Quick Sort

1
Quick Sort
2
Outline

• Prerequisites
• Insertion Sort
• Merge Sort
• Objectives
• Understand Quick Sort
• Reference
• HTDP Section 25.2

3
Background

• Sorting takes an unordered collection and makes
  it an ordered one.
• Quick Sort is the fastest known sorting algorithm.

1 2 3 4 5
6
12
101
5
35
42
77
1 2 3 4 5
6
4
Divide and Conquer

• Divide and Conquer cuts the problem in two parts
  each time, but uses the result of both parts
• cut the problem in two until the problem is
  trivial
• solve for both parts
• combine the solutions

5
Quick Sort

• Another divide-and-conquer algorithm
• Divide the unsorted list into 2 parts until one
  of the parts is empty
• Arbitrarily choose the first item as the "pivot
  value"
• One part contains everything smaller than the
  pivot value
• The other part contains everything larger than
  the same pivot value
• Append the sub-problem solutions

6
67
45
23
14
6
33
36
42
7
67
45
23
14
6
33
36
42
67
6
14
36
45
33
23
42
8
67
45
23
14
6
33
36
42
67
6
14
36
45
33
23
42
6
14
33
67
45
42
23
9
67
45
23
14
6
33
36
42
67
6
14
36
45
33
23
42
6
14
33
67
45
42
23
6
14
10
67
45
23
14
6
33
36
42
67
6
14
36
45
33
23
42
6
14
33
67
45
42
23
6
14
6
14
11
67
45
23
14
6
33
36
42
67
6
14
36
45
33
23
42
6
14
33
67
45
42
23
6
14
6
14
6
14
33
23
67
45
42
12
67
45
23
14
6
33
36
42
67
6
14
36
45
33
23
42
6
14
33
23
67
45
42
6
14
6
14
6
14
33
23
67
45
42
6
14
33
23
67
45
42
36
13
67
45
23
14
6
33
36
42
6
14
33
23
67
45
42
36
14
Summary

• Divide the unsorted collection into two
• Until one of the sub-lists is empty
• Then append the sub-problem solutions

15
Comparing Quick Sort to Merge Sort

• On a list that is not previously sorted, Quick
  Sort runs 2-3 times faster than Merge Sort
• However, if the data are already sorted, Quick
  Sort is as slow as Insertion Sort
• Moral of the story
• If you want speed, use Quick Sort
• But make sure the data are in random order
• It might be worth the time to check the data
  first to see if it is sorted.

16
quick-sort.scm
17
Code Used

• pick-list (listof number) ck number -gt
  (listof number)
• (define (pick-list lst ck n)
• (if (empty? lst)
• empty
• (if (ck (first lst) n)
• (cons (first lst) (pick-list (rest lst)
  ck n))
• (pick-list (rest lst) ck n))))
• quick-sort unsorted list -gt sorted list
• (define (quick-sort lst)
• (if (empty? lst)
• empty
• (append
• (quick-sort (pick-list lst lt (first lst)))
• (list (first lst))
• (quick-sort (pick-list lst gt (first
  lst))))))

18
Questions?
19
Summary

• You should now know
• Quick Sort

20
(No Transcript)