In doing computer simulations, such as

the one I wrote for simulating the results of part 2 of Rumor Mill, one often uses a random number generator that's built into the computer language. These generators are based on a seed (some arbitrary number) and are mixed up at each step that calls for a random number. There are only a finite number of seeds, and each one is based mechanically on the previous, so they necessarily repeat after a while.

The seed is kept internally, away from the programmer's view, so the programmer can't ask for, say, the next random number after .753372.

If one suspects that the repetition cycle is actually occuring within the length of the run that he needs, what algorithm can you put into the program to find the period with which your results are repeating (and are therefore no longer random, or rather no longer independent trials)? Assume you do not have room to store all the numbers as they arrive, nor can you afford the time it would take to compare each new number to all the preceding numbers.

Then also, how do you determine where the repetition cycle begins (after what iteration of the loop of trials).

The following is a VB.Net program that implements the algorithm described in my previous post.

Explanation: PhonyRandom is a terrible random number generator--it doesn't even try to generate anything random, but it has the necessary characteristics to use as a surrogate for a real random number generator for purposes of this test. PhonyRandom will return the following sequence of integers: 246, 245, 244, 243, 242, 241, 240, 239, 238, 237, 236... 3, 2, 1, 237, 236, 235, etc. Thus this generator has a period of 237, and begins repeating at position 10 (where we see the first 237).

The Main program knows nothing about this. Its mission is to determine the period and first point where the sequence begins to repeat. Running this program produces the following output in a console window:

Period is 237

Repetition starts at position 10

...which is exactly what we were looking for. If you change the class to use a period greater than 1000, the output will be

period is more than 1000

...which is also what we'd expect.

_________________________________________

Option Strict On

Module Module1

Class PhonyRandom

Dim m_number As Integer

Public Sub New()

m_number = 247

End Sub

Public Function NextNo() As Integer

Dim period As Integer = 237

m_number -= 1

If m_number < 1 Then m_number = period

Return m_number

End Function

End Class

Sub Main()

Dim maxTrials As Integer = 1000

Dim r As New PhonyRandom

' Assume the test will need maxTrials random numbers...

Dim i As Integer

For i = 1 To maxTrials

r.NextNo() 'gets a random and discards it.

Next

Dim CompareTo As Integer = r.NextNo

For i = 1 To maxTrials

If r.NextNo = CompareTo Then

Exit For

End If

Next

If i < maxTrials Then

Dim period As Integer = i

Console.WriteLine("Period is {0}", period)

r = New PhonyRandom

Dim r2 As New PhonyRandom

For i = 1 To period

r.NextNo()

Next

i = 0

Dim x, y As Integer

Do

i += 1

x = r.NextNo

y = r2.NextNo

Loop Until x = y

Console.WriteLine("Repetition starts at position {0}", i)

Else

Console.WriteLine("period is more than {0}", maxTrials)

End If

Console.ReadLine()

End Sub

End Module

_________________________________________