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Chapter 10 - Sorting

10.8 Heapsort 10.9 Quicksort. Chapter 10 - Sorting. 10.8 Heapsort Heapsort Algorithm Algorithm to Build a Heap Analysis of Heapsort Algorithm Code for Heapsort. 10.8, pgs. 599-601. Heapsort. Merge sort time is O( n log n ) but still requires, temporarily, n extra storage locations.

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Chapter 10 - Sorting

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  1. 10.8 Heapsort 10.9 Quicksort Chapter 10 - Sorting

  2. 10.8 Heapsort Heapsort Algorithm Algorithm to Build a Heap Analysis of Heapsort Algorithm Code for Heapsort 10.8, pgs. 599-601

  3. Heapsort Sorting • Merge sort time is O(n log n) but still requires, temporarily, n extra storage locations. • Heapsortis also O(n log n), but does not require any additional storage. • A max heap is used as its data structure with the largest value at the top. • Once we have a heap, we can remove one item at a time from the heap and place it at the bottom of the heap. • We then reheap by moving the larger of a node’s two children up the heap if needed, so the new heap will have the next largest item as its root. • As we continue to remove items from the heap, the heap size shrinks and the number of the removed items increases. • After we have removed the last element, the array will be sorted.

  4. Heapsort Sorting Max Heap? Yes! 89 74 76 37 32 39 66 18 20 29 26 6 28

  5. Heapsort Sorting 89 74 76 37 32 39 66 18 20 29 26 6 28

  6. Heapsort Sorting 6 74 76 37 32 39 66 18 20 29 26 89 28

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  47. Heapsort Sorting 6 20 18 26 28 29 32 66 37 76 39 89 74

  48. Heapsort Sorting 6 20 18 26 28 29 32 66 37 76 39 89 74

  49. Revising the Heapsort Algorithm Sorting • If we implement the heap as an array • each element removed will be placed at the end of the array, and • the heap part of the array decreases by one element

  50. Algorithm for In-Place Heapsort Sorting • Build a heap by rearranging the elements in an unsorted array. 1.1 while n is less than table.length 1.2 Increment n by 1. This inserts a new item into the heap 1.3 Restore the heap property • while the heap is not empty • Remove the first item from the heap by swapping it with the last item in the heap and restoring the heap property

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