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Unformatted text preview: CS 373: Combinatorial Algorithms, Fall 2000 Homework 4 (due October 26, 2000 at midnight) Name: Net ID: Alias: U 3 / 4 1 Name: Net ID: Alias: U 3 / 4 1 Name: Net ID: Alias: U 3 / 4 1 Homeworks may be done in teams of up to three people. Each team turns in just one solution, and every memeber of a team gets the same grad. Since 1-unit graduate students are required to solve problems that are worth extra credit for other students, 1-unit grad students may not be on the same team as 3/4-unit grad students or undergraduates. Neatly print your name(s), NetID(s), and the alias(es) you used for Homework 0 in the boxes above. Please also tell us whether you are an undergraduate, 3/4-unit grad student, or 1-unit grad student by circling U, 3 / 4 , or 1, respectively. Staple this sheet to the top of your homework. RequiredProblems 1. (10 points) A certain algorithms professor once claimed that the height of an n-node Fibonacci heap is of height O (log n ) . Disprove his claim by showing that for a positive integer n , a sequence of Fibonacci heap operations that creates a Fibonacci heap consisting of just one tree that is a (downward) linear chain of n nodes. 2. (20 points) Fibonacci strings are defined as follows: F 1 = b F 2 = a F n = F n- 1 F n- 2 for all n > 2 where the recursive rule uses concatenation of strings, so...
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This note was uploaded on 12/15/2009 for the course 942 cs taught by Professor A during the Spring '09 term at University of Illinois at Urbana–Champaign.
- Spring '09