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Heapsort

Heapsort. Section 8.8. Heapsort. Merge sort time is O( n log n ) but still requires, temporarily, n extra storage locations Heapsort does not require any additional storage As its name implies, heapsort uses a heap to store the array. First Version of a Heapsort Algorithm.

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Heapsort

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  1. Heapsort Section 8.8

  2. Heapsort • Merge sort time is O(n log n) but still requires, temporarily, n extra storage locations • Heapsort does not require any additional storage • As its name implies, heapsort uses a heap to store the array

  3. First Version of a Heapsort Algorithm • When used as a priority queue, a heap maintains a smallest value at the top • The following algorithm • places an array's data into a heap, • then removes each heap item (O(n log n)) and moves it back into the array • This version of the algorithm requires n extra storage locations Heapsort Algorithm: First Version 1. Insert each value from the array to be sorted into a priority queue (heap). 2. Set i to 0 3. while the priority queue is not empty 4. Remove an item from the queue and insert it back into the array at position i 5. Increment i

  4. Revising the Heapsort Algorithm • In heaps we've used so far, each parent node value was less than the values of its children • We can build a heap so that each parent node value is larger than its children • Then, • move the top item to the bottom of the heap • reheap, ignoring the item moved to the bottom

  5. Trace of Heapsort 89 74 76 37 32 39 66 18 20 29 26 6 28 Go to End

  6. Trace of Heapsort (cont.) 89 74 76 37 32 39 66 18 20 29 26 6 28

  7. Trace of Heapsort (cont.) 89 74 76 37 32 39 66 18 20 29 26 6 28

  8. Trace of Heapsort (cont.) 6 74 76 37 32 39 66 18 20 29 26 89 28

  9. Trace of Heapsort (cont.) 76 74 6 37 32 39 66 18 20 29 26 89 28

  10. Trace of Heapsort (cont.) 76 74 37 6 32 39 66 18 20 29 26 89 28

  11. Trace of Heapsort (cont.) 76 74 37 26 32 39 66 18 20 29 6 89 28

  12. Trace of Heapsort (cont.) 76 74 37 26 32 39 66 18 20 29 6 89 28

  13. Trace of Heapsort (cont.) 76 74 37 26 32 39 66 18 20 29 6 89 28

  14. Trace of Heapsort (cont.) 76 74 37 26 32 39 66 18 20 29 6 89 28

  15. Trace of Heapsort (cont.) 29 74 37 26 32 39 66 18 20 76 6 89 28

  16. Trace of Heapsort (cont.) 74 29 37 26 32 39 66 18 20 76 6 89 28

  17. Trace of Heapsort (cont.) 74 66 37 26 32 39 29 18 20 76 6 89 28

  18. Trace of Heapsort (cont.) 74 66 37 26 32 39 29 18 20 76 6 89 28

  19. Trace of Heapsort (cont.) 74 66 37 26 32 39 29 18 20 76 6 89 28

  20. Trace of Heapsort (cont.) 74 66 37 26 32 39 29 18 20 76 6 89 28

  21. Trace of Heapsort (cont.) 28 66 37 26 32 39 29 18 20 76 6 89 74

  22. Trace of Heapsort (cont.) 66 28 37 26 32 39 29 18 20 76 6 89 74

  23. Trace of Heapsort (cont.) 66 39 37 26 32 28 29 18 20 76 6 89 74

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  25. Trace of Heapsort (cont.) 66 39 37 26 32 28 29 18 20 76 6 89 74

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  29. Trace of Heapsort (cont.) 39 29 37 26 32 28 18 66 20 76 6 89 74

  30. Trace of Heapsort (cont.) 39 29 37 26 32 28 18 66 20 76 6 89 74

  31. Trace of Heapsort (cont.) 39 29 37 26 32 28 18 66 20 76 6 89 74

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  39. Trace of Heapsort (cont.) 20 29 32 26 6 28 18 66 37 76 39 89 74

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  41. Trace of Heapsort (cont.) 32 29 26 20 6 28 18 66 37 76 39 89 74

  42. Trace of Heapsort (cont.) 32 29 26 20 6 28 18 66 37 76 39 89 74

  43. Trace of Heapsort (cont.) 32 29 26 20 6 28 18 66 37 76 39 89 74

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  45. Trace of Heapsort (cont.) 18 29 26 20 6 28 32 66 37 76 39 89 74

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  47. Trace of Heapsort (cont.) 29 28 26 20 6 18 32 66 37 76 39 89 74

  48. Trace of Heapsort (cont.) 29 28 26 20 6 18 32 66 37 76 39 89 74

  49. Trace of Heapsort (cont.) 29 28 26 20 6 18 32 66 37 76 39 89 74

  50. Trace of Heapsort (cont.) 29 28 26 20 6 18 32 66 37 76 39 89 74

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