Shuffle elements of an array/n numbers uniformly randomly. Possibley in expected O(n) time

Question

Is it possible to shuffle elements of an n-sized array uniformly, i.e. the probability of any of the n! combinations occurring is the same, in expected O(n) tim

Answer 1

What you want is random sample of set, that samples each element with equal probability.

Answer 2

For each array position:

Select a random number from current position to end of array

Swap current position with random position

That should give you O(n) without the challenge of finding an unused array position. This assumes you can use an in-place swap and that you don't have to create a new array.

Answer 3

You should look at the Fisher-Yates shuffle.

From the article:

Properly implemented, the Fisher–Yates shuffle is unbiased, so that every permutation is equally likely. The modern version of the algorithm is also rather efficient, requiring only time proportional to the number of items being shuffled and no additional storage space.

So it meets your requirements. It's pretty easy to implement too.