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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?