Non-repetitive random seek in a range Algorithm

Question

I\'m looking for an efficient algorithm that produces random values within a range, without repetitions.

In pseudo-code: (in class Rand)

  Rand(long from         


        

Answer 1

Some thoughts for a starting point:

1) Supposes that you have a function f(x) which is a permutation on 1..N where N is larger than your range. If you apply it to x within the range it may produce an illegal value - one outside your range. You could define a permutation within your range by simply calling f again on the illegal value. You will eventually come to a legal value because the sequence x, f(x), f^2(x), f^3(x) must eventually cycle and if the worst comes to the worst it will come back in at x.

2) There are switching networks which allow you to produce all possible permutations on N objects for special N - one example is http://en.wikipedia.org/wiki/Clos_network#Bene.C5.A1_network_.28m_.3D_n_.3D_2.29 (Funny URL - Benes network). You can get an arbitrary permutation on N objects, where N may I think have to be a power of 2, by setting the switches at random. Since there will be K switches there are 2^K ways of setting them which means that you do not have M! permutations with equal probability but perhaps you won't mind this, or can minimise the non-randomness by repeating this multiple times, or something.

3) If you are prepared to achieve near-randomness by applying many different base permutations many different times you could try alternately adding mod N across the whole range and then splitting the range into sub-ranges and e.g. for some stretch of p-1 values within the range apply the permutation produced by multiplying by some k mode p. The hope would be that although each individual step is pretty basic by appling enough of them and making them diverse enough the result would be close to being random, especially if you chose the parameters at random.