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 18R

Explanation of Solution

Given:

It is given that if d(n) is O(f(n)) and f(n) is O(g(n)) then d(n) is O(g(n)).

Big-Oh notation:

In big-Oh notation, let “f” and “g” be functions from the integers or the real numbers to the real numbers. It means that f(x) is “O(g(x))” if there are constants “C” and “k” such that

|f(x)|C|g(x)|    where  (x > k)

Proof:

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

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Students have asked these similar questions
Show that f (n) is O(g(n)) if and only if g(n) is Ω( f (n)).
7. Prove or disprove: f(n) + g(n) = 0 (min(f(n), g(n)))
Suppose that f(n) is O(g(n)), g(n) is O(h(n)), h(n) = l(n) + k(n) where l(n) is O(f(n)/2). Which of the following may not hold. O k² (n) is N(f(n)) O f(n) + g(n) is E(h(n)) O 2f(n) is N(e(n)) O e(n)h(n) is O(g² (n) + f(n))

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Data Structures and Algorithms in Java

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