Heapsort and d-Heap Neil Tang 02/14/2008

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Presentation transcript:

Heapsort and d-Heap Neil Tang 02/14/2008 CS223 Advanced Data Structures and Algorithms

CS223 Advanced Data Structures and Algorithms Class Overview d-Heap Sort using a heap Heapsort CS223 Advanced Data Structures and Algorithms

CS223 Advanced Data Structures and Algorithms d-Heap A d-Heap is exactly like a binary heap except that all the nodes have d children. CS223 Advanced Data Structures and Algorithms

CS223 Advanced Data Structures and Algorithms d-Heap Insertion takes O(logdN). deleteMin takes O(dlogdN) Computing the position of a child or the parent takes much more time unless d is a power of 2. CS223 Advanced Data Structures and Algorithms

CS223 Advanced Data Structures and Algorithms Sort using a Heap Perform N deleteMin operations. Every time, copy the deleted element (min) to a new array. Copy the elements back to the original array. Time complexity: NlogN. CS223 Advanced Data Structures and Algorithms

CS223 Advanced Data Structures and Algorithms Heapsort CS223 Advanced Data Structures and Algorithms

CS223 Advanced Data Structures and Algorithms Heapsort CS223 Advanced Data Structures and Algorithms

CS223 Advanced Data Structures and Algorithms Heapsort Build a (max)heap. Swap the first and the last element in the current heap. Update heap size and porcolateDown(1) Go back to the 2nd step until the array is sorted. Time complexity (worst case): O(N+N*logN) = O(NlogN). Theorem: The average number of comparisons used to heapsort a random permutation of N distinct items is 2NlogN-O(NloglogN). CS223 Advanced Data Structures and Algorithms