Algorithm to select a single, random combination of values?

Question

Say I have y distinct values and I want to select x of them at random. What\'s an efficient algorithm for doing this? I could just call rand(

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 non-destructive on the input array (as a partial shuffle would be) but this is optional

adapted from here

update

another approach using only a single call to PRNG (pseudo-random number generator) in [0,1] by IVAN STOJMENOVIC, "ON RANDOM AND ADAPTIVE PARALLEL GENERATION OF COMBINATORIAL OBJECTS" (section 3), of O(N) (worst-case) complexity