Please answer the question in the screenshot. Please give full reasoning for the solution. ### Problem: Computing the nth Fibonacci number**Input:**- \( n \geq 1 \)**Output:** - The nth number in the Fibonacci sequence.---#### Recursive Approach**Algorithm:** `REC-FIBONACCI(n)````textif n = 1 or n = 2, return (1);else T1 = REC-FIBONACCI(n - 1); T2 = REC-FIBONACCI(n - 2); return (T1 + T2);```Explanation:- If \( n \) is 1 or 2, the function returns 1.- Otherwise, it recursively calculates the Fibonacci numbers for \( n - 1 \) and \( n - 2 \) and returns their sum.---#### Iterative Approach**Algorithm:** `ITERATIVE-FIBONACCI(n)````textif n = 1 or n = 2 return (1);else M[1] = 1, M[2] = 1 for i = 3 to n do M[i] = M[i - 1] + M[i - 2] return (M[n])```Explanation:- If \( n \) is 1 or 2, the function returns 1.- Otherwise, it initializes the first two Fibonacci numbers \( M[1] \) and \( M[2] \) to 1.- It then iteratively fills the array from \( M[3] \) to \( M[n] \) by summing the previous two values.- Finally, it returns \( M[n] \).---### Time Complexity Analysis- The **recursive approach** has exponential time complexity due to the repeated calculations, which results in \( O(2^n) \).- The **iterative approach** has linear time complexity \( O(n) \) as it calculates each Fibonacci number exactly once.**Discussion Point:**What are the upper bounds for the time complexity of the two solutions to the Fibonacci number?

Task :- Find out the upper bound time complexities for given solutions.

Answered: Problem: Computing the nth Fibonacci…

Engineering

Computer Science

Problem: Computing the nth Fibonacci number Input: n >= 1; o Output: the nth number in the Fibonacci sequence.

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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