Lecture 19

Learning objectives

After this class, you should be able to:

1. Given a BST and a sequence of insert and delete operations on it, draw the tree that results from these operations.
2. Find the smallest and largest elements in a tree, and the successor and predecessor of an element.
3. Write code to implement features of a binary search tree, such as insertion, deletion, finding the smallest and largest element, and finding the successor and predecessor of an element.
4. Derive the time complexities for the above operations on a binary search tree.
5. Give that advantages and disadvantages of a binary search tree over other data structures that we have discussed in class.
6. Identify applications where a binary search tree will be useful.

Reading assignment

1. Section 6.5 (excluding threaded trees) and section 6.6 (excluding 6.6.1).
2. None.

Exercises and review questions

• Exercises and review questions on current lecture's material
  1. Insert the following elements into a binary search tree in the order given below and draw the resulting binary search tree: 11, 7, 5, 13, 9, 15.
  2. Draw the binary search tree constructed by inserting the following numbers in the order given below, and then answer the following questions: 42, 36, 71, 18, 39, 53, 80, 5, 22, 64, 79.
     1. List the nodes encountered when you search for the number 22.
     2. Draw the tree that results after deleting the node with value 22.
     3. Draw the tree that results after deleting the node with value 80 from the tree in (2).
     4. Draw the tree that results after deleting the node with value 42 from the tree in (3).
  3. In any question below, you may assume that functions to implement features that precede that question exit.
     1. Write code to find the smallest element of a BST. (If your group Number % 8 = 0)
     2. Write code to find the largest element of a BST. (If your group Number % 8 = 1)
     3. Write code to delete a node that has fewer than 2 children. (If your group Number % 8 = 2)
     4. Write code to find the successor of a node that has a right child. (If your group Number % 8 = 3)
     5. Write a code or pseudocode to find the successor of a node that has no right child. You may assume that pointers to parents exist. (If your group Number % 8 = 4)
     6. Write code to find the predecessor of a node that has a left child. (If your group Number % 8 = 5)
     7. Write a code or pseudocode to find the predecessor of a node that has no left child. You may assume that pointers to parents exist. (If your group Number % 8 = 6)
     8. Write code to delete a node that has two children (If your group Number % 8 = 7)
  4. Give an application where a BST is better than other data structures discussed in class, and one where another data structure is better than a BST.

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