Assignment Specification:

Part A:

Question 1

1. The INORDER traversal output of a binary tree is U, N, I, V, E, R, S, I, T, Y and the POSTORDER traversal output of the same tree is N, U, V, R, E, T, I, S, I, Y. Construct the tree and determine the output of the PREORDER traversal output.
2. One main difference between a binary search tree (BST) and an AVL (Adelson-Velski and Landis) tree is that an AVL tree has a balance condition, that is, for every node in the AVL tree, the height of the left and right subtrees differ by at most 1. Starting with an empty BST and AVL tree, insert elements into the two trees with the following keys: 27, 32, 89, 45, 10, 63, 57, 17
3. Based on what you have done for Question 1b, what is the big-O (worst case) complexity of the total time required to build a binary search tree (BST) consisting of nodes? Explain your answer. The answer without explanation gains no mark. (Hint. A tricky question. The question asks for worst-case complexity. Think properly.)
4. Similarly, from what you have done for Question 1b, what is the big-o (worst case) complexity of the total time required to build an AVL tree consisting of nodes? Explain your answer. The answer without explanation gains no mark. (Hint. The question asks for worst-case complexity.)
   

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