1Computer Sciences

2 HEAP SORT TUTORIAL 4

Objective O(n lg n) worst case like merge sort. Sorts in place like insertion sort. A heap can be stored as an array A. Root of tree is A[1]. Parent of A[i ] = A[i/2]. Left child of A[i ] = A[2i ]. Right child of A[i ] = A[2i + 1]. Computing is fast with binary representation implementation.

Heap data structure Heap is a nearly complete binary tree. “Heap is almost- complete binary tree.” Height of node = # of edges on a longest simple path from the node down to a leaf. Height of heap = height of root = (lg n). Computer Sciences4

Maintaining the heap property Computer Sciences5

Building a heap ( a bottom-up manner ) Computer Sciences6

The heap-sort algorithm Computer Sciences7

Exercises Illustrate the operation of heapSort on the below array: {17, 1, 9, 14, 2, 8, 3} a)b) Computer Sciences8

c)d) Computer Sciences9

e)f) Computer Sciences10

g) h) 9 Computer Sciences11

i) j) 3 Computer Sciences12

k) l) Sorted Computer Sciences13

a)b) Build a maxHeap from the below array: {15, 9, 20, 13, 4, 59} Exercises Computer Sciences14

c) d) Computer Sciences15

e)f) Computer Sciences16

g) h) Computer Sciences17

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