/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 5 Write an algorithm that finds th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 5

Write an algorithm that finds the greatest common divisor of two integers.

Short Answer

Expert verified
The provided steps describe the Euclidean algorithm for computing the greatest common divisor of two integers and discusses a possible implementation. This algorithm functions by iterative division and remainder calculation until the remainder is 0.

Step by step solution

01

Understanding the Euclidian Algorithm

Euclidean Algorithm is a way to find the greatest common divisors (GCDs) of two numbers. In this process, the larger number is to be divided by the smaller one. Then, divide the divisor by the remaining, continuing this process until the remainder is 0; the GCD is the last non-zero remainder.
02

Implementation of the Algorithm

Start by checking if the second number is 0. If it is, return the first number because the GCD of a number and 0 is the number itself. If the second number is not 0, recursively call the function, swapping the positions of the numbers and replacing the first number with the modulus of the two numbers.
03

Base Case

The algorithm stops when there is no remainder left - that is when the second number becomes 0, which is the base case of our recursive implementation. You return the first number in this case because the GCD of a number and 0 is the number itself.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Write an algorithm that finds the \(m\) smallest numbers in a list of \(n\) numbers.

Explain in English what functions are in the following sets. (a) \(n^{C(1)}\) (b) \(O\left(n^{O(1)}\right)\) (c) \(O\left(O\left(n^{O(1)}\right)\right)\)

Show directly that \(f(n)=n^{2}+3 n^{3} \in \Theta\left(n^{3}\right) .\) That is, use the definitions of \(O\) and \(\Omega\) to show that \(f(n)\) is in both \(O\left(n^{3}\right)\) and \(\Omega\left(n^{3}\right)\)

What is the time complexity \(T(n)\) of the nested loops below? For simplicity, you may assume that \(n\) is a power of \(2 .\) That is, \(n=2^{k}\) for some positive integer \(k\) : \\[ \begin{array}{l} i=n_{i} \\ \text { while }(i>=1)\\{ \\ \qquad \begin{array}{c} j=i \\ \text { while }(j<=n) \end{array} \end{array} \\] < body of the inner while loop> \(\quad\) I/ Needs \(\Theta(1)\) \\[ j=2^{*} j \\] } \\[ i=|1 / 2| \\] }

Using the definitions of \(O\) and \(\Omega\), show that \\[ 6 n^{2}+20 n \in O\left(n^{3}\right) \quad \text { but } \quad 6 n^{2}+20 n \notin \Omega\left(n^{3}\right) \\]
See all solutions

Recommended explanations on Computer Science Textbooks

Issues in Computer Science

Read Explanation

Computer Network

Read Explanation

Cloud Services

Read Explanation

Computer Organisation and Architecture

Read Explanation

Databases

Read Explanation

Blockchain Technology

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.