Quicksort混乱

Question

I'm going through the quicksort and whichever article i see, i get more confused.

1) This implementation is really good http://gauss.ececs.uc.edu/Courses/C321/html/quicksort.java.html

But as i understand, after each pass, the pivot index is in correct position.

Then ideally we should be doing the following:

   public static void Quicksort(int A[], int f, int l)
   {
      if (f >= l) return;
      int pivot_index = partition(A, f, l);
      Quicksort(A, f, pivot_index-1); //*** pivot_index-1
      Quicksort(A, pivot_index+1, l);
   }

But tutorial uses Quicksort(A, f, pivot_index); .

I'm 200% sure that making the change 'pivot_index-1' will not improve any performance or reduce the complexity; but just want to make if my understanding is correct.

2) The implementation here works; but it doesn't place the pivot element at the correct position with each pass.

Answer 1

Two implementations I've seen:

• End index inclusive
• End index exclusive

Quicksort(A, f, pivot_index-1); is for the first case.

Quicksort(A, f, pivot_index); is for the second case.

Doing Quicksort(A, f, pivot_index); on the first case will still result in a sorted list, but will do a bit of extra work.

Doing Quicksort(A, f, pivot_index-1); on the second case probably won't result in a fully sorted list all the time.

Analysis of this implementation :

I can see why it works (it will swap the pivot with a greater element at a lower index), but that's not the QuickSort I know, and it might be doing slightly more work than required.