Choosing k out of n

Question

I want to choose k elements uniformly at random out of a possible n without choosing the same number twice. There are two trivial approaches to this.

Answer 1

What you could use is the following algorithm (using javascript instead of pseudocode):

var k = 3;
var n = [1,2,3,4,5,6];

// O(k) iterations
for(var i = 0, tmp; i < k; ++i) {

    // Random index O(1)
    var index = Math.floor(Math.random() * (n.length - i));

    // Output O(1)
    console.log(n[index]);

    // Swap and lookup O(1)
    tmp = n[index];
    n[index] = n[n.length - i - 1];
    n[n.length - i - 1] = tmp;
}

In short, you swap the selected value with the last item and in the next iteration sample from the reduced subset. This assumes your original set is wholly unique.

The storage is O(n), if you wish to retrieve the numbers as a set, just refer to the last k entries from n.