战舰!

早在2003年(当时我17岁),我参加了一场《战舰》AI编码比赛。尽管我输了那场比赛,但我从中获得了很多乐趣,也学到了很多东西。

现在,我想恢复这个比赛,在搜索最好的战舰AI。

下面是这个框架,现在托管在Bitbucket上。

获胜者将获得+450声望奖励!比赛将于2009年11月17日开始。17号零时之前的投稿和编辑将不被接受。(中央标准时间) 尽早提交你的作品,这样你就不会错过机会!

为了保持这个目标,请遵循比赛的精神。

游戏规则:

游戏在10x10的网格上进行。 每个参赛者将5艘船(长度为2、3、3、4、5)中的每一艘放在他们的网格上。 没有船只可以重叠,但它们可以相邻。 然后选手们轮流向对手射击。 游戏的一个变体允许每次齐射多次,每艘幸存的船一次。 如果击球沉、命中或未命中,对手将通知选手。 当任何一名玩家的所有船只都沉没时,游戏就结束了。

比赛规则:

The spirit of the competition is to find the best Battleship algorithm. Anything that is deemed against the spirit of the competition will be grounds for disqualification. Interfering with an opponent is against the spirit of the competition. Multithreading may be used under the following restrictions: No more than one thread may be running while it is not your turn. (Though, any number of threads may be in a "Suspended" state). No thread may run at a priority other than "Normal". Given the above two restrictions, you will be guaranteed at least 3 dedicated CPU cores during your turn. A limit of 1 second of CPU time per game is allotted to each competitor on the primary thread. Running out of time results in losing the current game. Any unhandled exception will result in losing the current game. Network access and disk access is allowed, but you may find the time restrictions fairly prohibitive. However, a few set-up and tear-down methods have been added to alleviate the time strain. Code should be posted on stack overflow as an answer, or, if too large, linked. Max total size (un-compressed) of an entry is 1 MB. Officially, .Net 2.0 / 3.5 is the only framework requirement. Your entry must implement the IBattleshipOpponent interface.

得分:

Best 51 games out of 101 games is the winner of a match. All competitors will play matched against each other, round-robin style. The best half of the competitors will then play a double-elimination tournament to determine the winner. (Smallest power of two that is greater than or equal to half, actually.) I will be using the TournamentApi framework for the tournament. The results will be posted here. If you submit more than one entry, only your best-scoring entry is eligible for the double-elim.

好运!玩得开心!


编辑1: 多亏弗里德,他在飞船上发现了一个错误。是否是可用的函数。问题已经解决了。请下载框架的更新版本。

编辑2: 由于人们对将统计数据持久化到磁盘等非常感兴趣,所以我添加了一些非计时设置和删除事件,它们应该能够提供所需的功能。这是一个半突破性的变化。也就是说:修改了接口,添加了功能,但不需要body。请下载框架的更新版本。

编辑3: 错误修复1:GameWon和GameLost只在超时的情况下被调用。 错误修复2:如果引擎在每一款游戏中都暂停计时,那么竞争将永远不会结束。 请下载框架的更新版本。

编辑4: 比赛结果:


当前回答

“战舰”是一个经典的计算机科学np完全问题。

http://en.wikipedia.org/wiki/List_of_NP-complete_problems

(寻找战舰-它在那里,在游戏和谜题下)

其他回答

我预测,能够逆向设计对手随机种子和呼叫模式的人将获胜。

但不确定这种可能性有多大。

我在这里没有放入实际的代码,但我将冒险进行一些一般性的观察:

因为所有的飞船都至少有2个细胞大小,你可以使用我在《太空探索V》中看到的一个优化——当它“寻找”一个目标时,只向菱形图案的交替细胞开火。这将消除一半的方格,同时仍然保证你最终会找到所有船只。 在许多游戏中,寻找目标时的随机射击模式从统计上来说会产生最好的结果。

我的电脑现在正在戴尔维修,但这是我上周在哪里:

namespace Battleship
{
    using System;
    using System.Collections.ObjectModel;
    using System.Drawing;
    using System.Collections.Generic;
    using System.Linq;

    public class BSKiller4 : OpponentExtended, IBattleshipOpponent
    {
        public string Name { get { return "BSKiller4"; } }
        public Version Version { get { return this.version; } }

        public bool showBoard = false;

        Random rand = new Random();
        Version version = new Version(0, 4);
        Size gameSize;

        List<Point> nextShots;
        Queue<Point> scanShots;

        char[,] board;

        private void printBoard()
        {
            Console.WriteLine();
            for (int y = 0; y < this.gameSize.Height; y++)
            {
                for (int x = 0; x < this.gameSize.Width; x++)
                {
                    Console.Write(this.board[x, y]);
                }
                Console.WriteLine();
            }
            Console.ReadKey();
        }

        public void NewGame(Size size, TimeSpan timeSpan)
        {
            this.gameSize = size;
            board = new char[size.Width, size.Height];
            this.nextShots = new List<Point>();
            this.scanShots = new Queue<Point>();
            fillScanShots();
            initializeBoard();
        }

        private void initializeBoard()
        {
            for (int y = 0; y < this.gameSize.Height; y++)
            {
                for (int x = 0; x < this.gameSize.Width; x++)
                {
                    this.board[x, y] = 'O';
                }
            }
        }

        private void fillScanShots()
        {
            int x, y;
            int num = gameSize.Width * gameSize.Height;
            for (int j = 0; j < 3; j++)
            {
                for (int i = j; i < num; i += 3)
                {
                    x = i % gameSize.Width;
                    y = i / gameSize.Height;
                    scanShots.Enqueue(new Point(x, y));
                }
            }
        }

        public void PlaceShips(ReadOnlyCollection<Ship> ships)
        {
            foreach (Ship s in ships)
            {
                s.Place(new Point(
                        rand.Next(this.gameSize.Width),
                        rand.Next(this.gameSize.Height)),
                        (ShipOrientation)rand.Next(2));
            }
        }

        public Point GetShot()
        {
            if (showBoard) printBoard();
            Point shot;

            shot = findShotRun();
            if (shot.X != -1)
            {
                return shot;
            }

            if (this.nextShots.Count > 0)
            {
                shot = this.nextShots[0];
                this.nextShots.RemoveAt(0);
            }
            else
            {
                shot = this.scanShots.Dequeue();
            }

            return shot;
        }

        public void ShotHit(Point shot, bool sunk)
        {
            this.board[shot.X, shot.Y] = 'H';
            if (!sunk)
            {
                addToNextShots(new Point(shot.X - 1, shot.Y));
                addToNextShots(new Point(shot.X, shot.Y + 1));
                addToNextShots(new Point(shot.X + 1, shot.Y));
                addToNextShots(new Point(shot.X, shot.Y - 1));
            }
            else
            {
                this.nextShots.Clear();
            }
        }



        private Point findShotRun()
        {
            int run_forward_horizontal = 0;
            int run_backward_horizontal = 0;
            int run_forward_vertical = 0;
            int run_backward_vertical = 0;

            List<shotPossibilities> possible = new List<shotPossibilities>(5);

            // this only works if width = height for the board;
            for (int y = 0; y < this.gameSize.Height; y++)
            {
                for (int x = 0; x < this.gameSize.Width; x++)
                {
                    // forward horiz
                    if (this.board[x, y] == 'M')
                    {
                        run_forward_horizontal = 0;
                    }
                    else if (this.board[x, y] == 'O')
                    {
                        if (run_forward_horizontal >= 2)
                        {
                            possible.Add(
                                new shotPossibilities(
                                    run_forward_horizontal,
                                    new Point(x, y),
                                    true));
                        }
                        else
                        {
                            run_forward_horizontal = 0;
                        }
                    }
                    else
                    {
                        run_forward_horizontal++;
                    }

                    // forward vertical
                    if (this.board[y, x] == 'M')
                    {
                        run_forward_vertical = 0;
                    }
                    else if (this.board[y, x] == 'O')
                    {
                        if (run_forward_vertical >= 2)
                        {
                            possible.Add(
                                new shotPossibilities(
                                    run_forward_vertical,
                                    new Point(y, x),
                                    false));
                        }
                        else
                        {
                            run_forward_vertical = 0;
                        }
                    }
                    else
                    {
                        run_forward_vertical++;
                    }


                    // backward horiz
                    if (this.board[this.gameSize.Width - x - 1, y] == 'M')
                    {
                        run_backward_horizontal = 0;
                    }
                    else if (this.board[this.gameSize.Width - x - 1, y] == 'O')
                    {
                        if (run_backward_horizontal >= 2)
                        {
                            possible.Add(
                                new shotPossibilities(
                                    run_backward_horizontal,
                                    new Point(this.gameSize.Width - x - 1, y),
                                    true));
                        }
                        else
                        {
                            run_backward_horizontal = 0;
                        }
                    }
                    else
                    {
                        run_backward_horizontal++;
                    }


                    // backward vertical
                    if (this.board[y, this.gameSize.Height - x - 1] == 'M')
                    {
                        run_backward_vertical = 0;
                    }
                    else if (this.board[y, this.gameSize.Height - x - 1] == 'O')
                    {
                        if (run_backward_vertical >= 2)
                        {
                            possible.Add(
                                new shotPossibilities(
                                    run_backward_vertical,
                                    new Point(y, this.gameSize.Height - x - 1),
                                    false));
                        }
                        else
                        {
                            run_backward_vertical = 0;
                        }
                    }
                    else
                    {
                        run_backward_vertical++;
                    }

                }

                run_forward_horizontal = 0;
                run_backward_horizontal = 0;
                run_forward_vertical = 0;
                run_backward_vertical = 0;
            }
            Point shot;

            if (possible.Count > 0)
            {
                shotPossibilities shotp = possible.OrderByDescending(a => a.run).First();
                //this.nextShots.Clear();
                shot = shotp.shot;
                //if (shotp.isHorizontal)
                //{
                //    this.nextShots.RemoveAll(p => p.X != shot.X);
                //}
                //else
                //{
                //    this.nextShots.RemoveAll(p => p.Y != shot.Y);
                //}
            }
            else
            {
                shot = new Point(-1, -1);
            }

            return shot;
        }

        private void addToNextShots(Point p)
        {
            if (!this.nextShots.Contains(p) &&
                p.X >= 0 &&
                p.X < this.gameSize.Width &&
                p.Y >= 0 &&
                p.Y < this.gameSize.Height)
            {
                if (this.board[p.X, p.Y] == 'O')
                {
                    this.nextShots.Add(p);
                }
            }
        }

        public void GameWon()
        {
            this.GameWins++;
        }

        public void NewMatch(string opponent)
        {
            System.Threading.Thread.Sleep(5);
            this.rand = new Random(System.Environment.TickCount);
        }
        public void OpponentShot(Point shot) { }
        public void ShotMiss(Point shot)
        {
            this.board[shot.X, shot.Y] = 'M';
        }
        public void GameLost()
        {
            if (showBoard) Console.WriteLine("-----Game Over-----");
        }
        public void MatchOver() { }
    }


    public class OpponentExtended
    {
        public int GameWins { get; set; }
        public int MatchWins { get; set; }
        public OpponentExtended() { }
    }

    public class shotPossibilities
    {
        public shotPossibilities(int r, Point s, bool h)
        {
            this.run = r;
            this.shot = s;
            this.isHorizontal = h;
        }
        public int run { get; set; }
        public Point shot { get; set; }
        public bool isHorizontal { get; set; }
    }
}

我不能参与,但如果我有时间,我将实现以下算法:

首先,当我发现被击中时,我不会立即追击剩下的船只——我会建立一个船的位置表,并在开始完全击沉它们之前确定我是否至少一次击中了所有五艘船。(注意,这是一个糟糕的策略多镜头变体-见评论)

Hit the center (see final note below - 'center' is just a convenience for description) Hit the spot 4 to the right of the center Hit the spot 1 down and one to the right of the center Hit the spot four to the right of the previous hit Continue in that pattern (should end up with diagonal lines separated by 3 spaces filling the board) This should hit all 4 and 5 length boats, and a statistically large number of 3 and 2 boats. Start randomly hitting spots inbetween the diagonals, this will catch the 2 and 3 length boats that haven't already been noticed.

一旦我检测到5个命中,我将确定这5个命中是否在不同的船上。这是相对容易的,只要在两个命中点在同一水平或垂直线上,并且彼此之间有5个位置(可能是同一条船上的两个命中点)的位置附近多拍几次就可以了。如果他们是分开的船,那么继续击沉所有的船。如果发现它们是同一艘船,继续上面的填充模式,直到所有5艘船都被定位。

该算法是一种简单的填充算法。关键的特点是,它不会浪费时间去击沉它知道的船只,当仍然有它不知道的船只时,它不会使用低效的填充模式(即,完全随机的模式将是浪费的)。

最后指出:

一)“中心”是棋盘上的一个随机起点。这消除了该算法的主要弱点。 B)虽然描述表明从一开始就立即绘制对角线,但理想情况下,算法只是在这些对角线上的“随机”位置射击。这有助于防止竞争对手计算他们的船只被可预测的模式击中的时间。

这描述了一个“完美”的算法,因为它可以让所有船只在(9x9)/2+10次射击之内。

但是,它可以显著改善:

一旦一艘船被击中,在做“内部”对角线之前确定它的大小。你可能已经找到了2号船,在这种情况下,内部对角线可以简化以更快地找到3号船。

确定游戏的各个阶段并采取相应的行动。这种算法可能在游戏的某一点上很好,但其他算法可能会在游戏的最后产生更好的收益。此外,如果其他玩家非常接近击败你,另一个算法可能会更好-例如,一个高风险的算法可能更容易失败,但当它起作用时,它会很快起作用,你可能会击败比你更接近胜利的对手。

识别竞争对手的打法——这可能会给你一些线索,让你知道他们是如何规划船只位置的(比如,他们自己的算法很有可能最快速地识别出他们如何放置自己的船只——如果你唯一的工具是锤子,那么所有的东西看起来都像钉子)

亚当

我的条目。

没有什么特别的,我也没有时间把我所有的好主意都加上去。

但它似乎玩得相当不错。我们将看到它在竞争中的表现:

(将此文件放入Missouri.cs并添加到项目中。)

using System;
using System.Collections.ObjectModel;
using System.Drawing;
using System.Collections.Generic;
using System.Linq;
using System.Diagnostics;

namespace Battleship
{
    // The Empire of Japan surrendered on the deck of the USS Missouri on Sept. 2, 1945
    public class USSMissouri : IBattleshipOpponent
    {
        public String  Name    { get { return name; } }
        public Version Version { get { return ver;  } }

#region IBattleship Interface
        // IBattleship::NewGame
        public void NewGame(Size gameSize, TimeSpan timeSpan)
        {
            size      = gameSize;
            shotBoard = new ShotBoard(size);
            attackVector = new Stack<Attack>();
        }

        // IBattleship::PlaceShips
        public void PlaceShips(ReadOnlyCollection<Ship> ships)
        {
            HunterBoard board;
            targetBoards = new List<HunterBoard>();
            shotBoard    = new ShotBoard(size);
            foreach (Ship s in ships)
            {
                board = new HunterBoard(this, size, s);
                targetBoards.Add(board);

                // REWRITE: to ensure valid board placement.
                s.Place(
                    new Point(
                        rand.Next(size.Width),
                        rand.Next(size.Height)),
                    (ShipOrientation)rand.Next(2));
            }
        }

        // IBattleship::GetShot
        public Point GetShot()
        {
            Point p = new Point();

            if (attackVector.Count() > 0)
            {
                p = ExtendShot();
                return p;
            }

            // Contemplate a shot at every-single point, and measure how effective it would be.
            Board potential = new Board(size);
            for(p.Y=0; p.Y<size.Height; ++p.Y)
            {
                for(p.X=0; p.X<size.Width; ++p.X)
                {
                    if (shotBoard.ShotAt(p))
                    {
                        potential[p] = 0;
                        continue;
                    }

                    foreach(HunterBoard b in targetBoards)
                    {
                        potential[p] += b.GetWeightAt(p);
                    }
                }
            }

            // Okay, we have the shot potential of the board.
            // Lets pick a weighted-random spot.
            Point shot;
            shot = potential.GetWeightedRandom(rand.NextDouble());

            shotBoard[shot] = Shot.Unresolved;

            return shot;
        }

        public Point ExtendShot()
        {
            // Lets consider North, South, East, and West of the current shot.
            // and measure the potential of each
            Attack attack = attackVector.Peek();

            Board potential = new Board(size);

            Point[] points = attack.GetNextTargets();
            foreach(Point p in points)
            {
                if (shotBoard.ShotAt(p))
                {
                    potential[p] = 0;
                    continue;
                }

                foreach(HunterBoard b in targetBoards)
                {
                    potential[p] += b.GetWeightAt(p);
                }
            }

            Point shot = potential.GetBestShot();
            shotBoard[shot] = Shot.Unresolved;
            return shot;
        }

        // IBattleship::NewMatch
        public void NewMatch(string opponent)
        {
        }
        public void OpponentShot(Point shot)
        {
        }
        public void ShotHit(Point shot, bool sunk)
        {
            shotBoard[shot] = Shot.Hit;

            if (!sunk)
            {
                if (attackVector.Count == 0) // This is a first hit, open an attackVector
                {   
                    attackVector.Push(new Attack(this, shot));
                }
                else
                {
                    attackVector.Peek().AddHit(shot);    // Add a hit to our current attack.
                }
            }

            // What if it is sunk?  Close the top attack, which we've been pursuing.
            if (sunk)
            {
                if (attackVector.Count > 0)
                {
                    attackVector.Pop();
                }
            }
        }
        public void ShotMiss(Point shot)
        {
            shotBoard[shot] = Shot.Miss;

            foreach(HunterBoard b in targetBoards)
            {
                b.ShotMiss(shot);  // Update the potential map.
            }
        }
        public void GameWon()
        {
            Trace.WriteLine  ("I won the game!");
        }
        public void GameLost()
        {
            Trace.WriteLine  ("I lost the game!");
        }
        public void MatchOver()
        {
            Trace.WriteLine("This match is over.");
        }

#endregion 

        public ShotBoard theShotBoard
        {
            get { return shotBoard; }
        }
        public Size theBoardSize
        {
            get { return size; }
        }

        private Random rand = new Random();
        private Version ver = new Version(6, 3); // USS Missouri is BB-63, hence version 6.3
        private String name = "USS Missouri (abelenky@alum.mit.edu)";
        private Size size;
        private List<HunterBoard> targetBoards;
        private ShotBoard shotBoard;
        private Stack<Attack> attackVector;
    }

    // An Attack is the data on the ship we are currently working on sinking.
    // It consists of a set of points, horizontal and vertical, from a central point.
    // And can be extended in any direction.
    public class Attack
    {
        public Attack(USSMissouri root, Point p)
        {
            Player = root;
            hit = p;
            horzExtent = new Extent(p.X, p.X);
            vertExtent = new Extent(p.Y, p.Y);
        }

        public Extent HorizontalExtent
        {
            get { return horzExtent; }
        }
        public Extent VerticalExtent
        {
            get { return vertExtent; }
        }
        public Point  FirstHit
        {
            get { return hit; }
        }

        public void AddHit(Point p)
        {
            if (hit.X == p.X) // New hit in the vertical direction
            {
                vertExtent.Min = Math.Min(vertExtent.Min, p.Y);
                vertExtent.Max = Math.Max(vertExtent.Max, p.Y);
            }
            else if (hit.Y == p.Y)
            {
                horzExtent.Min = Math.Min(horzExtent.Min, p.X);
                horzExtent.Max = Math.Max(horzExtent.Max, p.X);
            }
        }
        public Point[] GetNextTargets() 
        {
            List<Point> bors = new List<Point>();

            Point p;

            p = new Point(hit.X, vertExtent.Min-1);
            while (p.Y >= 0 && Player.theShotBoard[p] == Shot.Hit)
            {
                if (Player.theShotBoard[p] == Shot.Miss)
                {
                    break; // Don't add p to the List 'bors.  
                }
                --p.Y;
            }
            if (p.Y >= 0 && Player.theShotBoard[p] == Shot.None) // Add next-target only if there is no shot here yet.
            {
                bors.Add(p);
            }

            //-------------------

            p = new Point(hit.X, vertExtent.Max+1);
            while (p.Y < Player.theBoardSize.Height && Player.theShotBoard[p] == Shot.Hit)
            {
                if (Player.theShotBoard[p] == Shot.Miss)
                {
                    break; // Don't add p to the List 'bors.  
                }
                ++p.Y;
            }
            if (p.Y < Player.theBoardSize.Height && Player.theShotBoard[p] == Shot.None)
            {
                bors.Add(p);
            }

            //-------------------

            p = new Point(horzExtent.Min-1, hit.Y);
            while (p.X >= 0 && Player.theShotBoard[p] == Shot.Hit)
            {
                if (Player.theShotBoard[p] == Shot.Miss)
                {
                    break; // Don't add p to the List 'bors.  
                }
                --p.X;
            }
            if (p.X >= 0 && Player.theShotBoard[p] == Shot.None)
            {
                bors.Add(p);
            }

            //-------------------

            p = new Point(horzExtent.Max+1, hit.Y);
            while (p.X < Player.theBoardSize.Width && Player.theShotBoard[p] == Shot.Hit)
            {
                if (Player.theShotBoard[p] == Shot.Miss)
                {
                    break; // Don't add p to the List 'bors.  
                }
                ++p.X;
            }
            if (p.X < Player.theBoardSize.Width && Player.theShotBoard[p] == Shot.None)
            {
                bors.Add(p);
            }

            return bors.ToArray();
        }

        private Point hit; 
        private Extent horzExtent;
        private Extent vertExtent;
        private USSMissouri Player;
    }

    public struct Extent
    {
        public Extent(Int32 min, Int32 max)
        {
            Min = min;
            Max = max;
        }
        public Int32 Min;
        public Int32 Max;
    }

    public class Board  // The potential-Board, which measures the full potential of each square.
    {
        // A Board is the status of many things.
        public Board(Size boardsize)
        {
            size = boardsize;
            grid = new int[size.Width , size.Height];
            Array.Clear(grid,0,size.Width*size.Height);
        }

        public int this[int c,int r]
        {
            get { return grid[c,r];  }
            set { grid[c,r] = value; }
        }
        public int this[Point p]
        {
            get { return grid[p.X, p.Y];  }
            set { grid[p.X, p.Y] = value; }
        }

        public Point GetWeightedRandom(double r)
        {
            Int32 sum = 0;
            foreach(Int32 i in grid)
            {
                sum += i;
            }

            Int32 index = (Int32)(r*sum);

            Int32 x=0, y=0;
            for(y=0; y<size.Height; ++y)
            {
                for(x=0; x<size.Width; ++x)
                {
                    if (grid[x,y] == 0) continue; // Skip any zero-cells
                    index -= grid[x,y];
                    if (index < 0) break;
                }
                if (index < 0) break;
            }

            if (x == 10 || y == 10)
                throw new Exception("WTF");

            return new Point(x,y);
        }

        public Point GetBestShot()
        {
            int max=grid[0,0];
            for(int y=0; y<size.Height; ++y)
            {
                for (int x=0; x<size.Width; ++x)
                {
                    max = (grid[x,y] > max)? grid[x,y] : max;
                }
            }

            for(int y=0; y<size.Height; ++y)
            {
                for (int x=0; x<size.Width; ++x)
                {
                    if (grid[x,y] == max)
                    {
                        return new Point(x,y);
                    }
                }
            }
            return new Point(0,0);
        }

        public bool IsZero()
        {
            foreach(Int32 p in grid)
            {
                if (p > 0)
                {
                    return false;
                }
            }
            return true;
        }

        public override String ToString()
        {
            String output = "";
            String horzDiv = "   +----+----+----+----+----+----+----+----+----+----+\n";
            String disp;
            int x,y;

            output += "      A    B    C    D    E    F    G    H    I    J    \n" + horzDiv;

            for(y=0; y<size.Height; ++y)
            {
                output += String.Format("{0} ", y+1).PadLeft(3);
                for(x=0; x<size.Width; ++x)
                {
                    switch(grid[x,y])
                    {
                        case (int)Shot.None:       disp = "";  break;
                        case (int)Shot.Hit:        disp = "#"; break;
                        case (int)Shot.Miss:       disp = "."; break;
                        case (int)Shot.Unresolved: disp = "?"; break;
                        default:                   disp = "!"; break;
                    }

                    output += String.Format("| {0} ", disp.PadLeft(2));
                }
                output += "|\n" + horzDiv;
            }

            return output;
        }

        protected Int32[,] grid;
        protected Size     size;
    }

    public class HunterBoard
    {
        public HunterBoard(USSMissouri root, Size boardsize, Ship target)
        {
            size = boardsize;
            grid = new int[size.Width , size.Height];
            Array.Clear(grid,0,size.Width*size.Height);

            Player = root;
            Target = target;
            Initialize();
        }

        public void Initialize()
        {
            int x, y, i;

            for(y=0; y<size.Height; ++y)
            {
                for(x=0; x<size.Width - Target.Length+1; ++x)
                {
                    for(i=0; i<Target.Length; ++i)
                    {
                        grid[x+i,y]++;
                    }
                }
            }

            for(y=0; y<size.Height-Target.Length+1; ++y)
            {
                for(x=0; x<size.Width; ++x)
                {
                    for(i=0; i<Target.Length; ++i)
                    {
                        grid[x,y+i]++;
                    }
                }
            }
        }

        public int this[int c,int r]
        {
            get { return grid[c,r];  }
            set { grid[c,r] = value; }
        }
        public int this[Point p]
        {
            get { return grid[p.X, p.Y];  }
            set { grid[p.X, p.Y] = value; }
        }

        public void ShotMiss(Point p)
        {
            int x,y;
            int min, max;

            min = Math.Max(p.X-Target.Length+1, 0);
            max = Math.Min(p.X, size.Width-Target.Length);
            for(x=min; x<=max; ++x)
            {
                DecrementRow(p.Y, x, x+Target.Length-1);
            }

            min = Math.Max(p.Y-Target.Length+1, 0);
            max = Math.Min(p.Y, size.Height-Target.Length);
            for(y=min; y<=max; ++y)
            {
                DecrementColumn(p.X, y, y+Target.Length-1);
            } 

            grid[p.X, p.Y] = 0;
        }

        public void ShotHit(Point p)
        {
        }

        public override String ToString()
        {
            String output = String.Format("Target size is {0}\n", Target.Length);
            String horzDiv = "   +----+----+----+----+----+----+----+----+----+----+\n";
            int x,y;

            output += "      A    B    C    D    E    F    G    H    I    J    \n" + horzDiv;
            for(y=0; y<size.Height; ++y)
            {
                output += String.Format("{0} ", y+1).PadLeft(3);
                for(x=0; x<size.Width; ++x)
                {
                    output += String.Format("| {0} ", grid[x,y].ToString().PadLeft(2));
                }
                output += "|\n" + horzDiv;
            }
            return output;
        }

        // If we shoot at point P, how does that affect the potential of the board?
        public Int32 GetWeightAt(Point p)
        {
            int x,y;
            int potential = 0;
            int min, max;

            min = Math.Max(p.X-Target.Length+1, 0);
            max = Math.Min(p.X, size.Width-Target.Length);
            for(x=min; x<=max; ++x)
            {
                if (Player.theShotBoard.isMissInRow(p.Y, x, x+Target.Length-1) == false)
                {
                    ++potential;
                }
            }

            min = Math.Max(p.Y-Target.Length+1, 0);
            max = Math.Min(p.Y, size.Height-Target.Length);
            for(y=min; y<=max; ++y)
            {
                if (Player.theShotBoard.isMissInColumn(p.X, y, y+Target.Length-1) == false)
                {
                    ++potential;
                }
            } 

            return potential;
        }

        public void DecrementRow(int row, int rangeA, int rangeB)
        {
            int x;
            for(x=rangeA; x<=rangeB; ++x)
            {
                grid[x,row] = (grid[x,row]==0)? 0 : grid[x,row]-1;
            }
        }
        public void DecrementColumn(int col, int rangeA, int rangeB)
        {
            int y;
            for(y=rangeA; y<=rangeB; ++y)
            {
                grid[col,y] = (grid[col,y]==0)? 0 : grid[col,y]-1;
            }
        }

        private Ship Target = null;
        private USSMissouri Player;
        private Int32[,] grid;
        private Size     size;
    }

    public enum Shot
    {
        None = 0,
        Hit = 1,
        Miss = 2,
        Unresolved = 3
    };

    public class ShotBoard
    {
        public ShotBoard(Size boardsize)
        {
            size = boardsize;
            grid = new Shot[size.Width , size.Height];

            for(int y=0; y<size.Height; ++y)
            {
                for(int x=0; x<size.Width; ++x)
                {
                    grid[x,y] = Shot.None;
                }
            }
        }

        public Shot this[int c,int r]
        {
            get { return grid[c,r];  }
            set { grid[c,r] = value; }
        }
        public Shot this[Point p]
        {
            get { return grid[p.X, p.Y];  }
            set { grid[p.X, p.Y] = value; }
        }

        public override String ToString()
        {
            String output = "";
            String horzDiv = "   +----+----+----+----+----+----+----+----+----+----+\n";
            String disp;
            int x,y;

            output += "      A    B    C    D    E    F    G    H    I    J    \n" + horzDiv;

            for(y=0; y<size.Height; ++y)
            {
                output += String.Format("{0} ", y+1).PadLeft(3);
                for(x=0; x<size.Width; ++x)
                {
                    switch(grid[x,y])
                    {
                        case Shot.None:       disp = "";  break;
                        case Shot.Hit:        disp = "#"; break;
                        case Shot.Miss:       disp = "."; break;
                        case Shot.Unresolved: disp = "?"; break;
                        default:              disp = "!"; break;
                    }

                    output += String.Format("| {0} ", disp.PadLeft(2));
                }
                output += "|\n" + horzDiv;
            }
            return output;
        }

        // Functions to find shots on the board, at a specific point, or in a row or column, within a range
        public bool ShotAt(Point p)
        {
            return !(this[p]==Shot.None);
        }
        public bool isMissInColumn(int col, int rangeA, int rangeB)
        {
            for(int y=rangeA; y<=rangeB; ++y)
            {
                if (grid[col,y] == Shot.Miss)
                {
                    return true;
                }
            }
            return false;
        }
        public bool isMissInRow(int row, int rangeA, int rangeB)
        {
            for(int x=rangeA; x<=rangeB; ++x)
            {
                if (grid[x,row] == Shot.Miss)
                {
                    return true;
                }
            }
            return false;
        }
        protected Shot[,] grid;
        protected Size     size;
    }
}