// Example of the Random.Sample( ) method.
using System;

// This derived class converts the uniformly distributed random 
// numbers generated by base.Sample( ) to another distribution.
public class RandomProportional : Random
{
    // Sample generates a distribution proportional to the value 
    // of the random numbers, in the range [ 0.0, 1.0 ).
    protected override double Sample( )
    {
        return Math.Sqrt( base.Sample( ) );
    }
}

public class RandomSampleDemo  
{
    static void Main( )
    {	
        const int rows = 4, cols = 6;
        const int runCount = 1000000;
        const int distGroupCount = 10;
        const double intGroupSize = 
            ( (double)int.MaxValue + 1.0 ) / (double)distGroupCount;

        RandomProportional randObj = new RandomProportional( );

        int[ ]      intCounts = new int[ distGroupCount ];
        int[ ]      realCounts = new int[ distGroupCount ];

        Console.WriteLine( 
            "This example of Random.Sample( ) " +
            "generates the following output." );
        Console.WriteLine( 
            "\nThe derived RandomProportional class overrides " +
            "the Sample method to \ngenerate random numbers " +
            "in the range [0.0, 1.0). The distribution \nof " +
            "the numbers is proportional to the number values. " +
            "For example, \nnumbers are generated in the " +
            "vicinity of 0.75 with three times the \n" +
            "probability of those generated near 0.25." );
        Console.WriteLine( 
            "\nRandom doubles generated with the NextDouble( ) " +
            "method:\n" );

        // Generate and display [rows * cols] random doubles.
        for( int i = 0; i < rows; i++ )
        {
            for( int j = 0; j < cols; j++ )
                Console.Write( "{0,12:F8}", randObj.NextDouble( ) );
            Console.WriteLine( );
        }

        Console.WriteLine( 
            "\nRandom integers generated with the Next( ) " +
            "method:\n" );

        // Generate and display [rows * cols] random integers.
        for( int i = 0; i < rows; i++ )
        {
            for( int j = 0; j < cols; j++ )
                Console.Write( "{0,12}", randObj.Next( ) );
            Console.WriteLine( );
        }

        Console.WriteLine( 
            "\nTo demonstrate the proportional distribution, " +
            "{0:N0} random \nintegers and doubles are grouped " +
            "into {1} equal value ranges. This \n" +
            "is the count of values in each range:\n",
            runCount, distGroupCount );
        Console.WriteLine( 
            "{0,21}{1,10}{2,20}{3,10}", "Integer Range",
            "Count", "Double Range", "Count" );
        Console.WriteLine( 
            "{0,21}{1,10}{2,20}{3,10}", "-------------",
            "-----", "------------", "-----" );

        // Generate random integers and doubles, and then count 
        // them by group.
        for( int i = 0; i < runCount; i++ )
        {
            intCounts[ (int)( (double)randObj.Next( ) / 
                intGroupSize ) ]++;
            realCounts[ (int)( randObj.NextDouble( ) * 
                (double)distGroupCount ) ]++;
        }

        // Display the count of each group.
        for( int i = 0; i < distGroupCount; i++ )
            Console.WriteLine( 
                "{0,10}-{1,10}{2,10:N0}{3,12:N5}-{4,7:N5}{5,10:N0}",
                (int)( (double)i * intGroupSize ),
                (int)( (double)( i + 1 ) * intGroupSize - 1.0 ),
                intCounts[ i ],
                ( (double)i ) / (double)distGroupCount,
                ( (double)( i + 1 ) ) / (double)distGroupCount,
                realCounts[ i ] );
    }
}

/*
This example of Random.Sample( ) generates the following output.

The derived RandomProportional class overrides the Sample method to
generate random numbers in the range [0.0, 1.0). The distribution
of the numbers is proportional to the number values. For example,
numbers are generated in the vicinity of 0.75 with three times the
probability of those generated near 0.25.

Random doubles generated with the NextDouble( ) method:

  0.70274545  0.71861388  0.68071795  0.84034066  0.93354743  0.85663774
  0.81804688  0.35177836  0.59208519  0.96031602  0.80442745  0.68718948
  0.98765094  0.88136820  0.40016694  0.78735843  0.30468930  0.60884722
  0.99724610  0.64792400  0.87542366  0.86193142  0.88573527  0.67682807

Random integers generated with the Next( ) method:

  2143307129  1985560852  1491542209  1624708626   545912171  2144440214
  1605065299  1294719830  1191410879  1120886902  1915435155  1514194175
  1795364867  1695595242  1754564804  1407165303  2026939619  1965958920
  1531822446  1145720706  1458838319  1924643339   804498107   445927707

To demonstrate the proportional distribution, 1,000,000 random
integers and doubles are grouped into 10 equal value ranges. This
is the count of values in each range:

        Integer Range     Count        Double Range     Count
        -------------     -----        ------------     -----
         0- 214748363     9,916     0.00000-0.10000    10,014
 214748364- 429496728    29,978     0.10000-0.20000    29,965
 429496729- 644245093    50,204     0.20000-0.30000    49,975
 644245094- 858993458    69,870     0.30000-0.40000    70,150
 858993459-1073741823    89,875     0.40000-0.50000    90,180
1073741824-1288490187   110,448     0.50000-0.60000   109,995
1288490188-1503238552   130,290     0.60000-0.70000   130,218
1503238553-1717986917   149,652     0.70000-0.80000   149,300
1717986918-1932735282   170,367     0.80000-0.90000   169,737
1932735283-2147483647   189,400     0.90000-1.00000   190,466
*/