Answered: While working with Recursion, why do we…

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While working with Recursion, why do we need a base case? What will happen if we remove it? Explain with example

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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Computational Systems

The computation systems can be defined as the systems that are capable of solving a problem that includes calculations either mathematical or logical, and are able to produce the result as an output. For example, a simple calculator that is given a set of numbers and operators as input and produces the result as an output can be defined as a computational system. The above example is a simple illustration only, the computational systems range from simple devices to complex devices such as the systems that control the SpaceX companies, Starlink satellites which are being quite recently seen in the skies at many places globally.

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While working with Recursion, why do we need a base case?

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b. The reason that the recursive algorithm is so slow is because the algorithm used to simulate recursion. To compute FN, there is one call to FN-1 and FN-2. However, since FN-1 recursively makes a call to FN-2and FN-3, there are actually two separate calls to compute FN-2. If one traces out the entire algorithm, then we can see that FN-3 is computed three times, FN-4 is computed five times, FN-5 is computed eight times, and so on. As shown Figure Q2b, the growth of redundant calculations is expensive. F6. „F5 F4 F3 F3 'F2 F3 F2 FI FI FO FI FO `F2 F2 FI FI FI FO FI FO FI FO Figure Q2b Write a pseudo code that will reduce the time complexity from o (2n ) to O (n) class of efficiency.
List three types of recursion with a high-level description and a mechanism for each to terminate recursion.