CSE331 HW3 - CSE 331 Introduction to Algorithm Analysis and...

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CSE 331: Introduction to Algorithm Analysis and Design Fall 2011 Homework 3 Due Friday, September 30, 2011 by 1:15pm in class IMPORTANT: Please submit each problem separately, i.e. each problem should begin on a new page and only the pages for one problem should be stapled together. Failure to do so might result in some problem(s) not being graded. For general homework policies and our suggestions, please see the policy document. For this homework, you can assume that addition, subtraction, multiplication and division of two numbers can be done in O (1) time. (Side question: Is this assumption justified?) No collaboration is allowed on the first problem. 1. (40 points ) ( You must work on this problem on your own: NO collaboration is allowed ) A forest with c components is a graph that is the union of c disjoint trees. Note that a tree is a forest with 1 component. Prove that an n -vertex forest with c components has n - c edges. (Recall that we have proved the statement above for c = 1 in class.) ( Hint : The above can be proven by induction.
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