By Laurence Boxer, Russ Miller

Equip your self for fulfillment with a cutting-edge method of algorithms to be had merely in Miller/Boxer's ALGORITHMS SEQUENTIAL AND PARALLEL: A UNIFIED strategy, 3E. This particular and practical textual content delivers an creation to algorithms and paradigms for contemporary computing structures, integrating the examine of parallel and sequential algorithms inside a targeted presentation. With quite a lot of useful workouts and fascinating examples drawn from primary program domain names, this publication prepares you to layout, examine, and enforce algorithms for contemporary computing structures.

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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. Rules for Analysis of Algorithms 23 that this step runs in Θ(k) time on average. Alternately, an O(log k) time binary search can be performed, as will be discussed in the chapter on Induction and Recursion, though this will not improve the overall asymptotic running time in the expected or worst case.

There is no limit. In the case where lim We now give some examples of how to determine asymptotic relationships based on taking limits of a quotient. EXAMPLE Let f (n) = n(n + 1) and g(n) = n2. 2 Then we can show that f (n) = Θ(g(n)) since lim n→ ∞ f (n) n2 + n = lim = g(n) n→ ∞ 2n2 (dividing both numerator and denominator by n2) 1+ lim n→ ∞ 2 1 n 1 = . 2 EXAMPLE If P(n) is a polynomial of degree d > 0, then P(n) = Θ(nd). This can be seen as d follows. The hypothesis implies P(n) = a ai ni for some set of coefficients 5ai6i=0 with ad ≠ 0.

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. xxx Reference Guide Models of Computation Model Communication diameter Bisection width RAM PRAM of size n Linear array of size n Mesh of size n Hypercube of size n Pyramid of base size n Mesh of trees of base size n Θ(1) equivalent to Θ(1) Θ(n) Θ(n1/2) Θ(log n) Θ(log n) Θ(log n) equivalent to Θ(n2) Θ(1) Θ(n1/2) Θ(n) Θ(n1/2) Θ(n1/2) Note that for the RAM, n represents the size of the memory.