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

One way to do this would be to generate a list of numbers between from and to, removing these at random until the bag is empty, at which point it's re-populated. To save on storage for large ranges, you can record picked numbers up to a point (re-picking when a duplicate is chosen), since the probability of picking a duplicate should be low initially. Determining the optimal transition point will probably be an empirical exercise.

EDIT: Some more thoughts.

For truly huge ranges, not even that will provide good performance under the memory limitation. One idea might be to store the candidates not as a list of numbers, but as an interval. So, initially, you choose between from and to, getting x1. Next time, pick from a number from the first subinterval or the second, with probability in proportion to the interval length. At each step, eliminate intervals which have zero length. This requires storing M + 2 integers (in the worst case), where M is the number of draws, or N/2 asymptotically for large N (in the worst case), where N is the initial interval size. Somebody might double-check me, though.