1. An Auto-generated Presentation
Heapsort
An Auto-generated Presentation

2. First, heapsort must build a heap
A ‘heap’ is a tree wherein each node is of a value equal to or less than its parent.
Additionally, a ‘binary tree’ is used, which adds the constraint that no parent may have more than two nodes; this allows heapsort to run within its own array, without additional space complexity.
Each limb is passed through in reverse order, if the largest child is larger than the parent, they are swapped

3. First, heapsort must build a heap4 7 43 98 38 98 75 66 7 94 80 12 12 33 66 31 8 25 43 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 43 98 38 75 66 94 80 33 31 25

4. First, heapsort must build a heap4 7 43 98 38 98 75 66 7 94 80 12 12 33 66 31 8 25 43 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 43 98 38 75 66 94 80 33 31 25

5. First, heapsort must build a heap4 7 43 98 38 98 75 66 43 94 80 12 12 33 66 31 8 25 7 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 43 98 38 75 66 94 80 33 31 25

6. First, heapsort must build a heap4 7 43 98 38 98 75 66 43 94 80 12 12 33 66 31 8 25 7 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 43 98 38 75 66 94 80 33 31 25

7. First, heapsort must build a heap4 7 43 98 38 98 75 66 43 94 80 12 12 33 66 31 8 25 7 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 43 98 38 75 66 94 80 33 31 25

8. First, heapsort must build a heap4 7 43 98 38 98 75 66 43 94 80 12 12 33 66 31 8 25 7 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 43 98 38 75 66 94 80 33 31 25

9. First, heapsort must build a heap4 7 43 98 94 98 75 66 43 43 80 12 12 33 66 31 8 25 7 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 43 98 94 75 66 80 33 31 25 38

10. First, heapsort must build a heap4 7 43 98 94 98 75 66 43 43 80 12 12 33 66 31 8 25 7 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 43 98 94 75 66 80 33 31 25 38

11. First, heapsort must build a heap4 7 98 98 94 43 75 66 43 43 80 12 12 33 66 31 8 25 7 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 98 94 43 75 66 80 33 31 25 38

12. First, heapsort must build a heap4 98 98 66 94 43 75 31 43 43 80 12 12 33 66 7 8 25 7 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 98 66 94 43 75 31 80 33 25 38

13. First, heapsort must build a heap98 94 98 66 80 43 75 31 43 43 4 12 12 33 66 7 8 25 7 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 98 94 66 80 43 75 31 33 25 38

14. The finished heap 98 94 98 66 80 43 75 31 43 43 4 12 12 33 66 7 8 25 7 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 98 94 66 80 43 75 31 33 25 38

15. Now, heapsort can sort the array
At this point heapsort functions much like a ‘reverse’ selection sort, only ‘selecting’ is hardly necessary; it knows exactly where the largest values are: at the top of the heap!
The first in the array is swapped with the last unsorted number, and the heap rebuilds itself.

16. Now, heapsort can sort the array38 94 98 66 80 43 75 31 43 43 4 12 12 33 66 7 8 25 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 38 94 98 66 80 43 75 31 33 25

17. Now, heapsort can sort the array98 94 75 66 80 43 66 31 43 43 4 12 12 33 38 7 8 25 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 98 94 75 66 80 43 31 33 38 25

18. Now, heapsort can sort the array7 94 75 66 80 43 66 31 43 43 4 12 12 33 38 7 8 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 94 75 66 80 43 31 33 38 25 98

19. Now, heapsort can sort the array94 80 75 66 43 43 66 31 43 7 4 12 12 33 38 7 8 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 94 80 75 66 43 31 33 38 25 98

20. Now, heapsort can sort the array25 80 75 66 43 43 66 31 43 7 4 12 12 33 38 7 8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 80 75 66 43 31 33 38 94 98

21. Now, heapsort can sort the array80 66 75 43 43 43 66 31 25 7 4 12 12 33 38 7 8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 80 66 75 43 31 25 33 38 94 98

22. Now, heapsort can sort the array8 66 75 43 43 43 66 31 25 7 4 12 12 33 38 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 66 75 43 31 25 33 38 80 94 98

23. Now, heapsort can sort the array75 66 66 43 43 43 38 31 25 7 4 12 12 33 8 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 75 66 43 38 31 25 33 80 94 98

24. Now, heapsort can sort the array7 66 66 43 43 43 38 31 25 7 4 12 12 33 8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 66 43 38 31 25 33 75 80 94 98

25. Now, heapsort can sort the array66 43 66 31 43 43 38 7 25 7 4 12 12 33 8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 66 43 31 38 25 33 75 80 94 98

26. Now, heapsort can sort the array8 43 66 31 43 43 38 7 25 7 4 12 12 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 43 66 31 38 25 33 75 80 94 98

27. Now, heapsort can sort the array66 43 43 31 43 12 38 7 25 7 4 8 12 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 66 43 31 38 25 33 75 80 94 98

28. Now, heapsort can sort the array33 43 43 31 43 12 38 7 25 7 4 8 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 33 43 31 38 25 66 75 80 94 98

29. Now, heapsort can sort the array43 43 43 31 33 12 38 7 25 7 4 8 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 43 31 33 38 25 66 75 80 94 98

30. Now, heapsort can sort the array12 43 43 31 33 12 38 7 25 7 4 8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 43 31 33 38 25 66 75 80 94 98

31. Now, heapsort can sort the array43 33 43 31 12 12 38 7 25 7 4 8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 43 33 31 38 25 66 75 80 94 98

32. Now, heapsort can sort the array8 33 43 31 12 12 38 7 25 7 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 33 43 31 38 25 66 75 80 94 98

33. Now, heapsort can sort the array43 33 38 31 12 12 8 7 25 7 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 43 33 38 31 25 66 75 80 94 98

34. Now, heapsort can sort the array4 33 38 31 12 12 8 7 25 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 33 38 31 25 43 66 75 80 94 98

35. Now, heapsort can sort the array38 33 12 31 12 4 8 7 25 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 38 33 31 25 43 66 75 80 94 98

36. Now, heapsort can sort the array7 33 12 31 12 4 8 7 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 33 31 25 38 43 66 75 80 94 98

37. Now, heapsort can sort the array33 31 12 25 12 4 8 7 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 33 31 25 38 43 66 75 80 94 98

38. Now, heapsort can sort the array7 31 12 25 12 4 8 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 31 25 33 38 43 66 75 80 94 98

39. Now, heapsort can sort the array31 25 12 7 12 4 8 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 31 25 33 38 43 66 75 80 94 98

40. Now, heapsort can sort the array7 25 12 7 12 4 8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 31 33 38 43 66 75 80 94 98

41. Now, heapsort can sort the array25 12 12 7 7 4 8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 31 33 38 43 66 75 80 94 98

42. Now, heapsort can sort the array8 12 12 7 7 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 31 33 38 43 66 75 80 94 98

43. Now, heapsort can sort the array12 8 12 7 7 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 31 33 38 43 66 75 80 94 98

44. Now, heapsort can sort the array4 8 12 7 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 31 33 38 43 66 75 80 94 98

45. Now, heapsort can sort the array12 8 4 7 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 31 33 38 43 66 75 80 94 98

46. Now, heapsort can sort the array7 8 4 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 31 33 38 43 66 75 80 94 98

47. Now, heapsort can sort the array8 7 4 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 31 33 38 43 66 75 80 94 98

48. Now, heapsort can sort the array7 7 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 31 33 38 43 66 75 80 94 98

49. Now, heapsort can sort the array7 7 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 31 33 38 43 66 75 80 94 98

50. Now, heapsort can sort the array4 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 31 33 38 43 66 75 80 94 98

51. Now, heapsort can sort the array7 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 31 33 38 43 66 75 80 94 98

52. Now, heapsort can sort the array4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 31 33 38 43 66 75 80 94 98

53. The array is now sorted! 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 31 33 38 43 66 75 80 94 98

54. Further information…
Heapsort has similar problem complexity as mergesort, but is often preferred due to its better space complexity. While on most architecture, depending on optimizations, quicksort performs better, heapsort has a much preferable worst case complexity.
Worst case performance Θ(nlog n)
Best case performance Θ(nlog n)
Average case performance Θ(nlog n)
Worst case space complexity Θ(n)

55. Purpose and Acknowledgement
This set of slides were automatically generated by a generator piloted by Erik Williams when he worked on a novel computer science homework which was designed to also contribute to an ongoing project conducted at SUNY Oneonta.
This slides are intended to facilitate the teaching effort of Heapsort. Feel free to polish the slides as you like as long as our effort can be properly acknowledged.
For more data structures and algorithms teaching materials, feel free to visit the website of our on-going project.
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