# Exercise 5.3.1

Professor Marceau objects to the loop invariant used in the proof of Lemma 5.5. He questions whether it is true prior to the first iteration. He reasons that we could just as easily declare that an empty subarray contains no 0-permutations. Therefore, the probability that an empty subarray contains a 0-permutation should be 0, thus invalidating the loop invariant prior to the first iteration. Rewrite the procedure

`RANDOMIZE-IN-PLACE`

so that its associated loop invariant applies to a nonempty subarray prior to the first iteration, and modify the proof of Lemma 5.5 for your procedure.

I'm not going to write any code since this is trivial.

We can pick up an element at random before entering the loop and replace it with the first one. Now our invariant holds initially for a 1-permutation.