I've came across Hoare's partition algorithm in Cormen. After analysis I think that the algorithm isn't working as I expected. Let's suppose that we've array [4,3,2,1], then in my opinion partition is returning 0, so next quicksort calls will be QS(A,1,0), QS(A,1,4), the second one is the same as first call so this array won't be sorted ever (infinite recursion).
Partition(A,p,r)
x = A[p]
i = p-1
j = r+1
while True do
repeat j-=1
until x>=A[j]
repeat i+=1
until x<=A[i]
if i<j then
swap(A[i], A[j])
else
return j
QS(A,p,r)
q = Partition(A,p,r)
QS(A,p,q)
QS(A,q+1,r)
