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Details. At this point our heap can easily implement a priority queue given that we start with an empty queue and add and remove elements as necessary. If we were given an array of numbers it might be useful to turn the array into a heap "in-place". BuildHeap.

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Details

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  1. Details • At this point our heap can easily implement a priority queue given that we start with an empty queue and add and remove elements as necessary. • If we were given an array of numbers it might be useful to turn the array into a heap "in-place"

  2. BuildHeap • Given an array of numbers how do we convert it into a heap. • We could iterate through the array and insert each number into heap but this requires us to have space big enough for twice the quantity of numbers we have. • We want to convert in place. • Note: We will assume that element 0 is not used. • Don't confuse with heapify. BuildHeap will use heapify

  3. BuildHeap • Assume that we have the number of elements in a variable called size Iterate i from element int(size/2) down to element 1 heapify(i)

  4. BuildHeap size = 26 87 68 43 6 77 33 9 11 19 99 6 23 89 2 14 22 27 35 7 42 12 71 1 5 3 67

  5. BuildHeap size = 26 87 68 43 6 77 33 9 13 11 19 99 6 23 89 2 14 Start at element int(size/2) 22 27 35 7 42 12 71 1 5 3 67

  6. BuildHeap size = 26 87 68 43 6 77 33 9 13 11 19 99 6 23 89 2 14 22 27 35 7 42 12 71 1 5 3 67 heapify

  7. BuildHeap size = 26 87 68 43 6 77 33 9 13 11 19 99 6 23 22 2 14 89 27 35 7 42 12 71 1 5 3 67 heapify

  8. BuildHeap size = 26 87 68 43 6 77 33 9 13 11 19 99 6 23 22 2 14 89 27 35 7 42 12 71 1 5 3 67 heapify

  9. BuildHeap size = 26 87 68 43 6 77 33 9 13 11 19 99 6 3 22 2 14 89 27 35 7 42 12 71 1 5 23 67 heapify

  10. BuildHeap size = 26 87 68 43 6 77 33 9 13 11 19 99 6 3 22 2 14 89 27 35 7 42 12 71 1 5 23 67 heapify

  11. BuildHeap size = 26 87 68 43 6 77 33 9 13 11 19 99 6 3 22 2 14 89 27 35 7 42 12 71 1 5 23 67 heapify

  12. BuildHeap size = 26 87 68 43 6 77 33 9 13 11 19 7 6 3 22 2 14 89 27 35 99 42 12 71 1 5 23 67 heapify

  13. BuildHeap size = 26 87 68 43 6 77 33 9 13 11 19 7 6 3 22 2 14 89 27 35 99 42 12 71 1 5 23 67 heapify

  14. BuildHeap size = 26 87 68 43 6 77 33 9 13 11 19 7 6 3 22 2 14 89 27 35 99 42 12 71 1 5 23 67 heapify

  15. BuildHeap size = 26 87 68 43 6 77 33 9 13 1 19 7 6 3 22 2 14 89 27 35 99 42 12 71 11 5 23 67 heapify

  16. BuildHeap size = 26 87 68 43 6 77 33 9 13 1 19 7 6 3 22 2 14 89 27 35 99 42 12 71 11 5 23 67 heapify

  17. BuildHeap size = 26 87 68 43 6 77 33 2 13 1 19 7 6 3 22 9 14 89 27 35 99 42 12 71 11 5 23 67 heapify

  18. BuildHeap size = 26 87 68 43 6 77 33 2 13 1 19 7 6 3 22 9 14 89 27 35 99 42 12 71 11 5 23 67 heapify

  19. BuildHeap size = 26 87 68 43 6 77 3 2 13 1 19 7 6 33 22 9 14 89 27 35 99 42 12 71 11 5 23 67 heapify

  20. BuildHeap size = 26 87 68 43 6 77 3 2 13 1 19 7 6 33 22 9 14 89 27 35 99 42 12 71 11 5 23 67 heapify

  21. BuildHeap size = 26 87 68 43 6 77 3 2 13 1 19 7 6 23 22 9 14 89 27 35 99 42 12 71 11 5 33 67 heapify

  22. BuildHeap size = 26 87 68 43 6 77 3 2 13 1 19 7 6 23 22 9 14 89 27 35 99 42 12 71 11 5 33 67 heapify

  23. BuildHeap size = 26 87 68 43 6 6 3 2 13 1 19 7 77 23 22 9 14 89 27 35 99 42 12 71 11 5 33 67 heapify

  24. BuildHeap size = 26 87 68 43 6 6 3 2 13 1 19 7 77 23 22 9 14 89 27 35 99 42 12 71 11 5 33 67 heapify

  25. BuildHeap size = 26 87 68 43 6 6 3 2 13 1 19 7 12 23 22 9 14 89 27 35 99 42 77 71 11 5 33 67 heapify

  26. BuildHeap size = 26 87 68 43 6 6 3 2 13 1 19 7 12 23 22 9 14 89 27 35 99 42 77 71 11 5 33 67 heapify

  27. BuildHeap size = 26 87 68 43 1 6 3 2 13 6 19 7 12 23 22 9 14 89 27 35 99 42 77 71 11 5 33 67 heapify

  28. BuildHeap size = 26 87 68 43 1 6 3 2 13 6 19 7 12 23 22 9 14 89 27 35 99 42 77 71 11 5 33 67 heapify

  29. BuildHeap size = 26 87 68 43 1 6 3 2 13 5 19 7 12 23 22 9 14 89 27 35 99 42 77 71 11 6 33 67 heapify

  30. BuildHeap size = 26 87 68 43 1 6 3 2 13 5 19 7 12 23 22 9 14 89 27 35 99 42 77 71 11 6 33 67 heapify

  31. BuildHeap size = 26 87 2 43 1 6 3 68 13 5 19 7 12 23 22 9 14 89 27 35 99 42 77 71 11 6 33 67 heapify

  32. BuildHeap size = 26 87 2 43 1 6 3 68 13 5 19 7 12 23 22 9 14 89 27 35 99 42 77 71 11 6 33 67 heapify

  33. BuildHeap size = 26 87 2 43 1 6 3 9 13 5 19 7 12 23 22 68 14 89 27 35 99 42 77 71 11 6 33 67 heapify

  34. BuildHeap size = 26 87 2 43 1 6 3 9 13 5 19 7 12 23 22 68 14 89 27 35 99 42 77 71 11 6 33 67 heapify

  35. BuildHeap size = 26 87 2 1 43 6 3 9 13 5 19 7 12 23 22 68 14 89 27 35 99 42 77 71 11 6 33 67 heapify

  36. BuildHeap size = 26 87 2 1 43 6 3 9 13 5 19 7 12 23 22 68 14 89 27 35 99 42 77 71 11 6 33 67 heapify

  37. BuildHeap size = 26 87 2 1 5 6 3 9 13 43 19 7 12 23 22 68 14 89 27 35 99 42 77 71 11 6 33 67 heapify

  38. BuildHeap size = 26 87 2 1 5 6 3 9 13 43 19 7 12 23 22 68 14 89 27 35 99 42 77 71 11 6 33 67 heapify

  39. BuildHeap size = 26 87 2 1 5 6 3 9 13 6 19 7 12 23 22 68 14 89 27 35 99 42 77 71 11 43 33 67 heapify

  40. BuildHeap size = 26 87 2 1 5 6 3 9 13 6 19 7 12 23 22 68 14 89 27 35 99 42 77 71 11 43 33 67 heapify

  41. BuildHeap size = 26 1 2 87 5 6 3 9 13 6 19 7 12 23 22 68 14 89 27 35 99 42 77 71 11 43 33 67 heapify

  42. BuildHeap size = 26 1 2 87 5 6 3 9 13 6 19 7 12 23 22 68 14 89 27 35 99 42 77 71 11 43 33 67 heapify

  43. BuildHeap size = 26 1 2 5 87 6 3 9 13 6 19 7 12 23 22 68 14 89 27 35 99 42 77 71 11 43 33 67 heapify

  44. BuildHeap size = 26 1 2 5 87 6 3 9 13 6 19 7 12 23 22 68 14 89 27 35 99 42 77 71 11 43 33 67 heapify

  45. BuildHeap size = 26 1 2 5 6 6 3 9 13 87 19 7 12 23 22 68 14 89 27 35 99 42 77 71 11 43 33 67 heapify

  46. BuildHeap size = 26 1 2 5 5 6 3 9 13 87 19 7 12 23 22 68 14 89 27 35 99 42 77 71 11 43 33 67 heapify

  47. BuildHeap size = 26 1 2 5 5 6 3 9 13 11 19 7 12 23 22 68 14 89 27 35 99 42 77 71 87 43 33 67 heapify

  48. BuildHeap size = 26 1 2 5 5 6 3 9 13 11 19 7 12 23 22 68 14 89 27 35 99 42 77 71 87 43 33 67 Questions?

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