Lecture 22

Learning objectives

After this class, you should be able to:

1. Define a heap.
2. Given a sequence of insertions and DeleteMax or DeleteMin in a max or min heap, draw the resulting heap.
3. Given a heap drawn as a tree, show its array representation.
4. Given the array representation of a heap, draw it as a tree.
5. Give the time complexity for insertion into a heap, and DeleteMax/Min on it.
6. Determine the children and parent of a node, given its index in its array representation.
7. Give applications of heaps.

Reading assignment

1. Section 6.9, except Floyd algorithm for initialization.

Exercises and review questions

• Exercises and review questions on current lecture's material
  1. Draw the max heap corresponding to the following array: 16 14 10 8 7 9 3 2 4 1.
  2. Show the heap that results from inserting 11 into the heap above.
  3. Show the heap that results from DeleteMax on the heap in question 1.
  4. Prove that the children of node i are 2i+1 and 2i+2, where the root is node 1.

• Questions on next lecture's material
  1. None.