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Unformatted text preview: CS 473 Homework 0 (due January 26, 2009) Spring 2010 CS 473: Undergraduate Algorithms, Spring 2010 Homework 0 Due Tuesday, January 26, 2009 in class • This homework tests your familiarity with prerequisite material—big-Oh notation, elementary algorithms and data structures, recurrences, graphs, and most importantly, induction—to help you identify gaps in your background knowledge. You are responsible for filling those gaps. The early chapters of any algorithms textbook should be sufficient review, but you may also want consult your favorite discrete mathematics and data structures textbooks. If you need help, please ask in office hours and / or on the course newsgroup. • Each student must submit individual solutions for these homework problems. For all future homeworks, groups of up to three students may submit (or present) a single group solution for each problem. • Please carefully read the course policies linked from the course web site. If you have any questions, please ask during lecture or office hours, or post your question to the course newsgroup. In particular: – Submit five separately stapled solutions, one for each numbered problem, with your name and NetID clearly printed on each page. Please do not staple everything together. – You may use any source at your disposal—paper, electronic, or human—but you must write your solutions in your own words, and you must cite every source that you use. – Unless explicitly stated otherwise, every homework problem requires a proof. – Answering “I don’t know” to any homework or exam problem (except for extra credit problems) is worth 25% partial credit. – Algorithms or proofs containing phrases like “and so on” or “repeat this process for all n ”, instead of an explicit loop, recursion, or induction, will receive 0 points. 1 CS 473 Homework 0 (due January 26, 2009) Spring 2010 1. (a) Write the sentence “I understand the course policies." (b) [ 5 pts ] Solve the following recurrences. State tight asymptotic bounds for each function in the form Θ( f ( n )) for some recognizable function f ( n ) . Assume reasonable but nontrivial....
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