The following decision algorithm, A, is proposed for the perfect square problem: Compute x^2 for integer x starting at x = 1 until x2 either equals or exceeds n. n is accepted in the former case and rejected otherwise. Based on A, what is the complexity class of the perfect square problem? Show your reasoning. (b) What is Heron's algorithm for finding the square root of a number?
The following decision algorithm, A, is proposed for the perfect square problem: Compute x^2 for integer x starting at x = 1 until x2 either equals or exceeds n. n is accepted in the former case and rejected otherwise. Based on A, what is the complexity class of the perfect square problem? Show your reasoning. (b) What is Heron's algorithm for finding the square root of a number?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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This question concerns computational complexity.
In this question, the perfect square problem is the problem of determining if a positive integer, n, is a perfect square i.e. if n = x^2 where x is a positive integer.
(a) The following decision algorithm, A, is proposed for the perfect square problem:
Compute x^2 for integer x starting at x = 1 until x2 either equals or exceeds n. n is accepted in the former case and rejected otherwise.
Based on A, what is the complexity class of the perfect square problem? Show your reasoning.
(b) What is Heron's algorithm for finding the square root of a number?
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