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Heapsort

Heapsort. CSE 373 Data Structures. Heap Sort. We use a Max-Heap Root node = A[1] Children of A[i] = A[2i], A[2i+1] Keep track of current size N (number of nodes). 7. 7. 5. 6. 2. 4. 5. 6. value. index. 1. 2. 3. 4. 5. 6. 7. 8. 2. 4. N = 5. Using Binary Heaps for Sorting.

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Heapsort

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  1. Heapsort CSE 373 Data Structures

  2. Heap Sort • We use a Max-Heap • Root node = A[1] • Children of A[i] = A[2i], A[2i+1] • Keep track of current size N (number of nodes) 7 7 5 6 2 4 5 6 value index 1 2 3 4 5 6 7 8 2 4 N = 5

  3. Using Binary Heaps for Sorting • Build a max-heap • Do N DeleteMax operations and store each Max element as it comes out of the heap • Data comes out in largest to smallest order • Where can we put the elements as they are removed from the heap? 7 Build Max-heap 5 6 2 4 DeleteMax 6 5 4 2 7

  4. 1 Removal = 1 Addition • Every time we do a DeleteMax, the heap gets smaller by one node, and we have one more node to store • Store the data at the end of the heap array • Not "in the heap" but it is in the heap array 6 6 5 4 2 7 value 5 4 index 1 2 3 4 5 6 7 8 2 7 N = 4

  5. Repeated DeleteMax 5 5 2 4 6 7 2 4 1 2 3 4 5 6 7 8 6 7 N = 3 4 4 2 5 6 7 2 5 1 2 3 4 5 6 7 8 6 7 N = 2

  6. Heap Sort is In-place • After all the DeleteMaxs, the heap is gone but the array is full and is in sorted order 2 2 4 5 6 7 value 4 5 index 1 2 3 4 5 6 7 8 6 7 N = 0

  7. Heapsort: Analysis • Running time • time to build max-heap is O(N) • time for N DeleteMax operations is N O(log N) • total time is O(N log N) • Can also show that running time is (N log N) for some inputs, • so worst case is(N log N) • Average case running time is also O(N log N) • Heapsort is in-place but not stable (why?)

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