algorithm - 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:

• maxValue is larger than n, and possibly much larger
• I don't care if the output list is sorted or not
• all integers must be chosen with equal probability

My initial idea was to construct a list of the integers [0..maxValue] then extract n elements at random without replacement. But that seems quite inefficient, especially if maxValue is large.

Any better solutions?

Answer 1

Here is an optimal algorithm, assuming that we are allowed to use hashmaps. It runs in O(n) time and space (and not O(maxValue) time, which is too expensive).

It is based on Floyd's random sample algorithm. See my blog post about it for details. The code is in Java:

private static Random rnd = new Random();

public static Set<Integer> randomSample(int max, int n) {
    HashSet<Integer> res = new HashSet<Integer>(n);
    int count = max + 1;
    for (int i = count - n; i < count; i++) {
        Integer item = rnd.nextInt(i + 1);
        if (res.contains(item))
            res.add(i);
        else
            res.add(item);
    }
    return res;
}