Lecture 13

Learning objectives

After this class, you should be able to:

1. Define a binary tree and a complete binary tree.
2. Show how the vertices of a binary tree can be represented in C++.
3. Show how a complete binary tree can be represented using an array.
4. Derive the relationship between the number of vertices and the height of a binary tree.
5. Given a binary tree, give the order in which vertices of the tree are visited by an inorder traversal.

Reading assignment

1. Section 4.2.
2. Lecture: Trees: Part 2 -- Binary trees.
3. Page 124.

Exercises and review questions

• Exercises and review questions on current lecture's material
  1. Prove the formulas that we showed for the positions of the parent and children of vertices in the array representation of a complete binary tree.
  2. Give the order in which vertices of the tree in figure 4.73 are visited by an inorder traversal.

• Questions on next lecture's material
  1. Give an example of a binary tree that is not a binary search tree.

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Last modified: 27 Sep 2011