Most efficient way of randomly choosing a set of distinct integers

Question

I\'m looking for the most efficient algorithm to randomly choose a set of n distinct integers, where all the integers are in some range [0..maxValue].

Constraints:<

Answer 1

Linear congruential generator modulo maxValue+1. I'm sure I've written this answer before, but I can't find it...

Answer 2

One way to do it without generating the full array.

Say I want a randomly selected subset of m items from a set {x1, ..., xn} where m <= n.

Consider element x1. I add x1 to my subset with probability m/n.

• If I do add x1 to my subset then I reduce my problem to selecting (m - 1) items from {x2, ..., xn}.
• If I don't add x1 to my subset then I reduce my problem to selecting m items from {x2, ..., xn}.

Lather, rinse, and repeat until m = 0.

This algorithm is O(n) where n is the number of items I have to consider.

I rather imagine there is an O(m) algorithm where at each step you consider how many elements to remove from the "front" of the set of possibilities, but I haven't convinced myself of a good solution and I have to do some work now!