawn promotion is extremely rare). </p> <p>UPDATE 2: You don't have to encode the end position's full coordinates. In most cases, the piece that's being moved can move to no more than X places. For example, a pawn can have a maximum of 3 move options at any given point. By realizing that maximum number of moves for each piece type, we can save bits on the encoding of the "destination". </p> <pre><code>Pawn: - 2 options for movement (e2e3 or e2e4) + 2 options for taking = 4 options to encode - 12 options for promotions - 4 promotions (knight, biship, rook, queen) times 3 squares (because you can take a piece on the last row and promote the pawn at the same time) - Total of 16 options, 4 bits Knight: 8 options, 3 bits Bishop: 4 bits Rook: 4 bits King: 3 bits Queen: 5 bits </code></pre> <p>So the spatial complexity per move of black or white becomes</p> <p>6 bits for the initial position + (variable number of bits based upon the type of the thing that's moved). </p>
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    1. POProgrammer Puzzle: Encoding a chess board state throughout a game
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    1. USAlex Weinstein
    1. USAlex Weinstein
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    1. COHmmm. I think you could use less than 128 bits to encode a move...
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      1. USAndrew Rollings
    2. COJust updated, I meant 128 combinations - clearly less than 128 bits :) :)
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      1. USAlex Weinstein
    3. COA game state is not the same as a move. Any given position can be thought of a vertex or node, and a legal move can be thought of an directed edge or arrow, forming a (directed acyclic) graph.
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      1. USShaggy Frog
 

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