A binary tree T has 9 nodes. The inorder and preorder traversals of T yield the following sequences: Inorder: E A C K F H D B G Preorder: F A E K C D H G B Draw the tree T.
Added by Teresa T.
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The first node in the preorder traversal is the root of the tree. So, F is the root of the tree. Show more…
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This question concerns binary search trees, amortized complexity, and heaps (20 marks total). (a) Define the properties that make a binary tree into a Binary Search Tree (BST). How would a "removeMin" operation be implemented for a BST? That is, show how to find and remove the minimum element of a BST. What is the Big-O complexity of removeMin, in terms of the height h and/or number of nodes n, of the BST? (b) Suppose that a sorting procedure, "BST-Sort", is implemented using a BST - in the same fashion as HeapSort, but instead using a BST. In this procedure, n elements are inserted one at a time into an initially-empty BST, and then removed from the BST using removeMin until the BST is again empty. Assume the BST is a simple one with no mechanism to maintain balance. What is the worst-case complexity of BST-Sort? Justify your answer and give a simple example with n=4.
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