5 log n € O(n) √n € O(logn³) nlogn € O(n) 4n € O(n log n)
Subject - Design & Anal
Please complete all the question carefully. Thank you in Advance.
1) For each of the following statements, indicate whether True or False. Justify your answer. Please see the attached image file
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Big O notation is used to describe the asymptotic behavior of a function or algorithm. It is a way to measure the efficiency of an algorithm by determining how the algorithm's performance varies with the size of the input.
The definition of big O notation is that a function f(n) is said to be in O(g(n)) if there exists some positive constant c and some value n0 such that for all n >= n0 f(n ) <= c * g(n). This means that f(n) does not grow faster than g(n) as n grows.
In addition, in order to determine whether the given statements are true or false, you need to know some basic properties of logarithmic and polynomial functions and how they compare in terms of growth rate.
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