Data Structures and Algorithms in Java
Data Structures and Algorithms in Java
6th Edition
ISBN: 9781118771334
Author: Michael T. Goodrich
Publisher: WILEY
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Chapter 4, Problem 25R

Explanation of Solution

Given:

It is given that the n2 is Ω(nlog n)

Big-Omega 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 f(n) = n2 and g(n) = nlog n

  • According to big-omega definition, f(n)Ωg(n) when positive constants “c(c>0) in real numbers, such that 0 cg(n)  f(n) for all n  n0.
  • In other words, it can written as follows:

    n2=c

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Question 3) Use the master theorem to give an asymptotic tight bound for the following recurrences. Tell me the values of a, b, the case from the master theorem that applies (and why), and the asymptotic tight bound. 3a) T(n) = : 2T (n/4) + n 3b) T(n) = 16T(n/4) + (√√n)³
If d(n) is odd, show that n is square.
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Chapter 4 Solutions

Data Structures and Algorithms in Java

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