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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: GaleShapley 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 GaleShapley 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
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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: MillerRabin 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 .
 Spring '12
 GS

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