Data Structures and Algorithms in Java
Data Structures and Algorithms in Java
6th Edition
ISBN: 9781119278023
Author: Michael T. Goodrich; Roberto Tamassia; Michael H. Goldwasser
Publisher: Wiley Global Education US
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Chapter 4, Problem 20R

Explanation of Solution

Given:

It is given that if f(n) is O(g(n)) if and only if the function g(n) is Ω(f(n))

Asymptotic notation:

In asymptotic notation for lower bound, let “f” and “g” be functions from the integers or the real numbers to the real numbers. It means that Ω(g(n)) = f(n) if there exist positive constants “c(c>0) in real numbers, such that 0 cg(n)  f(n) for all n  n0 .

Proof:

Let us assume that g(n) and f(n) be functions mapping nonnegative integers to real numbers

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