Lecture 20

Learning objectives

After this class, you should be able to:

1. Define an AVL search tree..
2. Derive bounds on the height of an AVL tree.
3. Write code to implement insertion into an AVL tree, and give its time complexity.
4. Given a sequence of insertions into an AVL tree, draw the tree.
5. Identify applications where a binary search tree will be useful.

Reading assignment

1. Section 6.7 introduction, and 6.7.2 (except deletion).
2. None.

Exercises and review questions

• Exercises and review questions on current lecture's material
  1. Insert the following elements into an AVL search tree in the order given below and draw the resulting tree: 10, 8, 4, 2, 0, 3, 7, 6, 5.
  2. Derive an upper bound on the height of an extended AVL tree, where the |difference in heights of a left subtree and a right subtree| < 2, using a procedure similar to that discussed in class.
  3. Write code to implement a single rotation on an AVL tree, when a node gets balance factor -2 due to an insertion into its left child's left subtree.

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

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Last modified: 20 Mar 2008