1. Heapsort and d-Heap Neil Tang 02/11/2010
CS223 Advanced Data Structures and Algorithms

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

3. CS223 Advanced Data Structures and Algorithms
d-Heap
A d-Heap is exactly like a binary heap except that all the nodes have no more than d children.
CS223 Advanced Data Structures and Algorithms

4. 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

5. 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

6. CS223 Advanced Data Structures and Algorithms
Heapsort
CS223 Advanced Data Structures and Algorithms

7. CS223 Advanced Data Structures and Algorithms
Heapsort
CS223 Advanced Data Structures and Algorithms

8. 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 percolateDown(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