Happy new year! Let's think sorting.

1. CS 321. Algorithm Analysis & Design
Lecture 1
Sorting

2. Announcements

3. Announcements
The course website is at http://cs321.xyz

4. Announcements
The course website is at http://cs321.xyz
Please take the informal survey on the website,
or send me an email with the subject [CS321].

5. Agenda

6. Agenda
Sorting Algorithms

7. Agenda
Sorting Algorithms
Lower Bounds

8. Agenda
Sorting Algorithms
Lower Bounds
Preference Aggregation

9. Sorting

10. 4 4 2 1 2 5 6
1 2 2 4 7 9 7
6 4 5 5 9 4 3
7 4 5 9 7 3 8

11. 4 4
21 2
5 6
1 2 2
4
7 97
6
4
5 5
9
43
7
4
5
97
3
8

12. Counting Sort

13. 45986 45382 39590 99921
75987 55321 78324 52011
12001 99215 54213
32007 14261 12345 77666
11100

14. 45986 45382 39590 99921
75987 55321 78324 52011
12001 99215 54213
32007 14261 12345 77666
11100

15. 45986 4538239590
9992175987
55321
78324
52011
12001
99215
54213
32007
14261 12345
77666
11100

16. 459864538239590
99921
7598755321
78324
52011
12001
99215
54213
32007
1426112345
77666
11100

17. Bucket Sort

18. 21 25 32 45 90 63 72

19. 21 25 32 45 90 63 72

20. 21 25 32 45 90 63 72

21. 21 25 32 45 90 63 72

22. 21 25 32 45 90 63 72

23. 21 25 32 45 90 63 72

24. 21 25 32 45 9063 72

25. 21 25 32 45 9063 72

26. 21 25 32 45 9063 72

27. 21 25 32 45 9063 72

28. 21 25 32 45 9063 72
21 25 32 45 9063 72

29. 21 25 32 45 9063 72
21 25 32 45 9063 72

30. 21 25 32 45 9063 72
21 25 32 45 9063 72

31. Bubble Sort

32. 21 25 32 45 63 72
35

33. 21 25 32 45 63 72
35

34. 21 25 32 45 63 72
35

35. 21 25 32 45 63 72
35

36. 21 25 32 45 63 72
35

37. 21 25 32 45 63 7235

38. 24 31 23 14 56 62 11
10 32 21 89 22 54 12
42 19 51 78 9 14 3
99 27 50 88 63 70 81

39. 24 31 23 14 56 62 11
10 32 21 89 22 54 12
42 19 51 78 9 14 3
99 27 50 88 63 70 81

40. 24 31 23 14 56 62 11
10 32 21 89 22 54 12
42 19 51 78 9 14 3
99 27 50 88 63 70 81

41. 24 3123 14 56 62 11
10 32 21 89 22 54 12
42 19 51 78 9 14 3
99 27 50 88 63 70 81

42. 24 3123 14 56 62 11
10 32 21 89 22 54 12
42 19 51 78 9 14 3
99 27 50 88 63 70 81

43. 24 312314 56 62 11
10 32 21 89 22 54 12
42 19 51 78 9 14 3
99 27 50 88 63 70 81

44. 21 25 32 45 63 72
35

45. 21 25 32 45 63 72
35
Use binary search to reduce the number of comparisons.

46. Insertion Sort

47. 21 25 32 41 55 63 72
10 22 45 53 62 64 90

48. 21 25 32 41 55 63 72
10 22 45 53 62 64 90

49. 21 25 32 41 55 63 72
10
22 45 53 62 64 90

50. 21
25 32 41 55 63 72
10
22 45 53 62 64 90

51. 21
25 32 41 55 63 72
10 22
45 53 62 64 90

52. 21 25
32 41 55 63 72
10 22
45 53 62 64 90

53. 21 25 32
41 55 63 72
10 22
45 53 62 64 90

54. 21 25 32 41
55 63 72
10 22
45 53 62 64 90

55. 21 25 32 41
55 63 72
10 22 45
53 62 64 90

56. 21 25 32 41
55 63 72
10 22 45
53
62 64 90

57. 21 25 32 41
55 63 72
10 22 45
53 62 64 90

63. Merging two sorted arrays of length n each
takes O(n) comparisons.

93. There are log n layers of recursion.

94. There are log n layers of recursion.
The work done at each layer is O(n).

95. There are log n layers of recursion.
The work done at each layer is O(n).
Total time spent is O(n log n).

96. Merge Sort

98. Pick a “pivot”.

99. Pick a “pivot”.

101. Recurse!

103. “Merging” is trivial.

107. The recursion tree may be very skewed.

108. Quick Sort

109. Sorting Algorithms
Counting Sort
Bubble Sort
Merge Sort
Quick Sort
Insertion Sort
O(n + k)
O(n2)
O(n log n)
O(n2)
O(n2)

110. Sorting Algorithms
Counting Sort
Bubble Sort
Merge Sort
Quick Sort
Insertion SortBinary
O(n + k)
O(n2)
O(n log n)
O(n2)
O(n2)

111. Sorting Algorithms
Counting Sort
Bubble Sort
Merge Sort
Quick Sort
Insertion SortBinary
Randomised
O(n + k)
O(n2)
O(n log n)
O(n2)
O(n2)

112. References

113. References
Look up “The Sound of Sorting” on Youtube.

114. References
Look up “The Sound of Sorting” on Youtube.
http://www.sorting-algorithms.com

115. Agenda
Sorting Algorithms
Lower Bounds
Preference Aggregation

117. Happy New Year