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.
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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
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