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 16R

Explanation of Solution

Given:

It is given that if d(n) is O(f(n)) and e(n) is O(g(n)) then it is described that the product of d(n)+e(n) is O(f(n)+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:

Assume that d(n) is O(f(n)), and e(n) is O(g(n))

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Students have asked these similar questions
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))
Suppose that f (n) = 0(g(n)) and f(n) = 0(h(n)), then it is ( always / sometimes / never ) the case that g(n) = 0(h(n)).
Prove or disprove that if f₁ (n) = N(9₁ (n)) and f2 (n) = N(92 (n)), then f₁ (n) + f2 (n) = 2 (min {9₁ (n), 92 (n)}).

Chapter 4 Solutions

Data Structures and Algorithms in Java

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