New PDF release: Algorithm Design: Foundations, Analysis, and Internet

By Michael Goodrich, Roberto Tamassia

ISBN-10: 0471383651

ISBN-13: 9780471383659

Michael Goodrich and Roberto Tamassia, authors of the profitable, information constructions and Algorithms in Java, 2/e, have written set of rules Engineering, a textual content designed to supply a accomplished creation to the layout, implementation and research of desktop algorithms and information buildings from a contemporary point of view. This e-book bargains theoretical research ideas in addition to algorithmic layout styles and experimental equipment for the engineering of algorithms.
marketplace: laptop Scientists; Programmers.

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Additional info for Algorithm Design: Foundations, Analysis, and Internet Examples

Example text

RankOf. and elemAtRank). and it is equal in performance to the linked-list implementation on all the other access operations. Regarding update operations. the 74 Chapter 2. alion in the posilion. based update operallon, (insertAfter. IOsertBefore, and remove). he rank-based update methods (insertAtRank and removeAtRankl, but for dif· ferent reason . In update operations IOsertF,rst and insertLast, the two implemen· talions have comparable performance. Considering space usage, note thai an array requires O(N) space, where N is the size of the array (unless we utilize an extendable array), while a doubly linked list uses 0(1/) space, where II is the number of elemenlS in the sequence.

F (II ) is 0 (11 ). since 0 ( 11 - I) + (II - 2) ) is O{II ). What is wrong with this "proor'? 19 Consider the Fibonacci function. F {II ), from the previous exercise. Show by induction that F {II ) is a ({3/2)n) . 20 Draw a visual justi fication of Theorem I. 1 Ib for the ca,e when n is odd. " - I unique. integers in the range [0, 11 - IJ. that is. there is one number from th IS range that IS not in A. Design an O{II)-time algorithm for finding that number. You are allowed to use only O{ I) additional space beside!

Tf Ihe running time of PI is a(i) ifi is a multiple of 3, and is constant otherwise? 2 Let P = PI P2 . ,P. be a sequence of 11 operalions, each either a red or blue operation. with PI being a red operalion and P2 being a blue operation, The running lime of the blue operations is always constanl. tant, but each red operation p, after that runs in lime that is twice as long as Ihe previous red operation, PI (with j < i). What is the amonized time of the red and blue operalions under the following conditions?

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Algorithm Design: Foundations, Analysis, and Internet Examples by Michael Goodrich, Roberto Tamassia

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