A particular random number generator returns positive integer n with probability 1/(2^n). (ie '1' with probability 1/2, '2' with probability 1/4, '3' with probability 1/8, etc.)

Using this random number generator, write an algorithm which chooses a random integer from 1 to 37 with equal probability.

(In reply to This little program should do the trick... by Erik O.)

I think the program I gave in an earlier post weights the upper range of number a bit heavily.  Two slight modifications should do the trick:

First-Run through the shuffleing part at least twice to distribute the numbers more fairly,

Second-In the output, use the first number taken from the array as a pointer to the real number to be displayed.

The program should then look more like:

Dim I, J, K, IntArray(37), Temp As Integer

' Fill Integer Array with values from 1 to 37
For I = 1 To 37
    IntArray(I) = I
Next I

'Shuffle Array
For K = 1 to 3

    For I = 1 To 37
        J = Rnd()
        Temp = IntArray(I)
        IntArray(I) = IntArray(J)
        IntArray(J) = Temp
    Next I

Next K

Print IntArray(IntArray(Rnd()))

Stop
End

Either of the modifications mentioned above should work fine independantly--using both is probably overkill.

 

Posted by Erik O. on 2004-06-08 14:44:16