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

实际上,我认为这个谜题最大的问题在于它本质上是两个步骤。一个步骤是放置你的船只,另一个步骤是找到敌人的船只(不管第二部分是如何分割的,除了尝试用随机因素打败时间外,它只是“运行你的算法”)。游戏中不存在决定并反击敌人策略的机制,这也是基于连续回合的“石头剪刀布”的类似竞争非常有趣的原因。

此外,我认为如果你将游戏指定为网络协议,然后提供框架以c#实现该协议,而不是规定所有解决方案都应该是c#,这将更酷,但这只是我的观点。

编辑:我取消我最初的观点,因为我没有足够仔细地阅读比赛规则。

其他回答

这是一个供人们玩的对手:

http://natekohl.net/files/FarnsworthOpponent.cs

与其使用固定的几何启发策略,我认为尝试估计任何特定的未探索空间拥有一艘船的潜在概率会很有趣。

为了做到这一点,你需要探索所有符合你当前世界观的船的可能配置,然后基于这些配置计算概率。你可以把它想象成探索一棵树:

扩大可能的战列舰国家http://natekohl.net/media/battleship-tree.png

在考虑了所有与你所了解的世界相冲突的树叶后(游戏邦注:例如,船只不能重叠,所有被击中的方块都必须是船只等),你可以计算船只在每个未探索位置出现的频率,从而估算船只位于那里的可能性。

这可以可视化为热图,其中热点更有可能包含船只:

每个未开发位置的概率热图http://natekohl.net/media/battleship-probs.png

我喜欢这个战列舰比赛的一个原因是上面的树几乎小到可以强制使用这种算法。如果这5艘船每艘都有150个可能的位置,那就是1505 = 750亿种可能性。这个数字只会越来越小,特别是如果你可以排除整艘船。

我上面链接的对手并没有探索整棵树;750亿美元仍然太大,无法在一秒钟内进入。不过,在一些启发式的帮助下,它确实试图估计这些概率。

这是我的入口!(最天真的解决方案)

“随机1.1”

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

    public class RandomOpponent : IBattleshipOpponent
    {
        public string Name { get { return "Random"; } }
        public Version Version { get { return this.version; } }

        Random rand = new Random();
        Version version = new Version(1, 1);
        Size gameSize;

        public void NewGame(Size size, TimeSpan timeSpan)
        {
            this.gameSize = size;
        }

        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()
        {
            return new Point(
                rand.Next(this.gameSize.Width),
                rand.Next(this.gameSize.Height));
        }

        public void NewMatch(string opponent) { }
        public void OpponentShot(Point shot) { }
        public void ShotHit(Point shot, bool sunk) { }
        public void ShotMiss(Point shot) { }
        public void GameWon() { }
        public void GameLost() { }
        public void MatchOver() { }
    }
}

这不是一个完全成熟的答案,但用常见的代码来混淆真实的答案似乎没有什么意义。 因此,我将本着开放源码的精神介绍一些扩展/通用类。 如果你使用这些,那么请更改名称空间或试图将所有内容编译到一个dll中是行不通的。

BoardView可以让您轻松地使用带注释的板。

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Drawing;
using System.IO;

namespace Battleship.ShuggyCoUk
{
    public enum Compass
    {
        North,East,South,West
    }

    class Cell<T>
    {
        private readonly BoardView<T> view;
        public readonly int X;
        public readonly int Y;
        public T Data;
        public double Bias { get; set; }

        public Cell(BoardView<T> view, int x, int y) 
        { 
            this.view = view; this.X = x; this.Y = y; this.Bias = 1.0;  
        }

        public Point Location
        {
            get { return new Point(X, Y); }
        }

        public IEnumerable<U> FoldAll<U>(U acc, Func<Cell<T>, U, U> trip)
        {
            return new[] { Compass.North, Compass.East, Compass.South, Compass.West }
                .Select(x => FoldLine(x, acc, trip));
        }

        public U FoldLine<U>(Compass direction, U acc, Func<Cell<T>, U, U> trip)
        {
            var cell = this;
            while (true)
            {
                switch (direction)
                {
                    case Compass.North:
                        cell = cell.North; break;
                    case Compass.East:
                        cell = cell.East; break;
                    case Compass.South:
                        cell = cell.South; break;
                    case Compass.West:
                        cell = cell.West; break;
                }
                if (cell == null)
                    return acc;
                acc = trip(cell, acc);
            }
        }

        public Cell<T> North
        {
            get { return view.SafeLookup(X, Y - 1); }
        }

        public Cell<T> South
        {
            get { return view.SafeLookup(X, Y + 1); }
        }

        public Cell<T> East
        {
            get { return view.SafeLookup(X+1, Y); }
        }

        public Cell<T> West
        {
            get { return view.SafeLookup(X-1, Y); }
        }

        public IEnumerable<Cell<T>> Neighbours()
        {
            if (North != null)
                yield return North;
            if (South != null)
                yield return South;
            if (East != null)
                yield return East;
            if (West != null)
                yield return West;
        }
    }

    class BoardView<T>  : IEnumerable<Cell<T>>
    {
        public readonly Size Size;
        private readonly int Columns;
        private readonly int Rows;

        private Cell<T>[] history;

        public BoardView(Size size)
        {
            this.Size = size;
            Columns = size.Width;
            Rows = size.Height;
            this.history = new Cell<T>[Columns * Rows];
            for (int y = 0; y < Rows; y++)
            {
                for (int x = 0; x < Rows; x++)
                    history[x + y * Columns] = new Cell<T>(this, x, y);
            }
        }

        public T this[int x, int y]
        {
            get { return history[x + y * Columns].Data; }
            set { history[x + y * Columns].Data = value; }
        }

        public T this[Point p]
        {
            get { return history[SafeCalc(p.X, p.Y, true)].Data; }
            set { this.history[SafeCalc(p.X, p.Y, true)].Data = value; }
        }

        private int SafeCalc(int x, int y, bool throwIfIllegal)
        {
            if (x < 0 || y < 0 || x >= Columns || y >= Rows)
            {    if (throwIfIllegal)
                    throw new ArgumentOutOfRangeException("["+x+","+y+"]");
                 else
                    return -1;
            }
            return x + y * Columns;
        }

        public void Set(T data)
        {
            foreach (var cell in this.history)
                cell.Data = data;
        }

        public Cell<T> SafeLookup(int x, int y)
        {
            int index = SafeCalc(x, y, false);
            if (index < 0)
                return null;
            return history[index];
        }

        #region IEnumerable<Cell<T>> Members

        public IEnumerator<Cell<T>> GetEnumerator()
        {
            foreach (var cell in this.history)
                yield return cell;
        }

        System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator()
        {
            return this.GetEnumerator();
        }

        public BoardView<U> Transform<U>(Func<T, U> transform)
        {
            var result = new BoardView<U>(new Size(Columns, Rows));
            for (int y = 0; y < Rows; y++)
            {
                for (int x = 0; x < Columns; x++)
                {
                    result[x,y] = transform(this[x, y]);
                }
            }
            return result;
        }

        public void WriteAsGrid(TextWriter w)
        {
            WriteAsGrid(w, "{0}");
        }

        public void WriteAsGrid(TextWriter w, string format)
        {
            WriteAsGrid(w, x => string.Format(format, x.Data));
        }

        public void WriteAsGrid(TextWriter w, Func<Cell<T>,string> perCell)
        {
            for (int y = 0; y < Rows; y++)
            {
                for (int x = 0; x < Columns; x++)
                {
                    if (x != 0)
                        w.Write(",");
                    w.Write(perCell(this.SafeLookup(x, y)));
                }
                w.WriteLine();
            }
        }

        #endregion
    }
}

有些扩展,有些复制了主框架中的功能,但应该由你自己完成。

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

namespace Battleship.ShuggyCoUk
{
    public static class Extensions
    {        
        public static bool IsIn(this Point p, Size size)
        {
            return p.X >= 0 && p.Y >= 0 && p.X < size.Width && p.Y < size.Height;
        }

        public static bool IsLegal(this Ship ship,
            IEnumerable<Ship> ships, 
            Size board,
            Point location, 
            ShipOrientation direction)
        {
            var temp = new Ship(ship.Length);
            temp.Place(location, direction);
            if (!temp.GetAllLocations().All(p => p.IsIn(board)))
                return false;
            return ships.Where(s => s.IsPlaced).All(s => !s.ConflictsWith(temp));
        }

        public static bool IsTouching(this Point a, Point b)
        {
            return (a.X == b.X - 1 || a.X == b.X + 1) &&
                (a.Y == b.Y - 1 || a.Y == b.Y + 1);
        }

        public static bool IsTouching(this Ship ship,
            IEnumerable<Ship> ships,
            Point location,
            ShipOrientation direction)
        {
            var temp = new Ship(ship.Length);
            temp.Place(location, direction);
            var occupied = new HashSet<Point>(ships
                .Where(s => s.IsPlaced)
                .SelectMany(s => s.GetAllLocations()));
            if (temp.GetAllLocations().Any(p => occupied.Any(b => b.IsTouching(p))))
                return true;
            return false;
        }

        public static ReadOnlyCollection<Ship> MakeShips(params int[] lengths)
        {
            return new System.Collections.ObjectModel.ReadOnlyCollection<Ship>(
                lengths.Select(l => new Ship(l)).ToList());       
        }

        public static IEnumerable<T> Shuffle<T>(this IEnumerable<T> source, Rand rand)
        {
            T[] elements = source.ToArray();
            // Note i > 0 to avoid final pointless iteration
            for (int i = elements.Length - 1; i > 0; i--)
            {
                // Swap element "i" with a random earlier element it (or itself)
                int swapIndex = rand.Next(i + 1);
                T tmp = elements[i];
                elements[i] = elements[swapIndex];
                elements[swapIndex] = tmp;
            }
            // Lazily yield (avoiding aliasing issues etc)
            foreach (T element in elements)
            {
                yield return element;
            }
        }

        public static T RandomOrDefault<T>(this IEnumerable<T> things, Rand rand)
        {
            int count = things.Count();
            if (count == 0)
                return default(T);
            return things.ElementAt(rand.Next(count));
        }
    }
}

我经常用的东西。

enum OpponentsBoardState
{
    Unknown = 0,
    Miss,
    MustBeEmpty,        
    Hit,
}

随机化。 安全但可测试,对测试有用。

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Drawing;

namespace Battleship.ShuggyCoUk
{
    public class Rand
    {
        Random r;

        public Rand()
        {
            var rand = System.Security.Cryptography.RandomNumberGenerator.Create();
            byte[] b = new byte[4];
            rand.GetBytes(b);
            r = new Random(BitConverter.ToInt32(b, 0));
        }

        public int Next(int maxValue)
        {
            return r.Next(maxValue);
        }

        public double NextDouble(double maxValue)
        {
            return r.NextDouble() * maxValue;
        }

        public T Pick<T>(IEnumerable<T> things)
        {
            return things.ElementAt(Next(things.Count()));
        }

        public T PickBias<T>(Func<T, double> bias, IEnumerable<T> things)
        {
            double d = NextDouble(things.Sum(x => bias(x)));
            foreach (var x in things)
            {
                if (d < bias(x))
                    return x;
                d -= bias(x);                
            }
            throw new InvalidOperationException("fell off the end!");
        }
    }
}

实际上,我认为这个谜题最大的问题在于它本质上是两个步骤。一个步骤是放置你的船只,另一个步骤是找到敌人的船只(不管第二部分是如何分割的,除了尝试用随机因素打败时间外,它只是“运行你的算法”)。游戏中不存在决定并反击敌人策略的机制,这也是基于连续回合的“石头剪刀布”的类似竞争非常有趣的原因。

此外,我认为如果你将游戏指定为网络协议,然后提供框架以c#实现该协议,而不是规定所有解决方案都应该是c#,这将更酷,但这只是我的观点。

编辑:我取消我最初的观点,因为我没有足够仔细地阅读比赛规则。

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;
    }
}