Answered: Prove that the following algorithmfor…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Prove that the following algorithmfor computing Fibonacci numbers is correct. function fib(n) comment Return (Fn−1, Fn) 1. if n is odd then 2. (a, b) := even(n − 1) 3. return(b, a + b) 4. else return(even(n)) function even(n) comment Return (Fn−1, Fn) when n is even 1. if n = 0 then return(1, 0) 2. else if n = 2 then return(1, 1) 3. else if n = 4 then return(2, 3) 4. (a, b) := fib(n/2 − 1) 5. c := a + b; d := b + c 6. return(b · d + a · c, c · (d + b))

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