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Posted 11 Feb 2011

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Fast Greatest Common Divisor (GCD) Algorithm

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5.00/5 (2 votes)
15 Feb 2011CPOL1 min read
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)


Written By
Engineer
United States United States
Dr. Alexander Bell (aka DrABell) is a seasoned full-stack Software (Win/Web/Mobile) and Data Engineer. He holds PhD in Electrical and Computer Engineering, authored 37 inventions and published 100+ technical articles; currently focused on Microsoft Azure Cloud and Android Mobile development projects. Alex participated in App Innovation Contests (AIC 2102/2013) w/multiple winning submissions. Sample apps/publications:

  1. HTML5/CSS3 graphic enhancement: buttons, inputs
  2. HTML5 Tables Formatting: Alternate Rows, Color Gradients, Shadows
  3. Azure web app: Engineering Calculator VOLTMATTER
  4. Azure: NYC real-time bus tracking app
  5. Quiz Engine powered by Azure cloud
  6. 'enRoute': Real-time NY City Bus Tracking Web App
  7. Advanced CSS3 Styling of HTML5 SELECT Element
  8. Aggregate Product function extends SQL
  9. YouTube™ API for ASP.NET

Comments and Discussions

 
GeneralThanks, Sandeep! Best regards/wishes, Alex Pin
DrABELL12-Feb-11 5:12
DrABELL12-Feb-11 5:12 
GeneralReason for my vote of 5 Deserves a 5 for detailed explanat... Pin
Sandeep Mewara11-Feb-11 21:58
mveSandeep Mewara11-Feb-11 21:58 

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