Answered: For the following you can either proove…

For the following you can either proove or disprove the following a)log_4(n^4) is O(n), for n ≥ 1 b) 2n is Ω(nk) for any real constant k ≥ 1

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 69E

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Counting sort

The counting sort algorithm sorts an array’s contents by counting the repetition of each element that occurs in the array. A counting sort algorithm is a stable algorithm that works the best when the range of elements in the array is small, say for example from 0 to 9. The count which is the number of repetitions of an element in the array is mapped to an index of an auxiliary array, which is then saved in an auxiliary array. The counting sort algorithm has a stable time complexity of the order of O(size of array + size of auxiliary array). Let’s discuss the algorithm in detail as follows.

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For the following you can either proove or disprove the following

a)log_4(n^4) is O(n), for n ≥ 1

b) 2n is Ω(nk) for any real constant k ≥ 1

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