04 - 15 Jan - Heap Sort
- 1. CS 321. Algorithm Analysis & Design Lecture 4 Heap Sort
- 2. 4 9 2 1 8 5 6
- 3. 4 9 2 1 8 5 6
- 4. 4 9 2 1 8 5 6
- 5. 4 9 2 1 8 5 6
- 6. 4 9 21 8 5 6
- 7. 4 9 21 8 5 6
- 8. 4 9 21 8 5 6
- 9. 4 9 21 8 5 6
- 10. 4 9 21 8 5 6
- 11. 4 9 21 8 5 6
- 12. 4 9 21 8 5 6
- 13. 4 9 21 8 5 6
- 14. 4 9 21 85 6
- 15. 4 9 21 85 6
- 16. 4 921 85 6
- 17. 4 921 85 6 Can we speed up the find-min operations?
- 18. 4 9 21 8 5 6 Organize the elements so that finding minimum is “easy”.
- 19. 4 9 21 8 5 6 Organize the elements so that deleting the minimum element is “easy”.
- 20. Store a set of n distinct numbers. Inserting a new element and deleting the minimum element can be done in time proportional to (log n). GOAL
- 21. All jumbled up 4 9 2 1 8
- 22. All jumbled up 4 9 2 1 8 3
- 23. All jumbled up 4 9 2 1 8 3 6
- 24. All jumbled up 4 9 2 1 8 3 Insert: O(1) 6
- 25. All jumbled up 4 9 2 1 8 3 Insert: O(1) Delete-Min: O(n) 6
- 26. All sorted 9 8 6 3 1
- 27. All sorted 9 8 6 3
- 28. All sorted 9 8 6 3 Delete-Min: O(1)
- 29. All sorted 9 8 6 3 Delete-Min: O(1) 4
- 30. All sorted 9 8 6 3 Delete-Min: O(1) 47
- 31. All sorted 9 8 6 3 Insert: O(n) Delete-Min: O(1) 47
- 32. In-between? Invariant: The first element of the array is the minimum.
- 33. In-between? Invariant: The first element of the array is the minimum.
- 34. In-between? Invariant: The first element of the array is the minimum.
- 35. In-between? Invariant: The first element of the array is the minimum.
- 36. In-between? Invariant: The first element of the array is the minimum.
- 37. In-between? Invariant: The first element of the array is the minimum.
- 38. In-between? Invariant: The first element of the array is the minimum.
- 39. In-between? Invariant: The first element of the array is the minimum.
- 40. 4 9 21 8 5 6
- 41. 6 1 59 24 8 x is a child of y: x is larger than y.
- 42. 6 1 59 24 8
- 43. 6 1 59 24 8
- 44. 6 1 59 24 8
- 45. 61 5924 8
- 47. 61 5924 8 6 1 59 24 8 1 2 3 4 5 6 7 1 2 3 4 5 6 7
- 48. 61 5924 8 6 1 59 24 8 1 2 3 4 5 6 7 1 2 3 4 5 6 7 left-child(i) = 2i
- 49. 61 5924 8 6 1 4 1 2 4 1 2 3 4 5 6 7
- 50. 61 5924 8 6 1 4 1 2 4 1 2 3 4 5 6 7 left-child(i) = 2i
- 53. left-child(i) = 2i i+k 2i + 2k i 2i
- 68. Heapify