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What else can we do with heaps?

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What else can we do with heaps?. Use the heap for sorting. Heapsort!. Basic Idea. Given an unsorted array we use BuildHeap to convert it into a heap While(heap is not empty) removeMin The heap is one smaller but the array hasn't changed

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What else can we do with heaps?

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  1. What else can we do with heaps? Use the heap for sorting. Heapsort!

  2. Basic Idea • Given an unsorted array we use BuildHeap to convert it into a heap • While(heap is not empty) • removeMin • The heap is one smaller but the array hasn't changed • Put the item just removed in the element just after the end of the heap • At conclusion the array is sorted

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

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

  5. HeapSort size = 25 2 removeMin = 1 3 5 5 6 22 9 11 19 7 12 23 89 68 14 Not in heap now 27 35 99 42 77 71 87 43 33 67

  6. HeapSort size = 25 2 3 5 5 6 22 9 11 19 7 12 23 89 68 14 1 27 35 99 42 77 71 87 43 33 67 heap is 1 element smaller, smallest element is at end of array

  7. HeapSort size = 25 2 3 5 5 6 22 9 11 19 7 12 23 89 68 14 1 27 35 99 42 77 71 87 43 33 67 Now do it again!

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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