Click here to Skip to main content
12,510,224 members (53,942 online)
Click here to Skip to main content
Add your own
alternative version

Tagged as

Stats

12.9K views
2 bookmarked
Posted

Fast Greatest Common Divisor (GCD) Algorithm

, 15 Feb 2011 CPOL
Rate this:
Please Sign up or sign in to vote.
The computational efficiency of the Euclid's algorithm is much higher that the alternatives

I would not recommend the Alternate 2 method for the following reasons:

1. First and foremost, the computational efficiency of the Euclid's algorithm at the core of my solution (see the following - ORIGINAL, RECOMMENDED) is significantly higher than of that simple iterations (essentially looping from the smaller half downward and checking divisibility of both variables) implemented in proposed alternative 1 (see the following):

// fast Euclid GCD algorithm for 2 integers: RECOMMENDED
      if (list.Length == 2)
      {
          Int64 a = list[0];
          Int64 b = list[1];
          while (b != 0)
          {
              GCD = b;
              b = a % b;
              a = GCD;
          }
          return GCD;

FYI: As per general theory, Euclidean algorithm should not take more steps to complete than 5 times the number of digits (base10) of the smallest number. Even more efficient algorithms than this classic, Euclidean one exist, but they are correspondingly, much more complex.
 

Note: FOLLOWING ALGORITHM (RE: Alternate 2) IS NOT RECOMMENDED DUE TO LOW EFFICIENCY

    //Find the larger of the two numbers, the GCD can not be more than half of the smaller number.
    max =  value1 > value2 ? (value2 / 2) : (value1 / 2);
    counter = max + 1;
 
    while ((!gcdFound) && (counter > 1))
    {
        counter--;
        gcdFound = ((value1 % counter) == 0) && ((value2 % counter) == 0);
    }

 

2. Passing array and corresponding array operations, implemented in my original algorithm, are essential for extending it to more than just two input variables. There is no need to re-write my function, because it could be simply overloaded for just 2 variables (just add the second function, taking 2 parameters and calling the original one), or the same result could be achieved by simply passing the 2 variables value1 and value2 like in example shown below:

Int64 _gcd = GCD(new Int64[] {value1, value2 });


Hope I've answered the question.

Kind Regards,
Alexander Bell

 

License

This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)

Share

About the Author

DrABELL
President Infosoft International Inc
United States United States
Dr. A. Bell is a full-stack software developer (Win/Web/Mobile). He holds PhD in EE/IT, published 300+ articles, authored 37 inventions and is credited for 10+ Enterprise level projects; currently focused on HTML5/CSS3, Javascript/jQuery, .NET/WPF/C#, Android/Angular.js, 'Big Data', AI, IoT. Alex participated in App Innovation Contests (AIC 2102/2013) with multiple winning submissions. Sample projects/pubs:
  1. Real-time NY Bus monitoring app (IoT)
  2. Semaphon™ semantic phone num-to-text converter
  3. Educational Web Portal
  4. Free Online NY Payroll Tax Calculator
  5. WebTV powered by Embedded YouTube Player (Goog #1 YouTube API for ASP.NET)
  6. Top-50 Digital Cameras (powered by iMark-DCAM rating engine)
  7. Pure CSS3 Slide Show
  8. Inflation Calculator
  9. CSS3 Modal Pop-up Dialog
  10. Multilingual Geocoder with Interactive Map
  11. Online Semantic Analyzer (Concordance Calculator)
  12. NY City Job Market and Agency Ratings
  13. Advanced CSS3 Table Formatting

You may also be interested in...

Pro
Pro

Comments and Discussions

 
GeneralThanks, Sandeep! Best regards/wishes, Alex Pin
DrABELL12-Feb-11 4:12
memberDrABELL12-Feb-11 4:12 
GeneralReason for my vote of 5 Deserves a 5 for detailed explanat... Pin
Sandeep Mewara11-Feb-11 20:58
mvpSandeep Mewara11-Feb-11 20:58 

General General    News News    Suggestion Suggestion    Question Question    Bug Bug    Answer Answer    Joke Joke    Praise Praise    Rant Rant    Admin Admin   

Use Ctrl+Left/Right to switch messages, Ctrl+Up/Down to switch threads, Ctrl+Shift+Left/Right to switch pages.

| Advertise | Privacy | Terms of Use | Mobile
Web02 | 2.8.160929.1 | Last Updated 15 Feb 2011
Article Copyright 2011 by DrABELL
Everything else Copyright © CodeProject, 1999-2016
Layout: fixed | fluid