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CS 430 – Fall 2022 Introduction to Algorithms - Homework 2 - Max Heap
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CS 430 – Fall 2022 INTRODUCTION TO ALGORITHMS HOMEWORK #2
DUE SEP. 28 (Wednesday, the end of day)
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• Teamwork is NOT allowed.
• Submit the PDF version of the assignment to the Blackboard.
• Late submissions will be accepted through Sep. 30 with a credit deduction. • All solutions should be explained.
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1. (5 points) A student claims that a preorder traversal of a max-heap will list out its keys in sorted order. Draw a small example of a max-heap that proves him wrong. Do any of the three binary tree traversals (preorder, inorder, postorder) list the keys of a max-heap in any particular order? Why?
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For tree traversals, please refer to the following example.
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2. (2 points) What are the minimum and maximum numbers of elements in a heap of height h? Argue for your solution.
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3. (3 points) The code for MAX-HEAPIFY is quite efficient in terms of constant factors, except possibly for the recursive call in line 10, which might cause some compilers to produce inefficient code. Write an efficient MAX-HEAPIFY that uses an iterative control construct (a loop) instead of recursion.
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