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 49C

Consider the following “justification” that the Fibonacci function, F(n) is O(n): Base case (n ≤ 2): F(1) = 1 and F(2) = 2.

Induction step (n > 2): Assume claim true for n′ < n. Consider n. F(n) = F(n − 2) + F(n − 1). By induction, F(n − 2) is O(n − 2) and F(n − 1) is O(n − 1). Then, F(n) is O((n − 2) + (n − 1)), by the identity presented in Exercise R-4.16.

Therefore, F(n) is O(n).

What is wrong with this “justification”?

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