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

The trick is to use a variation of shuffle or in other words a partial shuffle.

function random_pick( a, n ) 
{
  N = len(a);
  n = min(n, N);
  picked = array_fill(0, n, 0); backup = array_fill(0, n, 0);
  // partially shuffle the array, and generate unbiased selection simultaneously
  // this is a variation on fisher-yates-knuth shuffle
  for (i=0; i=0; i--) // O(n) times
  { 
    selected = backup[ i ];
    value = a[ N ];
    a[ N ] = a[ selected ];
    a[ selected ] = value;
    N++;
  }
  return picked;
}

NOTE the algorithm is strictly O(n) in both time and space, produces unbiased selections (it is a partial unbiased shuffling) and does not need hasmaps (which may not be available and/or usualy hide a complexity behind their implementation, e.g fetch time is not O(1), it might even be O(n) in worst case)

adapted from here