While it is in general difficult to find square roots, cube roots, and the likemodulo some divisor N, it is easy to find integer square roots and cube roots in ordinary, ratherthan modular arithmetic. Write an efficient algorithm for function kthroot(N.k) which on input ofan integer N and an exponent k, returns m = √N. You may assume k < log₂N. (HINT: Usebinary search.) Provide a preudocode and running time analysis.

Answered: While it is in general difficult to…

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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While it is in general difficult to find square roots, cube roots, and the like
modulo some divisor N, it is easy to find integer square roots and cube roots in ordinary, rather
than modular arithmetic. Write an efficient algorithm for function kthroot(N.k) which on input of
an integer N and an exponent k, returns m = √N. You may assume k < log₂N. (HINT: Use
binary search.) Provide a preudocode and running time analysis.

Expert Solution

Step 1: Concept of binary search algorithm :

It is an optimised search algorithm that searches for element in a list in log(n) time. It reduces its search area with every iteration and reaches to it's goal if it exists in log(n) time.

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