# hw3 - CSCI 4041 Algorithms and Data Structures(Fall09...

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CSCI 4041: Algorithms and Data Structures (Fall’09) Homework 3, Due 11/10/09 Answer all of the following questions, and always explain your answer. Good Luck! 1. (30 points) This questions considers operations and properties of Binary Search Trees (BSTs): (a) (15 points) Prove that no matter what node we start at in a height- h BST, k successive calls to TREE-SUCCESSOR will take O ( k + h ) time. (b) (15 points) Professor Tree thinks he has discovered a remarkable property of BSTs. Suppose that the search for key k in a binary search tree ends up in a leaf. Consider three sets: A , the keys to the left of the search path; B , the keys on the search path; and C , the keys to the right of the search path. Professor Tree claims that any three keys a A , b B , and c C must satisfy a b c . Give a simple counterexample to the professor’s claim. 2. (40 points) Suppose you are taking n courses, each with a ﬁnal project that still needs to be completed. Each project will be scored using an integer on a scale of

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## This note was uploaded on 09/18/2010 for the course CSCI 4041 taught by Professor Karypis during the Spring '08 term at Minnesota.

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hw3 - CSCI 4041 Algorithms and Data Structures(Fall09...

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