Given the runtime, f(n) = n° + n +n+1 show thata. f(n) = 0(n*)b. f(n) = e(n³)c. f(n) = (n²)

The given Function f(n) = n3 + n2 + n + 1 The higest power in the given function is n3 So ,…

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Given the runtime, (n) = n° + n +n+1 show that a. f(n) = 0(n*) b. f(n) = e(n³) c. f(n) = (n²)

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter8: Arrays And Strings

Section: Chapter Questions

Problem 24PE

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Concept explainers

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.

Question

Given the runtime, f(n) = n° + n +n+1 show that
a. f(n) = 0(n*)
b. f(n) = e(n³)
c. f(n) = (n²)

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