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# What is the effect in the time required to solve a problem ISBN: 9780073383095 37

## Solution for problem 20E Chapter 3.3

Discrete Mathematics and Its Applications | 7th Edition

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Problem 20E

What is the effect in the time required to solve a problem when you double the size of the input from n to 2n, assuming that the number of milliseconds the algorithm uses to solve the problem with input size n is each of these function? [Express your answer in the simplest form possible, either as a ratio or a difference. Your answer may be a function of n or a constant.]a) log log n________________b) log n________________c) 100 n________________d) n log n________________e) n2________________f) n3________________g) 2n

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Solution:Step1Given thatAssuming that the number of milliseconds the algorithm uses to solve the problem with input size n is each of these function.we have to find what is the effect in the time required to solve a problem when you double the size of the input from n to 2nStep2a) log log nn value is expanded by two which is 2n, time change to loglog2n that is not multiplied. In this way the additional time is log 2n – log n = log log2 + . Accordingly, log 1+ .Step3b) log nn value is expanded by two which is 2n, time change to loglog2n that is not multiplied. In this way the time is log of n which makes it expanded by two/multiplied. Along these lines, log 2n - log n = log 2n/n. Which measures up to log2 = 1 millisecond.Step4c) 100 nn value is expanded by two which is 2n, the time which is a computational change...

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##### ISBN: 9780073383095

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