
ZOJ Problem Set  1314
Computer simulations often require random numbers. One way to generate pseudorandom 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 pseudorandom numbers (seed) between 0 and MOD1. 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 MOD1. For example, if STEP = 3 and MOD = 5, the function will generate the series of pseudorandom numbers 0, 3, 1, 4, 2 in a repeating cycle. In this example, all of the numbers between and including 0 and MOD1 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 MOD1, it will generate pseudorandom 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 MOD1. Your program will determine if choices of STEP and MOD will generate a uniform distribution of pseudorandom numbers.
3 5
3 5 Good Choice 15 20 Bad Choice 63923 99999 Good Choice Source: South Central USA 1996 