Generate an uniform random permutation

Question

I am not sure whether the following pseudo-code can generate an uniformly random permutation:

PERMUTATE(A): 
    n = A.length
    for i = 1 to n
        swap A[i] and A[random(1,n)]

It seems to be right, but can anyone give me a rigorous proof to verify its correctness or wrongness ?

Answer 1

This solution is biased, you want the Fisher Yates algorithm [which is similar] for non biased permutation. [basically, you need to swap with random(i,n) instead of with random(1,n)]

This thread discusses how and why your solution is biased.