# Homework list - CECS 228 Lectures Darin Goldstein 1...

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Unformatted text preview: CECS 228 Lectures Darin Goldstein* 1 Preliminaries: V,E|, proofs pg. 58: #27, pg. 85: # 11,25 2 Approximating solutions as n —> 00 (the Dat- ing Game) If you can’t get some of these until next lecture, that’s ﬁne. pg. 102 # 7, 11 1. Show that 2:121 : 9(log n). 2. Show that log(n!) ~ nlog n. 3 Asymptotics: deﬁnitions, the Force, and ex- amples pg. 191 # 7, 19, 21, 39, 61 4 Mathematical Induction(weak): Gauss’ ele- mentary school formula, Binomial Theorem, Tiling the plane pg. 330 # 7, 21, 27 5 Mathamatical Induction(strong): Egyptian unit fractions, Euclidean algorithm for the GOD pg. 230 # 23, 29 * [email protected] 6 Recursion/Induction: Towers of Hanoi, Pi- geonhole principle: elementary applications pg. 353 # 31, 33, 37 7 Our ﬁrst algorithm: Gale-Shapley matching Assume that you are given the following men and women with relative orders as follows: Man # 1: 3,1,2,4 Man # 2: 4,3,1,2 Man # 3: 4,3,2,1 Man # 4: 3,2,4,1 Woman # 1: 1,2,3,4 Woman # 2: 3,4,1,2 Woman # 3: 3,4,1,2 Woman # 4: 3,4,2,1 Determine (a) the matching that results from the standard Gale—Shapley algorithm and (b) the matching that results from the Gale-Shapley algorithm assuming the roles of the men and women are reversed. Show that both match- ings are stable. 8 Analysis of simple algorithms: Horner’s algo- rithm for evaluating a polynomial, randomiz- ing a list of numbers pg. 199 # 9, 13 9 Analysis of simple algorithms: making inser- tion sort smarter, quicksort pg. 322 # 53, 55 10 Analysis of simple algorithms: lower bound for sorting Draw an algorithm using the tree structure illustrated in class that correctly sorts 4 numbers. 11 Graphs: adjacency / incidence matrix and edge- list representations (memory efﬁciency), the complete graph, bipartite graphs pg. 618 # 3, 9, 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Graphs: network ﬂow, the matchmaker prob- lem Graphs: depth ﬁrst search, articulation points Graphs: strongly connected components Graphs: trees, binary search trees Graphs: balanced binary search trees (AVL trees) Graphs: heaps Graphs: Dijkstra’s algorithm for SSSP Sets and relations: reﬂexive, symmetric, tran- sitive, equivalence relations (the world of mod- ulus) Sets and relations: Lagrange’s theorem Integer algorithms: GCD, Euclidean algo- rithm, linear Diophantine equations Integer algorithms: Fibonacci numbers and Lame’s theorem Integer algorithms: Fermat’s Little Theorem, Chinese Remainder Theorem Integer algorithms: RSA Integer algorithms: Miller-Rabin primality testing ...
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## This note was uploaded on 02/17/2012 for the course CECS 228 taught by Professor Gs during the Spring '12 term at California State University Los Angeles .

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Homework list - CECS 228 Lectures Darin Goldstein 1...

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