1. EECS 311: Chapter 6 Notes Chris Riesbeck EECS Northwestern

2.  Unless otherwise noted, all tables, graphs and code from Mark Allen Weiss' Data Structures and Algorithm Analysis in C++, 3 rd ed, copyright © 2006 by Pearson Education, Inc.

3. Building the Initial Heap  Given a set of numbers  You could insert one by one  Complexity: O(n log n)  There's a better way…  Throw all numbers into the array  Fix from the bottom up (2 nd to last row)

4. Building a Heap Initial setProcess node 7

5. Building a Heap 2 Process node 5Process node 6

6. Building a Heap 3 Process node 3Process node 4

7. Building a Heap 4 Process node 1Process node 2

8. Building a Heap Complexity  The worst case this way is the sum of the heights of the nodes.  That sum = 2 h+1 – h  2 h+1 is the number of nodes N  Ergo, this algorithm is O(N) to build a heap