Given a real number x and a positive integer k, determine the number of multiplications used to find x^(2^k) starting with x and successively squaring (to find x^2, x^4, and so on). Is this a more efficient way to find x^(2^k) than by multiplying x by itself the appropriate number of times?

Given a real number x and a positive integer k, determine the number of multiplications used to find x^(2^k) starting with x and successively squaring (to find x^2, x^4, and so on). Is this a more efficient way to find x^(2^k) than by multiplying x by itself the appropriate number of times?

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 18SA

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Number theory is one of the most appealing topics in mathematics. Given one or more numeric values, a numeric algorithm performs some computation. The use of number theory in computing is important for applications like in the case of cryptographic algorithms. Number theory is also used in various applications such as calculating hash functions or in information security. Euclid’s algorithm is one of the oldest number-theoretic algorithms which is used to calculate the greatest common divisor of two numbers.

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Given a real number x and a positive integer k, determine
the number of multiplications used to find x^(2^k)
starting
with x and successively squaring (to find x^2, x^4, and so
on). Is this a more efficient way to find x^(2^k)
than by multiplying x by itself the appropriate number of times?

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