Assignment 2

Answer all questions – maximum 100 marks. You must score at least 50 to pass the assignment.

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- (15 marks) Design an algorithm for the following operations for a binary tree BT, and show the worst-case running times for each implementation:

preorderNext(x): return the node visited after node x in a pre-order traversal of BT.

postorderNext(x): return the node visited after node x in a post-order traversal of BT.

inorderNext(x): return the node visited after node x in an in-order traversal of BT.

- (25 marks) Design a recursive linear-time algorithm that tests whether a binary tree satisfies the search tree order property at every node.
- (20 marks) Exercise 8.2. Illustrate what happens when the sequence 1, 5, 2, 4, 3 is added to an empty ScapegoatTree, and show where the credits described in the proof of Lemma 8.3 go, and how they are used during this sequence of additions.
- (20 marks) Implement a commonly used hash table in a program that handles collision using linear probing. Using (K mod 13) as the hash function, store the following elements in the table: {1, 5, 21, 26, 39, 14, 15, 16, 17, 18, 19, 20, 111, 145, 146}.
- (20 marks) Exercise 6.7. Create a subclass of BinaryTree whose nodes have fields for storing preorder, post-order, and in-order numbers. Write methods preOrderNumber(), inOrderNumber(), and postOrderNumbers() that assign these numbers correctly. These methods should each run in
*O*(n) time.

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- 275 words per page
- 12 pt Arial/Times New Roman
- Double line spacing
- Any citation style (APA, MLA, Chicago/Turabian, Harvard)

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