Exercise 5.3.2

Professor Kelp decides to write a procedure that produces at random any permutation besides the identity permutation. He proposes the following procedure:

PERMUTE-WITHOUT-IDENTITY(A)
n = A.length
for i = 1 to n - 1
    swap A[i] with A[RANDOM(i + 1, n)]

Does this code do what Professor Kelp intends?

It does not. It always changes the position of each element. We cannot get the identity permutation, but we also can't get any permutation where an element is at the same place.