Quick Sort (10.9)

















How does Quick Sort work?

	if the size of the List is at least 2
	    select an item in the List to use as the pivot
	    partition the List into small, equal, large Lists
	       (small, equal, large compared to pivot)
	    recursively sort small
	    recursively sort large
	    concatenate small, equal, and large into one list
	end if



Show the steps of Quick Sort on the List.
Give the Lists after each partition and concatenate step.
Use the item in the middle position as the pivot.

	[9 8 1 6 4 3 7 5 2]

















Classwork
You may work with a partner.

Show the steps of Quick Sort on the List.
Give the Lists after each partition and concatenate step.
Use the item in the middle position as the pivot.

	[4 7 2 3 5 8 1 2 9]

















Quick Sort Code


quickSort ( list ) {

  if ( list.size > 1 ) {

    partition( list, small, equal, large );

    quickSort( small );
    quickSort( large );

    concat( small, equal, large, list );

  }

}

partition( list, small, equal, large ) {

  pivot = item in middle position of list

  for each item in list
    if item is smaller than pivot
      add item to small
    else if item is larger than pivot
      add item to large
    else
      add item to equal

}

concat( small, equal, large, list ) {

  for each item in small
    add item to list

  for each item in equal
    add item to list

  for each item in large
    add item to list

}



What's the running time for partition?

What's the running time for concat?

What's the running time for Quick Sort?

Does the running time for Quick Sort depend on
the kind of input you give it?

DEMO	(quick sort on sorted, reverse, random data)

















Selecting the Pivot


DEMO	(quick sort with bad pivots)


What's the Best-Case partitioning for Quick Sort?

How deep is the recursion in this case?

What's the Big-Oh for Quick Sort in the Best-Case?


What's the Worst-Case partitioning for Quick Sort?

How deep is the recursion in this case?

What's the Big-Oh for Quick Sort in the Worst-Case?


What's the Big-Oh for Quick Sort in the Average-Case?



What's the result of using the First or Last item as the Pivot?

What's the result of using the Middle item as the Pivot?

















Median Of Three


What's the median of a list of numbers?

Why not use the median value from the List as the Pivot?

How can you estimate the median?


Find the Median-of-three for each list of numbers.


	8 5 4 6 2 3 1

	4 9 3 5 7 6 2

















Quick Sort Partitioning


Why is the Quick Sort demo as slow as Merge Sort?


How does partitioning really work?

	1. swap the pivot with the first item
	2. scan from left to right for a large item
	   scan from right to left for a small item
	   if the large item is to the left of the small item
	       swap the two items and repeat
	3. swap the pivot with the small item


Show each step of partitioning on the List.


	1 8 5 9 4 3 7 2 6

















Classwork
You may work with a partner.

Show each step of partitioning on the List.


	2 7 2 5 3 9 1 2 8

















DEMO	(fast quick sort on sorted, reverse, random data)

















Quick Sort vs Merge Sort


What advantage does Quick Sort have over Merge Sort?

	quick sort is faster than merge sort
	partition can be done in-place, without using extra space
	merge sort requires twice the space


What advantage does Merge Sort have over Quick Sort?

	merge sort is O(n log n) in the worst case