Uniform Generator
Program |
RAND.C, RAND.CPP, RAND.PAS
|
Computer simulations often require random numbers. One way to generate pseudo-random
numbers is via a function of the form
seed(x+1) = [ seed(x) + STEP ] % MOD
where "%" is the modulus operator.
Such a function will generate pseudo-random numbers (seed) between 0 and MOD-1.
One problem with functions of this form is that they will always generate the
same pattern over and over. In order to minimize this effect, selecting the STEP
and MOD values carefully can result in a uniform distribution of all values between
(and including) 0 and MOD-1.
For example, if STEP=3 and MOD=5, the function will generate the series of pseudo-random
numbers 0, 3, 1, 4, 2 in a repeating cycle. In this example, all of the numbers
between and including 0 and MOD-1 will be generated every MOD iterations of the
function. Note that by the nature of the function to generate the same seed(x+1)
every time seed(x) occurs means that if a function will generate all the numbers
between 0 and MOD-1, it will generate pseudo-random numbers uniformly with every
MOD iterations.
If STEP = 15 and MOD = 20, the function generates the series 0, 15, 10, 5 (or
any other repeating series if the initial seed is other than 0). This is a poor
selection of STEP and MOD because no initial seed will generate all of the numbers
from 0 and MOD-1.
Your program will determine if choices of STEP and MOD will generate a uniform
distribution of pseudo-random numbers.
Input
Each line of input will contain a pair of integers for STEP and MOD in that order
(1<=STEP,MOD<=100000).
Output
For each line of input, your program should print the STEP value right-justified
in columns 1 through 10, the MOD value right-justified in columns 11 through 20
and either "Good Choice" or "Bad Choice" left-justified starting
in column 25. The "Good Choice" message should be printed when the selection
of STEP and MOD will generate all the numbers between and including 0 and MOD-1
when MOD numbers are generated. Otherwise, your program should print the message
"Bad Choice". After each output test set, your program should print
exactly one blank line.
Sample Input
3 5
15 20
63923 99999
Sample Output
3 5 Good Choice
15 20 Bad Choice
63923 99999 Good Choice