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What is the effect in the time required to solve a problem
Chapter 3, Problem 20E(choose chapter or problem)
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
Questions & Answers
QUESTION:
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
ANSWER: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 i