# Download e-book for iPad: Algorithms Sequential & Parallel: A Unified Approach (3rd by Laurence Boxer, Russ Miller

By Laurence Boxer, Russ Miller

ISBN-10: 1133366805

ISBN-13: 9781133366805

Equip your self for fulfillment with a state of the art method of algorithms on hand basically in Miller/Boxer's ALGORITHMS SEQUENTIAL AND PARALLEL: A UNIFIED procedure, 3E. This distinctive and sensible textual content promises an creation to algorithms and paradigms for contemporary computing platforms, integrating the research of parallel and sequential algorithms inside of a targeted presentation. With quite a lot of useful routines and interesting examples drawn from basic software domain names, this booklet prepares you to layout, study, and enforce algorithms for contemporary computing platforms.

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Extra info for Algorithms Sequential & Parallel: A Unified Approach (3rd Edition)

Example text

In particular, we write • loge x as ln x, • log2 x as lg x, and • log10 x as log x. We now continue with an example that uses logarithms. EXAMPLE Let f (n) = ln n and g(n) = n. Then, by applying L’Hopital’s Rule, we have lim n 1 = lim , n→ ∞ 1/n ln n lim 1 = lim n = ∞ . 1/n n→ ∞ n→ ∞ which evaluates as n→ ∞ Therefore, ln n = O(n). Copyright 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).

Therefore, we have n np+1 p p k > (n/2)(n/2) = . a 2p+1 k=1 Since 2p+1 is a constant, we have p p+1 a k = Ω 1n 2 . n k=1 In fact, we have shown that n n p+1 p p+1 ≤ ak ≤ n . 2p+1 k=1 That is, p p+1 a k = Θ 1n 2 . n k=1 Copyright 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience.

Therefore, n 1 a k = Θ(ln n). k=1 Copyright 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Asymptotic Relationships 19 Note: f (x) is nonincreasing a a 1 b 1 b n An illustration of bounding the summation a f (i) for i=1 a nonincreasing function f.