Selection in Expected Linear Time

Goal: Select ith smallest element from A[p..r].
Partition into A[p..q] and A[q+1..r]
If ith smallest element is in A[p..q]
then recurse on A[p..q]
else recurse on A[q+1..r]

Select(A, p, r, i)
1 $\;\;\;\;\;$if p = r
2 $\;\;\;\;\;$then return A[p]
3 $\;\;\;\;\;$else q = Partition(A, p, r)
4 $\;\;\;\;\;$ $\;\;\;\;\;$k = q - p + 1
5 $\;\;\;\;\;$ $\;\;\;\;\;$if i $\leq$ k
6 $\;\;\;\;\;$ $\;\;\;\;\;$then return Select(A, p, q, i)
7 $\;\;\;\;\;$ $\;\;\;\;\;$else return Select(A, q+1, r, i-k)