未来的棋子流动性

时间:2014-01-19 16:40:09

标签: c# chess

我目前正在用C#开发一个国际象棋引擎,我在开发代码时遇到了一些障碍,以确定任何给定棋子在1,2和3步中的未来移动性。基本的想法是奖励可以提高行动能力的奖励,并惩罚行动不便的作品。

棋盘表示为64个方格的数组,从0(a8)到63(h1),例如

Piece[] _chessboard = new Piece[64];

我使用这个棋盘位置作为例子:

Black Rooks on squares 3 & 19 (d8 & d6)
Black King on square 5 (f8)
Black Knight on squares 11 & 12 (d7 & e7)
Black Queen on square 16 (a6)
Black Pawns on squares 13, 14, 17, 18, 19 (f7, g7, b6 & c6)

White Rook on squares 58 & 42 (c1 & c3)
White King on square 53 (f2)
White Knight on square 40 (a3)
White Bishop on square 41 (b3)
White Pawns on squares 32, 35, 36, 37, 38 & 31 (a4, d4, e4, f4, g4 & h5)

以下是相同位置的FEN字符串:3r1k2/3nnpp1/qppr3P/P6P/P2PPPP1/NBR5/5K2/2R5

经过多次尝试失败后,我想出了以下数据结构(Linked List?),我希望这是通过正方形追踪移动性的最佳方式。

+--------+-------------+-----------+-------+
| Square | Predecessor | Successor | Depth |
+--------+-------------+-----------+-------+
|     41 | NULL        |        34 |     1 |
|     34 | 41          |        25 |     2 |
|     25 | 34          |        16 |     3 |
+--------+-------------+-----------+-------+

这个结构告诉我的是方形41上的白色主教1步移动到方形34,然后是2移动方形25和3移动方形16。上面的结构使用递归函数填充,该函数遍历Bishop可以在1,2和2中移动到的所有可能的正方形。 3招。这样的问题是所有低效的移动都将被记录下来,并且需要在被更有效的移动替换之前检测和删除这些移动。

例如,通过正方形34和25在3次移动中从正方形41移动到16是不高效的,因为它可以在2次移动中移动到方形16; 41至34合1移动然后34至16移动2次。我需要递归函数来检测这些低效的移动并删除它们,然后再将新的有效移动添加到数据结构中。

我需要递归函数执行得非常快,因为评估函数将使用它来搜索给定位置的最佳移动。

我正在寻找的是一些代码,它将查询(可能使用LINQ?)上面的数据结构,从上面的数据结构中返回一个低效移动列表,以便删除它们,例如。

IEnumerable<MoveNode> _moves = new List<MoveNode>();

function void AddMove( int from, int to, int depth )
{
    // locate the inefficient moves that need to be deleted
    IEnumerable<MoveNode> list_of_moves_to_delete = find_moves( from, to, depth );
    if ( list_of_moves_to_delete.Any() )
    {
        _moves.RemoveAll( list_of_moves_to_delete );
    }

    // then add the more efficient move
    _moves.Add( new MoveNode( from, to, depth ) );
}

function IEnumerable<MoveNode> find_moves( int from, int to, int depth )
{
    // TODO: return a list of moves that are inefficient; moves
    //       that need to be deleted and replaced by efficient
    //        moves.

}

// Sample calling code (adds the inefficient moves)...
AddMove( 41, 34, 1 );
AddMove( 34, 25, 2 );
AddMove( 25, 16, 3 );

// This one is for the efficient moves...
AddMove( 41, 34, 1 );
AddMove( 34, 16, 2 ); // when this is called it should find the inefficient moves
                      // and remove them first before adding this move

这只是一个示例,可能无法编译;我希望有一些巫师可以帮助我在这里编写find_moves函数,以便正确返回低效的动作,因为我不知道如何去做。

我希望我能在这里清楚地解释一切。

谢谢!

**编辑**

考虑到没有人发布任何建议,我会尝试简化一些事情。我正在寻找一种算法,用于更新数据结构(类似于上面给出的数据结构),其中包含棋盘上方块之间最有效的移动,这就是我正在寻找的。

例如:

假设我在方块41(b3)上为白主教递归生成了这些移动;在1次移动中它可以从41移动到34(b3-c4),然后从3移动到34(27(c4-d5),最后从27移动到20(d5-e6)3次移动。

这意味着它已经通过34和27从3方移动到方形41到20,但是一旦递归函数开始处理更有效的移动,它将需要在数据结构中搜索低效移动并删除它们。

如果有可能做到这样的话会很棒:


Replace these entries:
+--------+-------------+-----------+-------+
| Square | Predecessor | Successor | Depth |
+--------+-------------+-----------+-------+
|     41 | NULL        |        34 |     1 |
|     34 | 41          |        25 |     2 |
|     25 | 34          |        16 |     3 |
+--------+-------------+-----------+-------+

With this:
+--------+-------------+-----------+-------+
| Square | Predecessor | Successor | Depth |
+--------+-------------+-----------+-------+
|     41 | NULL        |        34 |     1 |
|     34 | 41          |        16 |     2 |
+--------+-------------+-----------+-------+

After processing 41-34-16 in 2 moves.

**编辑2 **

在对可能的解决方案进行一些分析和开发之后,我认为我可能通过采用与上面给出的数据结构不同的数据结构来破解它。

到目前为止,这是解决方案 - 欢迎所有批评者尽可能地尝试改进此版本。

public class MoveNode
{
    public Guid Id;
    public int DepthLevel;
    public int Node0Ref;
    public int Node1Ref;
    public int Node2Ref;
    public int Node3Ref;

    public MoveNode()
    {
        Id = Guid.NewGuid();
    }

    //  Copy constructor
    public MoveNode( MoveNode node )
        : this()
    {
        if ( node != null )
        {
            this.Node0Ref = node.Node0Ref;
            this.Node1Ref = node.Node1Ref;
            this.Node2Ref = node.Node2Ref;
            this.Node3Ref = node.Node3Ref;
        }
    }
}

class Program
{
    static List<MoveNode> _nodes = new List<MoveNode>();

    static IQueryable<MoveNode> getNodes()
    {
        return _nodes.AsQueryable();
    }

    static void Main( string[] args )
    {
        MoveNode parent = null;

        // Simulates a recursive pattern for the following moves:
        //
        //  41  ->  34 (1)
        //          34  ->  27 (2)
        //                  27  ->  20 (3)
        //                  27  ->  13 (3)
        //          34  ->  20 (2)
        //          34  ->  13 (2)
        //  41  ->  27 (1)
        //          27  ->  20 (2)
        //                  20  ->  13 (3)
        //  41  ->  20 (1)
        //          20  ->  13 (2)
        //  41  ->  13 (1)
        //
        parent = addMove( null, 41, 34, 1 );
        parent = addMove( parent, 34, 27, 2 );
        parent = addMove( parent, 27, 20, 3 );
        parent = addMove( parent, 27, 13, 3 );
        parent = addMove( _nodes[ 0 ], 34, 20, 2 );
        parent = addMove( _nodes[ 0 ], 34, 13, 2 );
        parent = addMove( null, 41, 27, 1 );
        parent = addMove( parent, 27, 20, 2 );
        parent = addMove( parent, 20, 13, 3 );
        parent = addMove( null, 41, 20, 1 );
        parent = addMove( parent, 20, 13, 2 );
        parent = addMove( null, 41, 13, 1 );

        StringBuilder validMoves = new StringBuilder();
        StringBuilder sb = new StringBuilder();

        sb.Append( "+--------+---------+---------+---------+---------+\n" );
        sb.Append( "| Depth  | Node 0  | Node 1  | Node 2  | Node 3  |\n" );
        sb.Append( "+--------+---------+---------+---------+---------+\n" );
        foreach ( MoveNode node in getNodes() )
        {
            sb.AppendFormat( "| {0,2}     | {1,3}     | {2,3}     | {3,3}     | {4,3}     |\n", node.DepthLevel, node.Node0Ref, node.Node1Ref, node.Node2Ref, node.Node3Ref );

            if ( node.DepthLevel == 1 )
                validMoves.AppendFormat( "{0}\n", convertToBoardPosition( node.Node0Ref, node.Node1Ref ) );

            else if ( node.DepthLevel == 2 )
                validMoves.AppendFormat( "{0}\n", convertToBoardPosition( node.Node1Ref, node.Node2Ref ) );

            else if ( node.DepthLevel == 3 )
                validMoves.AppendFormat( "{0}\n", convertToBoardPosition( node.Node2Ref, node.Node3Ref ) );
        }
        sb.Append( "+--------+---------+---------+---------+---------+\n" );

        Console.WriteLine( sb.ToString() );

        Console.WriteLine( "List of efficient moves:" );
        Console.WriteLine( validMoves.ToString() );

        Console.WriteLine( "Press any key to exit." );
        Console.ReadKey();
    }

    static MoveNode addMove( MoveNode parent, int from, int to, int depthLevel )
    {
        MoveNode node = null;

        var inefficientMoves = getNodesToBeRemoved( from, to, depthLevel );
        if ( inefficientMoves.Any() )
        {
            // remove them...
            HashSet<Guid> ids = new HashSet<Guid>( inefficientMoves.Select( x => x.Id ) );
            _nodes.RemoveAll( x => ids.Contains( x.Id ) );
        }

        node = new MoveNode( parent );

        node.DepthLevel = depthLevel;

        if ( depthLevel == 1 )
        {
            node.Node0Ref = from;
            node.Node1Ref = to;
        }
        else if ( depthLevel == 2 )
        {
            node.Node1Ref = from;
            node.Node2Ref = to;
        }
        else if ( depthLevel == 3 )
        {
            node.Node2Ref = from;
            node.Node3Ref = to;
        }

        _nodes.Add( node );

        return node;

    }

    static IEnumerable<MoveNode> getNodesToBeRemoved( int from, int to, int depth )
    {
        var predicate = PredicateBuilder.True<MoveNode>();
        if ( depth == 1 )
            predicate = predicate.And( p => p.Node0Ref == from );

        else if ( depth == 2 )
            predicate = predicate.And( p => p.Node1Ref == from );

        else if ( depth == 3 )
            predicate = predicate.And( p => p.Node2Ref == from );

        predicate = predicate
            .And( a => a.Node1Ref == to )
            .Or( a => a.Node2Ref == to )
            .Or( a => a.Node3Ref == to );

        return getNodes().Where( predicate );
    }

    static string convertToBoardPosition( int from, int to )
    {
        string a = Convert.ToChar( 97 + file( from ) ) + Convert.ToString( rank( from ) );
        string b = Convert.ToChar( 97 + file( to ) ) + Convert.ToString( rank( to ) );
        return a + '-' + b;
    }

    static int file( int x )
    {
        return ( x & 7 );
    }

    static int rank( int x )
    {
        return 8 - ( x >> 3 );
    }

}

我不确定有关复制和版权的版权规则。粘贴其他人的代码,因此您需要从here下载PredicateBuilder源代码才能运行我的代码。

上面的代码将产生以下输出:

+--------+---------+---------+---------+---------+
| Depth  | Node 0  | Node 1  | Node 2  | Node 3  |
+--------+---------+---------+---------+---------+
|  1     |  41     |  34     |   0     |   0     |
|  1     |  41     |  27     |   0     |   0     |
|  1     |  41     |  20     |   0     |   0     |
|  1     |  41     |  13     |   0     |   0     |
+--------+---------+---------+---------+---------+

List of efficient moves:
b3-c4
b3-d5
b3-e6
b3-f7

Press any key to exit.

3 个答案:

答案 0 :(得分:1)

听起来像一个有趣的方法......我认为大多数引擎只是使用近似值(例如给中间位置提供片值),因为直接计算它太昂贵了,额外的周期更好用了继续前进。

下面是我对下面的伪实现的尝试,我无法完全理解你的数据结构,所以这显然需要大量的修改,哦,它根本不是LINQ,抱歉:

///<summary>After calling with recurseDepth = 0 initially, reachedSquares will afterwards hold a number of key-value
/// pairs indicating the minimum number of moves required to reach that square from the initial startSquare.</summary>
void FindPathableSquares(int recurseDepth, Dictionary<int, int> reachedSquares, int startSquare){
    reachedSquares[startSquare] = recurseDepth
    // Can't reach all squares with most pieces. Would suggest at *most* 3 for this constant.
    if(recurseDepth >= MAX_RECURSE_DEPTH)
        return;
    // Appropriate move generation algorithm here.
    // Presumably you have some board state reference in scope.
    var reachable = GenerateMoves(startSquare);
    foreach(int mv in reachable){
        // Skip nodes already found. Interesting alternative, perhaps multiple paths to a square are
        // useful, in which case reward this in the evaluation somehow.
        if(reachedSquares.ContainsKey(mv))
            continue;
        FindPathableSquares(recurseDepth + 1, reachedSquares, mv);
    }
}
祝你好运,希望结果证明这是一个有价值的对手。

答案 1 :(得分:1)

我认为你正在倒退这件事。你根本不需要修剪每一步的低效动作。你提出这样做​​的递归方式是优雅的,但永远不会有效。

您只需生成一次移动即可到达的所有方块的列表。然后生成最多两个动作可以达到的所有方格的列表。有一种简单的方法可以做到这一点 - 获取前一个列表中的所有方块,并找到一次可以从它们到达的所有方块。将所有这些列表与原始列表组合,删除重复。然后找到你可以通过三个动作到达的所有方块。同样,删除重复,但不要担心你已经包含了效率低的方块,也就是说,包含在一步或两步列表中的方格。您希望在前两个列表中包含所有内容。

现在,如果你只想要数字的正方形,你可以通过计算很快得到它们。在三次或更少次移动中可以达到的平方数是最后一个列表的长度。两次或更少次移动可以达到的平方数是第二个列表的长度。因此,它们之间的差异是恰好三次移动可以达到的平方数。

如果你碰巧想要正好可以达到的三个方格列表,那么你可以使用高效的LINQ函数Except

顺便说一下,这个问题非常适合codereview.stackexchange.com,因为它更多地是关于你想要改进的已编写代码,而不是语言或技术的特定问题。

答案 2 :(得分:1)

使用jwg给出的建议我想我已经设法计算了广场上给定棋子的1,2和3次移动的所有潜在动作。

以下是感兴趣的人的示例代码 - 它使用原始帖子中给出的董事会样本,并计算白方主教在b3方面的潜在未来流动性。是否正确我还不确定,所以我必须验证结果的准确性。

public enum PieceType
{
    Empty = 0,
    WhitePawn = 1,
    WhiteKnight = 2,
    WhiteBishop = 3,
    WhiteRook = 4,
    WhiteQueen = 5,
    WhiteKing = 6,
    BlackPawn = 7,
    BlackKnight = 8,
    BlackBishop = 9,
    BlackRook = 10,
    BlackQueen = 11,
    BlackKing = 12
}

public enum PieceColor
{
    Unknown = -1,
    Black = 0,
    White = 1
}

public enum ContentType
{
    NotInspected,
    Empty,
    BlockedFriendlyNotMoveable,
    BlockedFriendlyMoveable,
    BlockedCapturable,
}

public class Node
{
    public List<Node> ReachableSquares = new List<Node>();
    public int Square;
    public int RecurseDepth;
    public ContentType Content;

    public Move FreeingMove;
    public Node FreeingMoveNode;

    public Node( int square )
    {
        Square = square;
    }        
}

[StructLayout( LayoutKind.Explicit )]
public struct Move
{
    [FieldOffset( 0 )]
    public MoveBytes b;

    [FieldOffset( 0 )]
    public int u;

}

public struct MoveBytes
{
    public int from;
    public int to;
    public PieceType promote;
    public sbyte bits;
}   

public class FutureMove
{
    public string Path;
    public int Depth;
    public ContentType Content;
    public string PathIds;
}

public class ChessBoard
{
    private PieceType[] _board = new PieceType[ 64 ];

    public ChessBoard()
    {
        for ( int n = 0; n < 64; n++ )
            _board[ n ] = PieceType.Empty;
    }

    public void SetupBoard( KeyValuePair<Int32, PieceType>[] pieces )
    {
        foreach ( var piece in pieces )
            Set( piece.Value, piece.Key );
    }

    public void Set( PieceType pieceType, Int32 square )
    {
        checkSquareThrowExceptionIfInvalid( square );

        _board[ square ] = pieceType;
    }

    public PieceType Get( Int32 square )
    {
        checkSquareThrowExceptionIfInvalid( square );

        return _board[ square ];
    }

    public Boolean Is( PieceType pieceType, Int32 square )
    {
        return Get( square ) == pieceType;
    }

    public ContentType Inspect( int sourceSquare, int targetSquare, out Move move )
    {
        checkSquareThrowExceptionIfInvalid( sourceSquare );
        checkSquareThrowExceptionIfInvalid( targetSquare );

        move = new Move();

        ContentType content = ContentType.NotInspected;

        PieceType pieceOnTargetSquare = _board[ targetSquare ];
        PieceType pieceOnSourceSquare = _board[ sourceSquare ];

        PieceColor pieceColorOnTargetSquare = PieceColor.Unknown;
        PieceColor pieceColorOnSourceSquare = PieceColor.Unknown;

        if ( pieceOnTargetSquare == PieceType.BlackPawn || pieceOnTargetSquare == PieceType.BlackKnight || pieceOnTargetSquare == PieceType.BlackBishop || pieceOnTargetSquare == PieceType.BlackRook || pieceOnTargetSquare == PieceType.BlackQueen || pieceOnTargetSquare == PieceType.BlackKing )
            pieceColorOnTargetSquare = PieceColor.Black;
        else
            pieceColorOnTargetSquare = PieceColor.White;

        if ( pieceOnSourceSquare == PieceType.WhitePawn || pieceOnSourceSquare == PieceType.WhiteKnight || pieceOnSourceSquare == PieceType.WhiteBishop || pieceOnSourceSquare == PieceType.WhiteRook || pieceOnSourceSquare == PieceType.WhiteQueen || pieceOnSourceSquare == PieceType.WhiteKing )
            pieceColorOnSourceSquare = PieceColor.White;
        else
            pieceColorOnSourceSquare = PieceColor.Black;

        switch ( pieceOnTargetSquare )
        {
            case PieceType.Empty:
                content = ContentType.Empty;
                break;

            case PieceType.WhitePawn:
                bool captureLeft = pieceColorOnTargetSquare == PieceColor.Black && Common.File( targetSquare ) > 0 && InspectSquare( targetSquare - 9 ) != PieceType.Empty;
                bool captureRight = pieceColorOnTargetSquare == PieceColor.Black && Common.File( targetSquare ) < 8 && InspectSquare( targetSquare - 7 ) != PieceType.Empty;
                bool moveForwardOneSquare = Common.Rank( targetSquare ) != 2 && InspectSquare( targetSquare - 8 ) == PieceType.Empty;
                bool moveForwardTwoSquares = Common.Rank( targetSquare ) == 2 && InspectSquare( targetSquare - 8 ) == PieceType.Empty;

                if ( !captureLeft && !captureRight && !moveForwardOneSquare && !moveForwardTwoSquares )
                    content = ContentType.BlockedFriendlyNotMoveable;
                else
                {
                    move.b.from = targetSquare;
                    if ( moveForwardTwoSquares )
                        move.b.to = targetSquare - 16;

                    else if ( moveForwardOneSquare )
                        move.b.to = targetSquare - 8;

                    else if ( captureLeft )
                        move.b.to = targetSquare - 9;

                    else if ( captureRight )
                        move.b.to = targetSquare - 7;

                    content = ContentType.BlockedFriendlyMoveable;
                }

                break;

            default:
                if ( ( pieceColorOnSourceSquare == PieceColor.Black && pieceColorOnTargetSquare == PieceColor.White ) || ( pieceColorOnSourceSquare == PieceColor.White && pieceColorOnTargetSquare == PieceColor.Black ) )
                    content = ContentType.BlockedCapturable;

                break;
        }

        return content;
    }

    public PieceType InspectSquare( int square )
    {
        return _board[ Common.GetMailboxAddress( square ) ];
    }

    public ChessBoard MakeMove( int from, int to )
    {
        ChessBoard newBoard = new ChessBoard();
        for ( int n = 0; n < 64; n++ )
            newBoard.Set( _board[ n ], n );

        newBoard.Set( _board[ from ], to );
        newBoard.Set( PieceType.Empty, from );

        return newBoard;
    }

    public ChessBoard MakeMove( Move move )
    {
        return MakeMove( move.b.from, move.b.to );
    }

    public void DisplayBoard()
    {
        StringBuilder sb = new StringBuilder();
        int rank = 8;

        sb.Append( "+------------------------+" );
        for ( int i = 0; i < 64; i++ )
        {
            if ( ( i & 7 ) == 0 )
            {
                sb.AppendLine();
                sb.Append( rank );
                rank--;
            }

            PieceType piece = Get( i );

            if ( piece == PieceType.Empty )
            {
                sb.Append( " . " );
                if ( ( i & 7 ) == 7 )
                {
                    sb.Append( "|" );
                }
                continue;
            }

            switch ( piece )
            {
                case PieceType.WhitePawn:
                    sb.Append( " P " );
                    break;

                case PieceType.WhiteKnight:
                    sb.Append( " N " );
                    break;

                case PieceType.WhiteBishop:
                    sb.Append( " B " );
                    break;

                case PieceType.WhiteRook:
                    sb.Append( " R " );
                    break;

                case PieceType.WhiteQueen:
                    sb.Append( " Q " );
                    break;

                case PieceType.WhiteKing:
                    sb.Append( " K " );
                    break;

                case PieceType.BlackPawn:
                    sb.Append( " p " );
                    break;

                case PieceType.BlackKnight:
                    sb.Append( " n " );
                    break;

                case PieceType.BlackBishop:
                    sb.Append( " b " );
                    break;

                case PieceType.BlackRook:
                    sb.Append( " r " );
                    break;

                case PieceType.BlackQueen:
                    sb.Append( " q " );
                    break;

                case PieceType.BlackKing:
                    sb.Append( " k " );
                    break;
            }

            if ( ( i & 7 ) == 7 )
            {
                sb.Append( "|" );
            }

        }
        sb.AppendLine();
        sb.Append( "+-a--b--c--d--e--f--g--h-+" );

        Console.WriteLine( sb.ToString() );
    }

    #region Helper functions

    private void checkSquareThrowExceptionIfInvalid( int square )
    {
        if ( square < 0 || square > 63 )
            throw new ArgumentOutOfRangeException( "square" );
    }

    #endregion

}

public partial class ChessEngine
{
    private const int PAWN_OFFSET_INDEXOR = 0;
    private const int KNIGHT_OFFSET_INDEXOR = 1;
    private const int BISHOP_OFFSET_INDEXOR = 2;
    private const int ROOK_OFFSET_INDEXOR = 3;
    private const int QUEEN_OFFSET_INDEXOR = 4;
    private const int KING_OFFSET_INDEXOR = 5;

    private const int MAX_RECURSE_DEPTH = 3;

    /* slide, offsets, and offset are basically the vectors that
     * pieces can move in. If slide for the piece is false, it can
     * only move one square in any one direction. offsets is the
     * number of directions it can move in, and offset is an array
     * of the actual directions. */

    private bool[] _slide = new bool[ 6 ] {
        false, false, true, true, true, false
    };

    private int[] _offsets = new int[ 6 ]  {
        0, 8, 4, 4, 8, 8
    };

    private int[][] _offset = new int[ 6 ][] {
        new int[] { 0, 0, 0, 0, 0, 0, 0, 0 }, /* pawns */
        new int[] { -21, -19, -12, -8, 8, 12, 19, 21 },/* knights */
        new int[] { -11, -9, 9, 11, 0, 0, 0, 0 }, /* bishops */
        new int[] { -10, -1, 1, 10, 0, 0, 0, 0 }, /* rooks */
        new int[] { -11, -10, -9, -1, 1, 9, 10, 11 }, /* queen */
        new int[] { -11, -10, -9, -1, 1, 9, 10, 11 } /* king */
    };

    private Stack<ChessBoard> _boardHistory = new Stack<ChessBoard>();

    public List<FutureMove> Calculate( ChessBoard board, int square )
    {
        Node root = new Node( square );

        root.ReachableSquares = calculateReachableSquares( board, root, 0 );

        foreach ( var node in root.ReachableSquares )
        {
            if ( node.Content != ContentType.Empty )
                continue;

            _boardHistory.Push( board );

            var tempBoard = board.MakeMove( root.Square, node.Square );

            var allReachableSquares = calculateReachableSquares( tempBoard, node, 1 );

            node.ReachableSquares = RemoveDuplicateSquares( allReachableSquares, root.ReachableSquares );

            foreach ( var innerNode in node.ReachableSquares )
            {
                if ( innerNode.Content != ContentType.Empty )
                    continue;

                _boardHistory.Push( tempBoard );

                tempBoard = tempBoard.MakeMove( node.Square, innerNode.Square );

                allReachableSquares = calculateReachableSquares( tempBoard, innerNode, 2 );

                innerNode.ReachableSquares = RemoveDuplicateSquares( allReachableSquares, node.ReachableSquares, root.ReachableSquares );

                tempBoard = _boardHistory.Pop();

            }

            board = _boardHistory.Pop();
        }

        checkBoardHistoryEmptyThrowExceptionIfNot();

        return getFutureMoves( root );
    }

    private List<Node> calculateReachableSquares( ChessBoard board, Node node, int recurseDepth )
    {
        if ( recurseDepth > MAX_RECURSE_DEPTH )
            return null;

        int indexor = -1;

        switch ( board.Get( node.Square ) )
        {
            case PieceType.WhiteBishop:
            case PieceType.BlackBishop:
                indexor = BISHOP_OFFSET_INDEXOR;
                break;
        }

        bool takeBackMove = false;

        if ( indexor >= 0 )
        {
            for ( int j = 0; j < _offsets[ indexor ]; ++j )
            {
                for ( int n = node.Square; ; )
                {
                    int oset = _offset[ indexor ][ j ];

                    n = Common.GetMailboxAddress( n, oset );
                    if ( n == -1 )
                        break;

                    Move move;
                    ContentType pieceOnSquare = board.Inspect( node.Square, n, out move );
                    if ( pieceOnSquare == ContentType.NotInspected )
                        throw new Exception( String.Format( "Unable to inspect square {0}", n ) );

                    Node newNode = new Node( n ) { Content = pieceOnSquare, RecurseDepth = recurseDepth + 1 };
                    if ( move.u > 0 )
                        newNode.FreeingMove = move;

                    node.ReachableSquares.Add( newNode );

                    // Do we need to move the piece out of the way?
                    if ( pieceOnSquare == ContentType.BlockedFriendlyMoveable && newNode.RecurseDepth < 3 )
                    {
                        // Yes, we do.
                        recurseDepth++;

                        // Put the current board on the stack to preserve state.
                        _boardHistory.Push( board );

                        // Make the move.
                        board = board.MakeMove( move );

                        pieceOnSquare = board.Inspect( node.Square, n, out move );
                        var freeingMoveNode = new Node( n ) { Content = pieceOnSquare, RecurseDepth = recurseDepth + 1 };
                        if ( move.u > 0 )
                            freeingMoveNode.FreeingMove = move;

                        freeingMoveNode.FreeingMoveNode = newNode;

                        node.ReachableSquares.Add( freeingMoveNode );

                        // Lets the method know we need to put the board back.
                        takeBackMove = true;
                    }
                    else if ( pieceOnSquare != ContentType.Empty )
                        break;

                }

                // Reverts to a previous board state.
                if ( takeBackMove )
                {
                    recurseDepth--;

                    takeBackMove = false;

                    board = _boardHistory.Pop();
                }
            }
        }

        return node.ReachableSquares;
    }

    /// <summary>
    ///  Compares <paramref name="firstList"/> with <paramref name="secondList"/> and
    ///  returns a list of squares that exist in both lists.
    /// </summary>
    static IEnumerable<int> Intersect( List<Node> firstList, List<Node> secondList )
    {
        return firstList.Select( a => a.Square )
            .Intersect( secondList.Select( a => a.Square ) )
            .ToList();
    }

    /// <summary>
    ///  Combines <paramref name="firstList"/> and <paramref name="secondList"/> to make a single list before 
    ///  comparing the combined list with <paramref name="thirdList"/> returning a list of squares that in the 
    ///  two lists.
    /// </summary>
    private IEnumerable<int> Intersect( List<Node> firstList, List<Node> secondList, List<Node> thirdList )
    {
        return firstList.Select( a => a.Square )
            .Union( thirdList.Select( a => a.Square ) )
            .Intersect( secondList.Union( firstList ).Select( a => a.Square ) )
            .ToList();
    }

    /// <summary>
    ///  Looks for duplicates squares in <paramref name="originalList"/> and returns a new
    ///  List without these duplicates.
    /// </summary>
    private List<Node> RemoveDuplicateSquares( List<Node> originalList, List<Node> comparerList )
    {
        List<Node> newList = originalList.ToList();

        IEnumerable<Int32> dups = Intersect( newList, comparerList );

        newList.RemoveAll( a => dups.Contains( a.Square ) );

        return newList;
    }

    /// <summary>
    ///  Looks for duplicates squares in <paramref name="originalList"/> and returns a new
    ///  List without these duplicates.
    /// </summary>
    private List<Node> RemoveDuplicateSquares( List<Node> originalList, List<Node> comparerList1, List<Node> comparerList2 )
    {
        List<Node> newList = originalList.ToList();

        IEnumerable<Int32> dups = Intersect( comparerList1, comparerList2, newList );

        newList.RemoveAll( a => dups.Contains( a.Square ) );

        return newList;
    }

    private void checkBoardHistoryEmptyThrowExceptionIfNot()
    {
        // Must ensure the board history is empty before exiting.
        if ( _boardHistory.Count > 0 )
            throw new Exception( "Board stack not empty." );
    }

    private List<FutureMove> getFutureMoves( Node node )
    {
        return getFutureMoves( node, null, null );
    }

    private List<FutureMove> getFutureMoves( Node node, String path, String pathIds )
    {
        List<FutureMove> rows = new List<FutureMove>();

        StringBuilder currentPath = new StringBuilder();
        StringBuilder currentPathIds = new StringBuilder();

        if ( path != null )
            currentPath.AppendFormat( "{0}", path );
        else
            currentPath.AppendFormat( "{0}", Common.ConvertToBoardPosition( node.Square ) );

        if ( pathIds != null )
            currentPathIds.AppendFormat( "{0}", pathIds );
        else
            currentPathIds.AppendFormat( "{0}", node.Square );

        foreach ( var n in node.ReachableSquares )
        {
            string temp = String.Format( "{0}-{1}", currentPath, Common.ConvertToBoardPosition( n.Square ) );
            string tempPathIds = String.Format( "{0}-{1}", currentPathIds, n.Square );

            if ( n.ReachableSquares.Any() )
            {
                rows.AddRange( getFutureMoves( n, temp, tempPathIds ) );
            }

            FutureMove fm = new FutureMove();
            fm.Depth = n.RecurseDepth;
            fm.Path = temp.ToString();
            fm.PathIds = tempPathIds;
            fm.Content = n.Content;

            rows.Add( fm );

        }

        return rows;
    }

}

public static class Common
{
    static int[] _mailbox = new int[ 120 ]  {
        -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
        -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
        -1,  0,  1,  2,  3,  4,  5,  6,  7, -1,
        -1,  8,  9, 10, 11, 12, 13, 14, 15, -1,
        -1, 16, 17, 18, 19, 20, 21, 22, 23, -1,
        -1, 24, 25, 26, 27, 28, 29, 30, 31, -1,
        -1, 32, 33, 34, 35, 36, 37, 38, 39, -1,
        -1, 40, 41, 42, 43, 44, 45, 46, 47, -1,
        -1, 48, 49, 50, 51, 52, 53, 54, 55, -1,
        -1, 56, 57, 58, 59, 60, 61, 62, 63, -1,
        -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
        -1, -1, -1, -1, -1, -1, -1, -1, -1, -1
    };

    static int[] _mailbox64 = new int[ 64 ] {
        21, 22, 23, 24, 25, 26, 27, 28,
        31, 32, 33, 34, 35, 36, 37, 38,
        41, 42, 43, 44, 45, 46, 47, 48,
        51, 52, 53, 54, 55, 56, 57, 58,
        61, 62, 63, 64, 65, 66, 67, 68,
        71, 72, 73, 74, 75, 76, 77, 78,
        81, 82, 83, 84, 85, 86, 87, 88,
        91, 92, 93, 94, 95, 96, 97, 98
    };

    public static int GetMailboxAddress( int square )
    {
        return _mailbox[ _mailbox64[ square ] ];
    }

    public static int GetMailboxAddress( int square, int offset )
    {
        return _mailbox[ _mailbox64[ square ] + offset ];
    }

    public static string ConvertToBoardPosition( int from, int to )
    {
        string a = Convert.ToChar( 97 + File( from ) ) + Convert.ToString( Rank( from ) );
        string b = Convert.ToChar( 97 + File( to ) ) + Convert.ToString( Rank( to ) );
        return a + '-' + b;
    }

    public static string ConvertToBoardPosition( int square )
    {
        string a = Convert.ToChar( 97 + File( square ) ) + Convert.ToString( Rank( square ) );
        return a;
    }

    public static int File( int x )
    {
        return ( x & 7 );
    }

    public static int Rank( int x )
    {
        return 8 - ( x >> 3 );
    }

    public static string ContentTypeValueToString( ContentType contentTypeEnumValue )
    {
        string contentTypeStr = string.Empty;

        switch ( contentTypeEnumValue )
        {
            case ContentType.BlockedCapturable:
                contentTypeStr = "Blocked, Capturable";
                break;

            case ContentType.BlockedFriendlyMoveable:
                contentTypeStr = "Blocked, Friendly, Moveable";
                break;

            case ContentType.BlockedFriendlyNotMoveable:
                contentTypeStr = "Blocked, Friendly, Not Moveable";
                break;

            case ContentType.Empty:
                contentTypeStr = "Empty";
                break;

            default:
                contentTypeStr = "Error!";
                break;
        }

        return contentTypeStr;
    }

}

// Main calling program 
class Program
{
    static void Main( string[] args )
    {

        ChessBoard cb = new ChessBoard();
        cb.SetupBoard( new KeyValuePair<Int32, PieceType>[] 
        { 
            // Setup Black pieces
            new KeyValuePair<Int32, PieceType>( 3, PieceType.BlackRook ),
            new KeyValuePair<Int32, PieceType>( 5, PieceType.BlackKing ), 
            new KeyValuePair<Int32, PieceType>( 11, PieceType.BlackKnight ), 
            new KeyValuePair<Int32, PieceType>( 12, PieceType.BlackKnight ), 
            new KeyValuePair<Int32, PieceType>( 13, PieceType.BlackPawn ), 
            new KeyValuePair<Int32, PieceType>( 14, PieceType.BlackPawn ), 
            new KeyValuePair<Int32, PieceType>( 16, PieceType.BlackQueen ), 
            new KeyValuePair<Int32, PieceType>( 17, PieceType.BlackPawn ), 
            new KeyValuePair<Int32, PieceType>( 18, PieceType.BlackPawn ), 
            new KeyValuePair<Int32, PieceType>( 19, PieceType.BlackRook ), 
            new KeyValuePair<Int32, PieceType>( 23, PieceType.BlackPawn ), 
            new KeyValuePair<Int32, PieceType>( 24, PieceType.BlackPawn ), 
            // Setup White pieces
            new KeyValuePair<Int32, PieceType>( 31, PieceType.WhitePawn ), 
            new KeyValuePair<Int32, PieceType>( 32, PieceType.WhitePawn ), 
            new KeyValuePair<Int32, PieceType>( 35, PieceType.WhitePawn ), 
            new KeyValuePair<Int32, PieceType>( 36, PieceType.WhitePawn ), 
            new KeyValuePair<Int32, PieceType>( 37, PieceType.WhitePawn ), 
            new KeyValuePair<Int32, PieceType>( 38, PieceType.WhitePawn ), 
            new KeyValuePair<Int32, PieceType>( 40, PieceType.WhiteKnight ), 
            new KeyValuePair<Int32, PieceType>( 41, PieceType.WhiteBishop ), 
            new KeyValuePair<Int32, PieceType>( 42, PieceType.WhiteRook ),
            new KeyValuePair<Int32, PieceType>( 53, PieceType.WhiteKing )
        }
        );

        cb.DisplayBoard();

        int square = 41;

        ChessEngine eng = new ChessEngine();
        List<FutureMove> futureMoves = eng.Calculate( cb, square );

        int move1 = futureMoves.Where( m => m.Depth == 1 ).Count();
        int move2 = futureMoves.Where( m => m.Depth == 2 ).Count();
        int move3 = futureMoves.Where( m => m.Depth == 3 ).Count();

        Console.WriteLine();
        Console.WriteLine( String.Format( "Number of potential squares reached in 1 move  {0,3} from square {1,2}", move1, square ) );
        Console.WriteLine( String.Format( "Number of potential squares reached in 2 moves {0,3} from square {1,2}", move2, square ) );
        Console.WriteLine( String.Format( "Number of potential squares reached in 3 moves {0,3} from square {1,2}", move3, square ) );

        Console.WriteLine();
        Console.WriteLine( "Press any key to exit." );
        Console.ReadKey();
    }

}