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Algorithm Analysis and Design

by: Earlene Cremin III

14

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3

Algorithm Analysis and Design CPSC 5115G

Marketplace > Columbus State University > ComputerScienence > CPSC 5115G > Algorithm Analysis and Design
Earlene Cremin III

GPA 3.91

Edward Bosworth

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Edward Bosworth
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This 3 page Class Notes was uploaded by Earlene Cremin III on Sunday October 11, 2015. The Class Notes belongs to CPSC 5115G at Columbus State University taught by Edward Bosworth in Fall. Since its upload, it has received 14 views. For similar materials see /class/221205/cpsc-5115g-columbus-state-university in ComputerScienence at Columbus State University.

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Date Created: 10/11/15
Presorting Arrays Some problems concerning arrays are more easily attacked when the array is rst sorted We are assuming that the array can be sorted by comparison using standard algorithms in time TN 6 N ologN Consider a problem related to arrays Let the algorithm as applied to sorted arrays have time complexity TspN Then the time complexity of the combined approach might be given as TPN TsPN N 3910gN Remember that this equation is not to be taken literally TN 6 N ologN does not imply that TN N ologN Uniqueness in an Array The brute force approach has time complexity TN 6 N2 This algorithm is best expressed using While loops Algorithm Uniqueness Al N N Unique TRUE J 1 DO XJ AJ K J 1 DO If XJ AK Then Unique FALSE Else K K l WHILE K S N AND Unique J J l WHILE J lt N AND Unique Return Unique Uniqueness in an Array The presort version of the algorithm has TN 6 N ologN Algorithm PreSortUniqueness Al N N Unique TRUE J 1 DO If AJ AJ 1 Then Unique FALSE Else J J 1 WHILE J lt N AND Unique Return Unique One can argue that the time complexity of this part of the algorithm is TspN N 2 on average and TspN N in the worst case Thus TspN 6 N Remembering that the array must be sorted prior to use of this algorithm we have TN 6 N ologN N or TN 6 N ologN

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