Pseudo 'random' even distribution table

In my last post, I discussed what a co-prime is and showed you to find them.

So, what's so special about relatively prime numbers? Well, then can be used to create an one-for-one distribution table that is seemingly random, but is deterministically calculated (created).

To understand what I mean, picture the face of a clock...

It has the hours 1 through 12, and if you and an hour to 12, you get 1. This can also be thought of as a single digit in a base 12 number system. Now we need a co-prime to 12. 7 is relatively prime to 12, so lets choose 7.

Starting at hour 1, if we add 7 hours, it will be 8. If we add 7 more hours, we will get 3. 7 more, 10. If we keep adding 7 hours to our clock, the hour hand will land on each of the different numbers exactly once before repeating itself, 12 steps later. Intrigued yet?

If, say, we find a co-prime to the largest number that can be represented by a byte (8-bits, 256 [also expressed as 2^8=256 or 8=Log2(256)]), we can create an array of bytes with a length of 256, containing each of the 256 different possible bytes, distributed in a seemingly random order. The discrete order, or sequence, in which each each number is visited it completely dependent on the value of the co-prime that was selected.

This table is now essentially a one-to-one, bijective mapping of one byte to another. To express this mapping to another party, say to map a stream of bytes back to their original values (decrypt), the entire table need not be exchanged, only the co-prime.

This provides a foundation for an encryption scheme who's technical requirements are similar to handling a cipher-block-chain (CBC) and its changing IV (initialization vector).

Now, it it easy to jump to the conclusion that such an encryption scheme is less secure than a CBC, but this is not necessarily the case. While this approach may be conceptually more simple, the difficulty of discovering the sequence can be made arbitrarily hard.

First of all, the number of relatively prime numbers to 256 is probably infinite. A co-prime to 256 does not have to be less than 256. Indeed, it may be several thousand time greater than 256. Additionally, any prime greater than 256 is, by definition, co-prime to 256, and likely will have a seemingly more 'random' distribution/appearance.

There is, however, a limit here. It does not have to do with the number of co-primes, but is instead limited by the number of possible sequences that can be represented by our array of 256 bytes; eventually, two different co-primes are going to map to the same unique sequence. The order matters, and we don't allow repetition to exist in our sequence. This is called a permutation without repetition, and can be expressed as 256! or 256 factorial and is instructing one to calculate the product of 256 * 255 * 254 * 253 * [...] * 6 * 5 * 4 * 3 * 2 * 1, which equals exactly this number:

857817775342842654119082271681232625157781520279485619859655650377269452553147589377440291360451408450375885342336584306157196834693696475322289288497426025679637332563368786442675207626794560187968867971521143307702077526646451464709187326100832876325702818980773671781454170250523018608495319068138257481070252817559459476987034665712738139286205234756808218860701203611083152093501947437109101726968262861606263662435022840944191408424615936000000000000000000000000000000000000000000000000000000000000000

Yeah, that's right, that number has exactly 63 zeros on the end and is 507 digits long. (As an aside, the reason there is so many zeros on the end of this number is, well for one it is highly composite, but more specifically, its prime factorization includes 2^255 and 5^63 and so 63 fives multiply with 63 of those twos to make 63 tens, and hence that many zeros.)

Above I said arbitrarily hard. So far we have only considered one table, but try and fathom the complexity of many tables. I present three different ways to use multiple tables; Nested, sequentially, and mangled.
Furthermore, the distribution tables can be discarded and replaced.

I will explain what those mean and finish this post tomorrow.

Topmost window always on top

This project was inspired by PowerMenu 1.51 by Thong Nyguyen. I wrote a small C# system tray application that provides some of the same functionality as PowerMenu. It can set/unset any application window as always on top or topmost. This is useful if you want to compare or edit two documents at once and you want to make a window float, sticky, or pin a window on top. I wrote this tool in C# and am giving you the source code here so you can see how it works. Since .NET does not support such level of control over other applications, our code must call the native WIN32 APIs SetWindowPos and FindWindow to accomplish this.

Besides being a system tray application (NotifyIcon), the application essentially has two main functions: GetWindowTitles(), which uses the Process class to return a list of windows' titles as an array of strings, and AssignTopmostWindow() which takes a windows title as a parameter.

But first, we must define our WIN32 API imports:

#region WIN32API
static readonly IntPtr HWND_TOPMOST = new IntPtr(-1);
static readonly IntPtr HWND_NOTOPMOST = new IntPtr(-2);
const UInt32 SWP_SHOWWINDOW = 0x0040;

[StructLayout(LayoutKind.Sequential)]
public struct RECT
{
    public int Left, Top, Right, Bottom;
    public RECT(int left,int top,int right,int bottom) {
        Left=left; Top=top; Right=right; Bottom=bottom; }
    public RECT(System.Drawing.Rectangle r) : this(r.Left, r.Top, r.Right, r.Bottom) { }
    public int X { get { return Left; } set { Right -= (Left - value); Left = value; } }
    public int Y { get { return Top; } set { Bottom -= (Top - value); Top = value; } }
    public int Height { get { return Bottom - Top; } set { Bottom = value + Top; } }
    public int Width { get { return Right - Left; } set { Right = value + Left; } }
    public static implicit operator System.Drawing.Rectangle(RECT r) {
        return new System.Drawing.Rectangle(r.Left, r.Top, r.Width, r.Height); }
    public static implicit operator RECT(System.Drawing.Rectangle r) { return new RECT(r); }
}

[DllImport("user32.dll", SetLastError = true)]
private static extern IntPtr FindWindow(String lpClassName, String lpWindowName);

[DllImport("user32.dll")]
[return: MarshalAs(UnmanagedType.Bool)]
public static extern bool GetWindowRect(HandleRef hwnd, out RECT lpRect);

[DllImport("user32.dll")]
[return: MarshalAs(UnmanagedType.Bool)]
private static extern bool SetWindowPos(IntPtr hWnd, IntPtr hWndInsertAfter,
                                        int x, int y, int cx, int cy, uint uFlags );
#endregion

Notice the RECT structure. The WIN32 RECT struct is different than the .NET version, and we need it to store and pass the window position during our call to SetWindowPos() or the window will likely disappear during resizing.

Here you can see in our implementation of AssignTopmostWindow, we get the window rectangle with GetWindowRect() and pass it straight to our call to SetWindowPos():

bool AssignTopmostWindow(string windowTitle,bool makeTopmost)
{
 IntPtr hWnd = FindWindow((string)null,windowTitle);
 
 RECT rect = new RECT();
 GetWindowRect(new HandleRef(this,hWnd),out rect);
 
 return SetWindowPos(hWnd,
              makeTopmost ? HWND_TOPMOST : HWND_NOTOPMOST,
              rect.X, rect.Y, rect.Width, rect.Height,
              SWP_SHOWWINDOW);
}

So your application is first going to want to get the titles of all the forms and windows:

string[] GetWindowTitles()
{
 List<string> winList = new List<string>();
 
 Process[] procArray = Process.GetProcesses();
 foreach(Process proc in procArray)
 {
  if(!string.IsNullOrWhiteSpace(proc.MainWindowTitle))
  {
   winList.Add(proc.MainWindowTitle);
  }
 }
 return winList.ToArray();
}

Then your application must then fill a listbox or somehow display this data to the user for selection. I choose to populate a dynamic context menu for my NotifyIcon application:

private MenuItem[] DynamicMenu()
{
 string[] titleArray = GetWindowTitles();
 
 List<MenuItem> menuList = new List<MenuItem>();
 foreach(string title in titleArray)
 {
  if(changeLog.ContainsKey(title))
  {
   if(changeLog[title])
   {
    menuList.Add(new MenuItem("* " + title, menuWinClick));
   }
   else
   {
    menuList.Add(new MenuItem(title, menuWinClick));
   }
  }
  else
  {
   menuList.Add(new MenuItem(title, menuWinClick));
  }
 }
 menuList.Add(new MenuItem("_____________"));
 menuList.Add(new MenuItem("About", menuAboutClick));
 menuList.Add(new MenuItem("Exit", menuExitClick));
 
 return menuList.ToArray();
}

Once the user has made a selection, a call to AssignTopmostWindow is made.

If your application should happen to exit without another call to AssignTopmostWindow(selectedTitle,false) to undo the topmost property, the window will remain topmost until reboot. As this is likely undesirable behavior, . My solution was to create a dictionary to keep track of the windows whose topmost property was modified, and 'roll back' those changes when your program/form is ending/closing:

private Dictionary<string,bool> changeLog = new Dictionary<string, bool>();

private void menuExitClick(object sender, EventArgs e)
{
 // Roll-back changes by
 //  unsetting every topmost window
 foreach(KeyValuePair<string,bool> entry in changeLog)
 {
  if(entry.Value) // If topmost
  {
   AssignTopmostWindow(entry.Key,false);
  }
 }   
 Application.Exit();
}

Here is the full code.

Greatest common divisor & Co-primeness

Below are three different methods for finding the greatest common divisor of a number. I provide a method using modulus, one using Euclid's method, and one that uses the Stein method.

Believe it or not, the modulus method has the best performance. I would have guessed the Stein method. Credit goes to blackwasp for the stein method.

public static uint FindGCDModulus(uint value1, uint value2)
{
        while(value1 != 0 && value2 != 0)
        {
                if (value1 > value2)
                {
                        value1 %= value2;
                }
                else
                {
                        value2 %= value1;
                }
        }
        return Math.Max(value1, value2);
}

public static uint FindGCDEuclid(uint value1, uint value2)
{
        while(value1 != 0 && value2 != 0)
        {
                if (value1 > value2)
                {
                        value1 -= value2;
                }
                else
                {
                        value2 -= value1;
                }
        }
        return Math.Max(value1, value2);
}

public static uint FindGCDStein(uint value1, uint value2)
{
        if (value1 == 0) return value2;
        if (value2 == 0) return value1;
        if (value1 == value2) return value1;

        bool value1IsEven = (value1 & 1u) == 0;
        bool value2IsEven = (value2 & 1u) == 0;
                       
        if (value1IsEven && value2IsEven)
        {
                return FindGCDStein(value1 >> 1, value2 >> 1) << 1;
        }
        else if (value1IsEven && !value2IsEven)
        {
                return FindGCDStein(value1 >> 1, value2);
        }
        else if (value2IsEven)
        {
                return FindGCDStein(value1, value2 >> 1);
        }
        else if (value1 > value2)
        {
                return FindGCDStein((value1 - value2) >> 1, value2);
        }
        else
        {
                return FindGCDStein(value1, (value2 - value1) >> 1);
        }
}

Here are the results of my benchmark tests:

Stein: 36.4657 milliseconds.
Euclid: 31.2369 milliseconds.
Modulus: 7.5199 milliseconds.



Yeah, I couldn't believe it either, the modulus approach is the fastest!

Here is the benchmark code that I created:

public class CodeStopwatch
{
        //int m_pointer;
        Stopwatch m_elapsed;
        
        public CodeStopwatch()
        {
                Reset();
        }

        public double Stop()
        {
                m_elapsed.Stop();
                return m_elapsed.Elapsed.TotalMilliseconds;
        }
        
        public void Reset()
        {
                GC.Collect(GC.MaxGeneration);
                m_elapsed = new Stopwatch();
                m_elapsed.Start();
        }
}

public class CoprimeBenchmark
{
        public delegate bool IsCoprimeDelegate(uint value1, uint value2);
        public List<uint> FindCoprimesDelegate(uint quantity,IsCoprimeDelegate isCoprime)
        {
                List<uint> results = new List<uint>();
                if(quantity<2) {
                        return results;
                }
                
                for (uint count = 2; count < quantity; count++)
                {
                        if(isCoprime(count,quantity))
                        {
                                results.Add(count);
                        }
                }
                return results;
        }
        
        public static bool IsCoprimeModulus(uint value1, uint value2)
        {
                return FindGCDModulus(value1, value2) == 1;
        }
        
        public static bool IsCoprimeEuclid(uint value1, uint value2)
        {
                return FindGCDEuclid(value1, value2) == 1;
        }
        
        public static bool IsCoprimeStein(uint value1, uint value2)
        {
                return FindGCDStein(value1, value2) == 1;
        }

        // [ Please refer to methods above. Ommited for brevity. ]
        public static uint FindGCDModulus(uint value1, uint value2) { ... }
        public static uint FindGCDEuclid(uint value1, uint value2) { ... }
        public static uint FindGCDStein(uint value1, uint value2) { ... }
}

Usage of above classes:

// Button OnClick event
void ButtonBenchmarkClick(object sender, EventArgs e)
{
        uint number = 50000;
        List<uint> resultsStein = new List<uint>();
        List<uint> resultsEuclid = new List<uint>();
        List<uint> resultsModulus = new List<uint>();
        
        CoprimeBenchmark cop = new CoprimeBenchmark();
        
        CodeStopwatch time = new CodeStopwatch();
        resultsStein = cop.FindCoprimesDelegate(number,CoprimeBenchmark.IsCoprimeStein);
        string stein = time.Stop().ToString();
        
        time = new CodeStopwatch();
        resultsEuclid = cop.FindCoprimesDelegate(number,CoprimeBenchmark.IsCoprimeEuclid);
        string euclid = time.Stop().ToString();
        
        time = new CodeStopwatch();
        resultsModulus = cop.FindCoprimesDelegate(number,CoprimeBenchmark.IsCoprimeModulus);
        string modulus = time.Stop().ToString();
        
        textBoxOutput.Text = "Stein:\t" + stein + " milliseconds." + Environment.NewLine;
        textBoxOutput.Text += "Euclid:\t" + euclid + " milliseconds." + Environment.NewLine;
        textBoxOutput.Text += "Modulus:\t" + modulus + " milliseconds." + Environment.NewLine;
        
        textBoxOutput.Text += Environment.NewLine + Environment.NewLine;
        foreach(uint a in resultsStein)
        {
                textBoxOutput.Text += a.ToString() + Environment.NewLine;
        }
        
        textBoxOutput.Text += Environment.NewLine + Environment.NewLine;
        foreach(uint b in resultsEuclid)
        {
                textBoxOutput.Text += b.ToString() + Environment.NewLine;
        }
        
        textBoxOutput.Text += Environment.NewLine + Environment.NewLine;
        foreach(uint c in resultsModulus)
        {
                textBoxOutput.Text += c.ToString() + Environment.NewLine;
        }
}

--

Now, I will take the fastest algorithm and show you the code for finding co-primness and a list of co-primes for a given number.

Finding co-primness is simple; Two numbers are relatively prime to each other if their greatest common divisor is equal to one.

My function FindCoprimes returns a List<uint> of co-primes given a number and a range

public static class Coprimes
{
        public static List<uint> FindCoprimes(uint number,uint min,uint max)
        {
                if(max<2 || min<2 || max<=min || number<1) {    return null;    }
                
                List<uint> results = new List<uint>();
                for(uint counter = min; counter<max; counter++) {
                        if(IsCoprime(number,counter)) {
                                results.Add(counter);
                        }
                }
                return results;
        }
       
        public static bool IsCoprime(uint value1, uint value2)
        {
                return FindGCDModulus(value1, value2) == 1;
        }
}

Pretty easy!

What is so special about co-primes? Well, one thing I use co-primes for is for making an evenly distributed table. For an explanation and the code, see my post on Evenly Distributed Tables.

Captcha: Drawing Text along a Bézier Spline

The following post/code will achieve something to the effect of:

All this code, and this article was inspired by planetclegg.com/projects/WarpingTextToSplines.html.
Explanation of the math and why it works will come shortly. In the meantime, please see the above link for a detailed explanation.

This code assumes you have already drawn some text on your GraphicsPath. Here is the code to transform your GraphicsPath text to follow a cubic Bézier Spline:

GraphicsPath BezierWarp(GraphicsPath text,Size size)
{
 // Control points for a cubic Bézier spline
 PointF P0 = new PointF();
 PointF P1 = new PointF();
 PointF P2 = new PointF();
 PointF P3 = new PointF();
 
 float shrink = 20;
 float shift = 0;
 
 P0.X = shrink;
 P0.Y = shrink+shift;
 P1.X = size.Width-shrink;
 P1.Y = shrink;
 P2.X = shrink;
 P2.Y = size.Height-shrink;
 P3.X = size.Width-shrink;
 P3.Y = size.Height-shrink-shift;

 // Calculate coefficients A thru H from the control points
 float A = P3.X - 3 * P2.X + 3 * P1.X - P0.X;
 float B = 3 * P2.X - 6 * P1.X + 3 * P0.X;
 float C = 3 * P1.X - 3 * P0.X;
 float D = P0.X;

 float E = P3.Y - 3 * P2.Y + 3 * P1.Y - P0.Y;
 float F = 3 * P2.Y - 6 * P1.Y + 3 * P0.Y;
 float G = 3 * P1.Y - 3 * P0.Y;
 float H = P0.Y;

 PointF[] pathPoints = text.PathPoints;
 RectangleF textBounds = text.GetBounds();
 
 for (int i =0; i  < pathPoints.Length; i++)
 {
  PointF pt = pathPoints[i];
  float textX = pt.X;
  float textY = pt.Y;
  
  // Normalize the x coordinate into the parameterized
  // value with a domain between 0 and 1.
  float t  =  textX / textBounds.Width;
  float t2 = (t * t);
  float t3 = (t * t * t);
  
  // Calculate spline point for parameter t
  float Sx = A * t3 + B * t2 + C * t + D;
  float Sy = E * t3 + F * t2 + G * t + H;
  
  // Calculate the tangent vector for the point
  float Tx = 3 * A * t2 + 2 * B * t + C;
  float Ty = 3 * E * t2 + 2 * F * t + G;

  // Rotate 90 or 270 degrees to make it a perpendicular
  float Px = - Ty;
  float Py =   Tx;
  
  // Normalize the perpendicular into a unit vector
  float magnitude = (float)Math.Sqrt((Px*Px) + (Py*Py));
  Px /= magnitude;
  Py /= magnitude;
  
  // Assume that input text point y coord is the "height" or
  // distance from the spline.  Multiply the perpendicular
  // vector with y. it becomes the new magnitude of the vector
  Px *= textY;
  Py *= textY;
  
  // Translate the spline point using the resultant vector
  float finalX = Px + Sx;
  float finalY = Py + Sy;
  
  pathPoints[i] = new PointF(finalX, finalY);
 }
 
 return new GraphicsPath(pathPoints,text.PathTypes);
}

Humorous Software License Agreement

Software Usage License Agreement
Copyright (C) [year] [copyright holders]

This software, it's code, or any fan fiction resulting from its enormous popularity, is provided "AS IS". That means that the software included with with this license is provided without warranty, regardless of any previous verbal contract you may have swindled out of the author with your fast words on the phone...
To the maximum extent permitted by law, the author of this software disclaims all liability for any damages, lost profits, lost socks, lost puppies, hair loss, or architectural fanaticism and cults that may occur as a result of using this software. Under no circumstances shall the author of this software, nor his pet cat 'Mr.Whiskers', be held legally, financially or morally liable for any claim of damages or liability resulting from the use of, abstinence from, ritualistic worshiping of, or illegal pirating of this software. This includes, but is not limited to, lost profits, stolen data, bankruptcy, autonomous homicidal cyborgs or man-eating miniature pony attacks.
Use at your own risk! This software comes with no guarantees of fitness for any purpose, so do not use it for the back-end of your fortune 500 business without at least hiring me first.

Information entropy and data compression

In my last post, I talked about Shannon data entropy and showed a class to calculate that. Lets take it one step further and actually compress some data based off the data entropy we calculated.

To do this, first we calculate how many bits are needed to compress each byte of our data. Theoretically, this is the data entropy, rounded up to the next whole number (Math.Ceiling). But this is not always the case, and the number of unique symbols in our data may be a number that is too large to be represented in that many number of bits. We calculate the number of bits needed to represent the number of unique symbols by getting its Base2 logarithm. This returns a decimal (double), so we use Math.Ceiling to round to up to the nearest whole number as well. We set entropy_Ceiling to which ever number is larger. If the entropy_Ceiling is 8, then we should immediately return, as we cannot compress the data any further.

We start by making a compression and decompression dictionary. We make these by taking the sorted distribution dictionary (DataEntropyUTF8.GetSortedDistribution) and start assigning X-bit-length value to each entry in the sorted distribution dictionary, with X being entropy_Ceiling. The compression dictionary has a byte as the key and an array of bool (bool[]) as the value, while the decompression dictionary has an array of bool as the key, and a byte as a value. You'll notice in the decompression dictionary we store the array of bool as a string, as using an actual array as a key will not work, as the dictionary's EqualityComparer will not assign the same hash code for two arrays of the same values.

Then, compression is as easy as reading each byte, and getting the value from the compression dictionary for that byte and adding it to a list of bool (List), then converting that array of bool to an array of bytes.

Decompression consists of converting the compressed array of bytes into an array of bool, then reading in X bools at a time and getting the byte value from the decompression library, again with X being entropy_Ceiling.




But first, to make this process easier, and to make our code more manageable and readable, I define several extension methods to help us out, since .NET provides almost no support for working with data on the bit level, besides the BitArray class. Here are the extension methods that to make working with bits easier:

public static class BitExtentionMethods
{
    //
    // List<bool> extention methods
    //
    public static List<bool> ToBitList(this byte source)
    {
        List<bool> temp = ( new BitArray(source.ToArray()) ).ToList();
        temp.Reverse();
        return temp;
    }
    
    public static List<bool> ToBitList(this byte source,int startIndex)
    {
        if(startIndex<0 || startIndex>7) {
            return new List<bool>();
        }
        return source.ToBitList().GetRange(startIndex,(8-startIndex));
    }
    
    //
    // bool[] extention methods
    //
    public static string GetString(this bool[] source)
    {
        string result = string.Empty;
        foreach(bool b in source)
        {
            if(b) {
                result += "1";
            } else {
                result += "0";
            }
        }
        return result;
    }
    
    public static bool[] ToBitArray(this byte source,int MaxLength)
    {
        List<bool> temp = source.ToBitList(8-MaxLength);
        return temp.ToArray();
    }
    
    public static bool[] ToBitArray(this byte source)
    {
        return source.ToBitList().ToArray();
    }

    //
    // BYTE extention methods
    //
    public static byte[] ToArray(this byte source)
    {
        List<byte> result = new List<byte>();
        result.Add(source);
        return result.ToArray();
    }
    
    //
    // BITARRAY extention methods
    //
    public static List<bool> ToList(this BitArray source)
    {
        List<bool> result = new List<bool>();
        foreach(bool bit in source)
        {
            result.Add(bit);
        }
        return result;
    }
    
    public static bool[] ToArray(this BitArray source)
    {
        return ToList(source).ToArray();
    }
}

Remember, these need to be the base class in a namespace, not in a nested class.


Now, we are free to write our compression/decompression class:

public class BitCompression
{
    // Data to encode
    byte[] data;
    // Compressed data
    byte[] encodeData;
    // # of bits needed to represent data
    int encodeLength_Bits;
    // Original size before padding. Decompressed data will be truncated to this length.
    int decodeLength_Bits;
    // Bits needed to represent each byte (entropy rounded up to nearist whole number)
    int entropy_Ceiling;
    // Data entropy class
    DataEntropyUTF8 fileEntropy;
    // Stores the compressed symbol table
    Dictionary<byte,bool[]> compressionLibrary;
    Dictionary<string,byte> decompressionLibrary;
    
    void GenerateLibrary()
    {
        byte[] distTable = new byte[fileEntropy.Distribution.Keys.Count];
        fileEntropy.Distribution.Keys.CopyTo(distTable,0);
        
        byte bitSymbol = 0x0;
        bool[] bitBuffer = new bool[entropy_Ceiling];
        foreach(byte symbol in distTable)
        {
            bitBuffer = bitSymbol.ToBitArray(entropy_Ceiling);
            compressionLibrary.Add(symbol,bitBuffer);
            decompressionLibrary.Add(bitBuffer.GetString(),symbol);
            bitSymbol++;
        }
    }
    
    public byte[] Compress()
    {
        // Error checking
        if(entropy_Ceiling>7 || entropy_Ceiling<1) {
            return data;
        }

        // Compress data using compressionLibrar
        List<bool> compressedBits = new List<bool>();
        foreach(byte bite in data) {    // Take each byte, find the matching bit array in the dictionary
            compressedBits.AddRange(compressionLibrary[bite]);
        }
        decodeLength_Bits = compressedBits.Count;
        
        // Pad to fill last byte
        while(compressedBits.Count % 8 != 0) {
            compressedBits.Add(false);  // Pad to the nearest byte
        }
        encodeLength_Bits = compressedBits.Count;
        
        // Convert from array of bits to array of bytes
        List<byte> result = new List<byte>();
        int count = 0;
        int shift = 0;
        int offset= 0;
        int stop  = 0;
        byte current = 0;
        do
        {
            stop = encodeLength_Bits - count;
            stop = 8 - stop;
            if(stop<0) {
                stop = 0;
            }
            if(stop<8)
            {
                shift = 7;
                offset = count;
                current = 0;
                
                while(shift>=stop)
                {
                    current |= (byte)(Convert.ToByte(compressedBits[offset]) << shift);
                    shift--;
                    offset++;
                }
                
                result.Add(current);
                count += 8;
            }
        } while(count < encodeLength_Bits);
        
        encodeData = result.ToArray();
        return encodeData;
    }
    
    public byte[] Decompress(byte[] compressedData)
    {
        // Error check
        if(compressedData.Length<1) {
            return null;
        }
        
        // Convert to bit array for decompressing
        List<bool> bitArray = new List<bool>();
        foreach(byte bite in compressedData) {
            bitArray.AddRange(bite.ToBitList());
        }
        
        // Truncate to original size, removes padding for byte array
        int diff = bitArray.Count-decodeLength_Bits;
        if(diff>0) {
            bitArray.RemoveRange(decodeLength_Bits-1,diff);
        }

        // Decompress
        List<byte> result = new List<byte>();
        int count = 0;
        do
        {
            bool[] word = bitArray.GetRange(count,entropy_Ceiling).ToArray();
            result.Add(decompressionLibrary[word.GetString()]);
            
            count+=entropy_Ceiling;
        } while(count < bitArray.Count);
        
        return result.ToArray();
    }
    
    public BitCompression(string filename)
    {
        compressionLibrary  = new Dictionary<byte, bool[]>();
        decompressionLibrary = new Dictionary<string, byte>();
        
        if(!File.Exists(filename))  {
            return;
        }
        
        data = File.ReadAllBytes(filename);
        fileEntropy = new DataEntropyUTF8();
        fileEntropy.ExamineChunk(data);
        
        int unique  = (int)Math.Ceiling(Math.Log((double)fileEntropy.UniqueSymbols,2f));
        int entropy = (int)Math.Ceiling(fileEntropy.Entropy);
        
        entropy_Ceiling = Math.Max(unique,entropy);
        encodeLength_Bits   = data.Length * entropy_Ceiling;
        
        GenerateLibrary();
    }
}

Please feel free to comment with ideas, suggestions or corrections.

Information Shannon Entropy

Shannon/data entropy is a measurement of uncertainty. Entropy can be used as a measure of randomness. Data entropy is typically expressed as the number of bits needed to encode or represent data. In the example below, we are working with bytes, so the max entropy for a stream of bytes is 8.

A file with high entropy means that each symbol is more-or-less equally as likely to appear next. If a file or file stream has high entropy, it is either probably compressed, encrypted or random. This can be used to detect packed executables, cipher streams on a network, or a breakdown of encrypted communication on a network that is expected to be always encrypted.

A text file will have low entropy. If a file has low data entropy, it mean that the file will compress well.

This post and code was inspired by Mike Schiffman's excelent explaination of data entropy on his Cisco Security Blog.

Here is what I wrote:

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

namespace DataEntropy
{
    public class DataEntropyUTF8
    {
        // Stores the number of times each symbol appears
        SortedList<byte,int>        distributionDict;
        // Stores the entropy for each character
        SortedList<byte,double> probabilityDict;
        // Stores the last calculated entropy
        double overalEntropy;
        // Used for preventing unnecessary processing
        bool isDirty;
        // Bytes of data processed
        int dataSize;
        
        public int DataSampleSize
        {
            get { return dataSize; }
            private set { dataSize = value; }
        }
        
        public int UniqueSymbols
        {
            get { return distributionDict.Count; }
        }
        
        public double Entropy
        {
            get { return GetEntropy(); }
        }
        
        public Dictionary<byte,int> Distribution
        {
            get { return GetSortedDistribution(); }
        }
        
        public Dictionary<byte,double> Probability
        {
            get { return GetSortedProbability(); }
        }
        
        public byte GetGreatestDistribution()
        {
            return distributionDict.Keys[0];
        }
        
        public byte GetGreatestProbability()
        {
            return probabilityDict.Keys[0];
        }
        
        public double GetSymbolDistribution(byte symbol)
        {
            return distributionDict[symbol];
        }
        
        public double GetSymbolEntropy(byte symbol)
        {
            return probabilityDict[symbol];
        }
        
        Dictionary<byte,int> GetSortedDistribution()
        {
            List<Tuple<int,byte>> entryList = new List<Tuple<int, byte>>();
            foreach(KeyValuePair<byte,int> entry in distributionDict)
            {
                entryList.Add(new Tuple<int,byte>(entry.Value,entry.Key));
            }
            entryList.Sort();
            entryList.Reverse();
            
            Dictionary<byte,int> result = new Dictionary<byte, int>();
            foreach(Tuple<int,byte> entry in entryList)
            {
                result.Add(entry.Item2,entry.Item1);
            }
            return result;
        }
        
        Dictionary<byte,double> GetSortedProbability()
        {
            List<Tuple<double,byte>> entryList = new List<Tuple<double,byte>>();
            foreach(KeyValuePair<byte,double> entry in probabilityDict)
            {
                entryList.Add(new Tuple<double,byte>(entry.Value,entry.Key));
            }
            entryList.Sort();
            entryList.Reverse();
            
            Dictionary<byte,double> result = new Dictionary<byte,double>();
            foreach(Tuple<double,byte> entry in entryList)
            {
                result.Add(entry.Item2,entry.Item1);
            }
            return result;
        }
        
        double GetEntropy()
        {
            // If nothing has changed, dont recalculate
            if(!isDirty) {
                return overalEntropy;
            }
            // Reset values
            overalEntropy = 0;
            probabilityDict = new SortedList<byte,double>();
            
            foreach(KeyValuePair<byte,int> entry in distributionDict)
            {
                // Probability = Freq of symbol / # symbols examined thus far
                probabilityDict.Add(
                    entry.Key,
                    (double)distributionDict[entry.Key] / (double)dataSize
                );
            }
            
            foreach(KeyValuePair<byte,double> entry in probabilityDict)
            {
                // Entropy = probability * Log2(1/probability)
                overalEntropy += entry.Value * Math.Log((1/entry.Value),2);
            }
            
            isDirty = false;
            return overalEntropy;
        }
        
        public void ExamineChunk(byte[] chunk)
        {
            if(chunk.Length<1 || chunk==null) {
                return;
            }
            
            isDirty = true;
            dataSize += chunk.Length;
            
            foreach(byte bite in chunk)
            {
                if(!distributionDict.ContainsKey(bite))
                {
                    distributionDict.Add(bite,1);
                    continue;
                }
                distributionDict[bite]++;
            }
        }
        
        public void ExamineChunk(string chunk)
        {
            ExamineChunk(StringToByteArray(chunk));
        }
        
        byte[] StringToByteArray(string inputString)
        {
            char[] c = inputString.ToCharArray();
            IEnumerable<byte> b = c.Cast<byte>();
            return b.ToArray();
        }
        
        void Clear()
        {
            isDirty = true;
            overalEntropy = 0;
            dataSize = 0;
            distributionDict = new SortedList<byte, int>();
            probabilityDict = new SortedList<byte, double>();
        }
        
        public DataEntropyUTF8(string fileName)
        {
            this.Clear();
            if(File.Exists(fileName))
            {
                ExamineChunk(  File.ReadAllBytes(fileName) );
                GetEntropy();
                GetSortedDistribution();
            }
        }
        
        public DataEntropyUTF8()
        {
            this.Clear();
        }
    }
}

C# developer humor - Chuck Norris.

These jokes were inspired by this link. I have modified them a bit to apply to the C or C# language.

• Chuck Nor­ris can make a class that is both abstract and constant.
• Chuck Nor­ris seri­al­izes objects straight into human skulls.
• Chuck Nor­ris doesn’t deploy web appli­ca­tions, he round­house kicks them into the server.
• Chuck Nor­ris always uses his own design pat­terns, and his favorite is the Round­house Kick.
• Chuck Nor­ris always programs using unsafe code.
• Chuck Nor­ris only enumerates roundhouse kicks to the face.
• Chuck Nor­ris demon­strated the mean­ing of float.PositiveInfinity by count­ing to it, twice.
• A lock statement doesn’t pro­tect against Chuck Nor­ris, if he wants the object, he takes it.
• Chuck Nor­ris doesn’t use VisualStudio, he codes .NET by using a hex edi­tor on the MSIL.
• When some­one attempts to use one of Chuck Nor­ris’ dep­re­cated meth­ods, they auto­mat­i­cally get a round­house kick to the face at com­pile time.
• Chuck Nor­ris never has a bug in his code, without exception!
• Chuck Nor­ris doesn’t write code. He stares at a com­puter screen until he gets the progam he wants.
• Code runs faster when Chuck Nor­ris watches it.
• Chuck Nor­ris meth­ods don't catch excep­tions because no one has the guts to throw any at them.
• Chuck Nor­ris will cast a value to any type, just by star­ing at it.
• If you catch { } a Chuc­kNor­ri­sEx­cep­tion, you’ll prob­a­bly die.
• Chuck Norris’s code can round­house kick all other classes' privates.
• C#'s vis­i­bil­ity lev­els are pub­lic, private, pro­tected, and “pro­tected by Chuck Nor­ris”. Don’t try to access a field with this last modifier!
• Chuck Nor­ris can divide by 0!
• The garbage col­lec­tor only runs on Chuck Nor­ris code to col­lect the bodies.
• Chuck Nor­ris can exe­cute 64bit length instruc­tions in a 32bit CPU.
• To Chuck Nor­ris, all other classes are IDisposable.
• Chuck Nor­ris can do mul­ti­ple inher­i­tance in C#.
• MSBuild never throws excep­tions to Chuck Nor­ris, not any­more. 753 killed Microsoft engi­neers is enough.
• Chuck Nor­ris doesn’t need unit tests, because his code always work. ALWAYS.
• Chuck Nor­ris has been coding in gener­ics since 1.1.
• Chuck Nor­ris’ classes can’t be decom­piled... don’t bother trying.

Here are some originals:

• If you try derive from a Chuck Norris Interface, you'll only get an IRoundhouseKick in-the-face.
• Chuck Nor­ris can serialize a dictionary to XML without implementing IXMLSerializable.
• Chuck Norris can decompile your assembly by only reading the MSIL.

Convert a Class or List of Class to a DataTable, using reflection.

Note by author:

   Since writing this, I have expanded on this idea quite a bit. I have written a lightweight ORM class library that I call EntityJustWorks.
   The full project can be found on GitHub or CodePlex.


   EntityJustWorks not only goes from a class to DataTable (below), but also provides:

• Populate the public properties of a class from a DataTable

• DataTable to class as a C# code file (using CodeDOM)

• DataTable to class Assembly (using Reflection.Emit)

• C# class to a SQL 'CREATE TABLE' or 'INSERT INTO' script

• SQL 'SELECT' statement to a List<T> of populated classes, each one resembling a row

Security Warning:
This library generates dynamic SQL, and has functions that generate SQL and then immediately executes it. While it its true that all strings funnel through the function Helper.EscapeSingleQuotes, this can be defeated in various ways and only parameterized SQL should be considered SAFE. If you have no need for them, I recommend stripping semicolons ; and dashes --. Also there are some Unicode characters that can be interpreted as a single quote or may be converted to one when changing encodings. Additionally, there are Unicode characters that can crash .NET code, but mainly controls (think TextBox). You almost certainly should impose a white list:
string clean = new string(dirty.Where(c => "abcdefghijklmnopqrstuvwxyz0123456789.,\"_ !@".Contains(c)).ToArray());

PLEASE USE the SQLScript.StoredProcedure and DatabaseQuery.StoredProcedure classes to generate SQL for you, as the scripts it produces is parameterized. All of the functions can be altered to generate parameterized instead of sanitized scripts. Ever since people have started using this, I have been maintaining backwards compatibility. However, I may break this in the future, as I do not wish to teach one who is learning dangerous/bad habits. This project is a few years old, and its already showing its age. What is probably needed here is a total re-write, deprecating this version while keep it available for legacy users after slapping big warnings all over the place. This project was designed to generate the SQL scripts for standing up a database for a project, using only MY input as data. This project was never designed to process a USER'S input.! Even if the data isn't coming from an adversary, client/user/manually entered data is notoriously inconsistent. Please do not use this code on any input that did not come from you, without first implementing parameterization. Again, please see the SQLScript.StoredProcedure class for inspiration on how to do that.

    This class uses generics to accepts a class type, and uses reflection to determine the name and type of the class's public properties. With that, a new DataTable is made and the DataColumnCollection is fleshed out. Then you can add rows to the DataTable by passing instances of the class with it's property fields containing values.

    Finally, we serialize the DataTable to an XML file, save it's Schema, then load it all back in again as a proof of concept.


Usage example:

List<Order> orders = new List<Order>();

// Fill in orders here ...
// orders.Add(new Order());

// Convert class to DataTable
DataTable ordersTable = ClassListToDataTable(orders);

// Set DataGrid's DataSource to DataTable
dataGrid1.DataSource = ordersTable;

Here is the Code:

public static DataTable ClassToDataTable<T>() where T : class
{
    Type classType = typeof(T);

    List<PropertyInfo> propertyList = classType.GetProperties().ToList();
    if (propertyList.Count < 1)
    {
        return new DataTable();
    }

    string className = classType.UnderlyingSystemType.Name;
    DataTable result = new DataTable(className);

    foreach (PropertyInfo property in propertyList)
    {
        DataColumn col = new DataColumn();
        col.ColumnName = property.Name;

        Type dataType = property.PropertyType;

        if (IsNullable(dataType))
        {
            if(dataType.IsGenericType)
            {
                dataType = dataType.GenericTypeArguments.FirstOrDefault();
            }
        }
        else
        {   // True by default
            col.AllowDBNull = false;
        }

        col.DataType = dataType;

        result.Columns.Add(col);
    }

    return result;
}

public static DataTable ClassListToDataTable<T>(List<T> ClassList) where T : class
{
   DataTable result = ClassToDataTable<T>();
   
   if(result.Columns.Count < 1)
   {
      return new DataTable();
   }
   if(ClassList.Count < 1)
   {
      return result;
   }
   
   foreach(T item in ClassList)
   {
      ClassToDataRow(ref result, item);
   }
   
   return result;
}

public static void ClassToDataRow<T>(ref DataTable Table, T Data) where T : class
{
    Type classType = typeof(T);
    string className = classType.UnderlyingSystemType.Name;

    // Checks that the table name matches the name of the class. 
    // There is not required, and it may be desirable to disable this check.
    // Comment this out or add a boolean to the parameters to disable this check.
    if (!Table.TableName.Equals(className))
    {
        return;
    }

    DataRow row = Table.NewRow();
    List<PropertyInfo> propertyList = classType.GetProperties().ToList();

    foreach (PropertyInfo prop in propertyList)
    {
        if (Table.Columns.Contains(prop.Name))
        {
            if (Table.Columns[prop.Name] != null)
            {
                row[prop.Name] = prop.GetValue(Data, null);
            }
        }
    }
    Table.Rows.Add(row);
}

public static bool IsNullable(Type Input)
{
    if (!Input.IsValueType) return true; // Is a ref-type, such as a class
    if (Nullable.GetUnderlyingType(Input) != null) return true; // Nullable
    return false; // Must be a value-type
}

Here is an example of how to serialize a DataTable to XML, and load it back again

string filePath = "order1.xml";
string schemaPath = Path.ChangeExtension(filePath,".xsd");

ordersTable.WriteXml(filePath);
ordersTable.WriteXmlSchema(schemaPath);

// Load
DataTable loadedTable = new DataTable();
loadedTable.ReadXmlSchema(schemaPath);
loadedTable.ReadXml(filePath);

// Set DataGrid's DataSource
dataGrid1.DataSource = dataTable;

The full project and source code for EntityJustWorks can be found on GitHub and CodePlex.

Procedural generation of cave-like maps for rogue-like games

This post is about procedural content generation of cave-like dungeons/maps for rogue-like games using what is known as the Cellular Automata method.

To understand what I mean by cellular automata method, imagine Conway's Game of Life. Many algorithms use what is called the '4-5 method', which means a tile will become a wall if it is a wall and 4 or more of its nine neighbors are walls, or if it is not a wall and 5 or more neighbors are walls. I start by filling the map randomly with walls or space, then visit each x/y position iteratively and apply the 4-5 rule. Usually this is preceded with 'seeding' the map by randomly filling each cell of the map with a wall or space, based on some weight (say, 40% of the time it chooses to place a wall). Then the automata step is applied multiple times over the entire map, precipitating walls and subsequently smoothing them. About 3 rounds is all that is required, with about 4-5 rounds being pretty typical amongst most implementations. Perhaps a picture of the the output will help you understand what I mean.

Using the automata-based method for procedural generation of levels will produce something similar to this:

Sure the dungeon generation by linking rooms approach has its place, but I really like the 'natural' look to the automata inspired method. I first originally discovered this technique on the website called Roguebasin. It is a great resource for information concerning the different problems involved with programming a rogue-like game, such as Nethack or Angband.

One of the major problems developers run into while employing this technique is the formation of isolated caves. Instead of one big cave-like room, you may get section of the map that is inaccessible without digging through walls. Isolated caves can trap key items or (worse) stairs leading to the next level, preventing further progress in the game. I have seen many different approaches proposed to solve this problem. Some suggestions I've seen include: 1) Discarding maps that have isolated caves, filling in the isolated sections, or finely tweaking the variables/rules to reduce occurrences of such maps. None of these are ideal (in my mind), and most require a way to detect isolated sections, which is another non-trivial problem in itself.

Despite this, I consider the problem solved because I have discovered a solution that is dead simple and almost** never fail because of the rules of the automata generation itself dictate such. I call my method 'Horizontal Blanking' because you can probably guess how it works now just from hearing the name. This step comes after the random filling of the map (initialization), but before the cellular automata iterations. After the map is 'seeded' with a random fill of walls, a horizontal strip in the middle of of the map is cleared of all walls. The horizontal strip is about 3 or 4 block tall (depending on rules). Clearing a horizontal strip of sufficient width will prevent a continuous vertical wall from being created and forming isolated caves in your maps. After horizontal blanking, you can begin applying the cellular automata method to your map.

** I say 'almost' because although it it not possible to get whole rooms that are disconnected from each other, it is possible to get tiny squares of blank space in the northern or southern walls that consist of about 4-5 blocks in total area. Often, these little holes will resolve themselves during the rounds of automata rules, but there still exists the possibility that one may persist. My answer to this edge case would be to use some rules around the placement of stairwells (and other must-find items) dictating that such objects must have a 2-3 block radius clear of walls to be placed.


See below for the code that produced the above screenshot, or click here to download the entire project with source code that you can compile yourself.

public class MapHandler
{
 Random rand = new Random();
 
 public int[,] Map;
 
 public int MapWidth   { get; set; }
 public int MapHeight  { get; set; }
 public int PercentAreWalls { get; set; }
 
 public MapHandler()
 {
  MapWidth = 40;
  MapHeight = 21;
  PercentAreWalls = 40;
  
  RandomFillMap();
 }

 public void MakeCaverns()
 {
  // By initilizing column in the outter loop, its only created ONCE
  for(int column=0, row=0; row <= MapHeight-1; row++)
  {
   for(column = 0; column <= MapWidth-1; column++)
   {
    Map[column,row] = PlaceWallLogic(column,row);
   }
  }
 }
 
 public int PlaceWallLogic(int x,int y)
 {
  int numWalls = GetAdjacentWalls(x,y,1,1);

  
  if(Map[x,y]==1)
  {
   if( numWalls >= 4 )
   {
    return 1;
   }
   return 0;   
  }
  else
  {
   if(numWalls>=5)
   {
    return 1;
   }
  }
  return 0;
 }
 
 public int GetAdjacentWalls(int x,int y,int scopeX,int scopeY)
 {
  int startX = x - scopeX;
  int startY = y - scopeY;
  int endX = x + scopeX;
  int endY = y + scopeY;
  
  int iX = startX;
  int iY = startY;
  
  int wallCounter = 0;
  
  for(iY = startY; iY <= endY; iY++) {
   for(iX = startX; iX <= endX; iX++)
   {
    if(!(iX==x && iY==y))
    {
     if(IsWall(iX,iY))
     {
      wallCounter += 1;
     }
    }
   }
  }
  return wallCounter;
 }
 
 bool IsWall(int x,int y)
 {
  // Consider out-of-bound a wall
  if( IsOutOfBounds(x,y) )
  {
   return true;
  }
  
  if( Map[x,y]==1  )
  {
   return true;
  }
  
  if( Map[x,y]==0  )
  {
   return false;
  }
  return false;
 }
 
 bool IsOutOfBounds(int x, int y)
 {
  if( x<0 data-blogger-escaped-else="" data-blogger-escaped-if="" data-blogger-escaped-return="" data-blogger-escaped-true="" data-blogger-escaped-x="" data-blogger-escaped-y="">MapWidth-1 || y>MapHeight-1 )
  {
   return true;
  }
  return false;
 }

Above is the main core of the logic.


Here is the rest of the program, such as filling, printing and blanking:

 
 public void PrintMap()
 {
  Console.Clear();
  Console.Write(MapToString());
 }
 
 string MapToString()
 {
  string returnString = string.Join(" ", // Seperator between each element
                                    "Width:",
                                    MapWidth.ToString(),
                                    "\tHeight:",
                                    MapHeight.ToString(),
                                    "\t% Walls:",
                                    PercentAreWalls.ToString(),
                                    Environment.NewLine
                                   );
  
  List<string> mapSymbols = new List();
  mapSymbols.Add(".");
  mapSymbols.Add("#");
  mapSymbols.Add("+");
  
  for(int column=0,row=0; row < MapHeight; row++ ) {
   for( column = 0; column < MapWidth; column++ )
   {
    returnString += mapSymbols[Map[column,row]];
   }
   returnString += Environment.NewLine;
  }
  return returnString;
 }
 
 public void BlankMap()
 {
  for(int column=0,row=0; row < MapHeight; row++) {
   for(column = 0; column < MapWidth; column++) {
    Map[column,row] = 0;
   }
  }
 }
 
 public void RandomFillMap()
 {
      // New, empty map
      Map = new int[MapWidth,MapHeight];
  
      int mapMiddle = 0; // Temp variable
      for(int column=0,row=0; row < MapHeight; row++) {
         for(column = 0; column < MapWidth; column++)
         {
       // If coordinants lie on the edge of the map
       // (creates a border)
       if(column == 0)
       {
      Map[column,row] = 1;
       }
       else if (row == 0)
       {
      Map[column,row] = 1;
       }
       else if (column == MapWidth-1)
       {
      Map[column,row] = 1;
       }
       else if (row == MapHeight-1)
       {
      Map[column,row] = 1;
       }
       // Else, fill with a wall a random percent of the time
       else
       {
      mapMiddle = (MapHeight / 2);
    
      if(row == mapMiddle)
      {
     Map[column,row] = 0;
      }
      else
      {
     Map[column,row] = RandomPercent(PercentAreWalls);
      }
       }
   }
      }
 }

 int RandomPercent(int percent)
 {
  if(percent>=rand.Next(1,101))
  {
   return 1;
  }
  return 0;
 }
 
 public MapHandler(int mapWidth, int mapHeight, int[,] map, int percentWalls=40)
 {
  this.MapWidth = mapWidth;
  this.MapHeight = mapHeight;
  this.PercentAreWalls = percentWalls;
  this.Map = new int[this.MapWidth,this.MapHeight];
  this.Map = map;
 }
}

And of course, the main function:

 
public static void Main(string[] args)
{
 char key  = new Char();
 MapHandler Map = new MapHandler();
 
 string instructions =
  "[Q]uit [N]ew [+][-]Percent walls [R]andom [B]lank" + Environment.NewLine +
  "Press any other key to smooth/step";

 Map.MakeCaverns();
 Map.PrintMap();
 Console.WriteLine(instructions);
 
 key = Char.ToUpper(Console.ReadKey(true).KeyChar);
 while(!key.Equals('Q'))
 {
  if(key.Equals('+')) {
   Map.PercentAreWalls+=1;
   Map.RandomFillMap();
   Map.MakeCaverns();
   Map.PrintMap();
  } else if(key.Equals('-')) {
   Map.PercentAreWalls-=1;
   Map.RandomFillMap();
   Map.MakeCaverns();
   Map.PrintMap();
  } else if(key.Equals('R')) {
   Map.RandomFillMap();
   Map.PrintMap();
  } else if(key.Equals('N')) {
   Map.RandomFillMap();
   Map.MakeCaverns();
   Map.PrintMap();
  } else if(key.Equals('B')) {
   Map.BlankMap();
   Map.PrintMap();
  } else if(key.Equals('D')) {
   // I set a breakpoint here...
  } else {
   Map.MakeCaverns();
   Map.PrintMap();
  }
  Console.WriteLine(instructions);
  key = Char.ToUpper(Console.ReadKey(true).KeyChar);
 }
 Console.Clear();
 Console.Write(" Thank you for playing!");
 Console.ReadKey(true);
}

See also: Roguebasin - Cellular Automata Method for Generating Random Cave-Like Levels