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Pyhton data's structural size and loop efficiency

  1. May 21, 2012 #1
    While programming to find the largest prime factor for a composite number i came across a problem that if the number taken as input exceeds a certain limit, the loop time turns out to be a very long one and some times even resembling the time taken by an infinite loop.The method used for finding the prime factors is a standard one in which we loop through natural number until the input equals the loop counter; finding its factors and then checking for it to be prime or not ;through another function by a similar method using a counter variable.? Alternatives for drastic time reduction ?
     
  2. jcsd
  3. May 22, 2012 #2
    I lost you at "composite".

    time reduction of what? you gonna show us some code?

    how about wrapping some 'C' or 'Fortran' code?
     
  4. May 22, 2012 #3

    AlephZero

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  5. May 22, 2012 #4
  6. May 22, 2012 #5
    I wrote about the time it takes to loop through natural number during program execution and wanted any time-efficient method for factorization.(They have wiki pages for that too :P)
     
  7. May 22, 2012 #6
    I guess the simplest algorithm would be something like this:

    (1) find an efficient way to generate all prime numbers up to the square root of the input. Something like Sieve. Or use a pre-calculated table if you know what the largest input number is.

    (2) start checking from the smallest prime=2 up.

    (3) as soon as you find a prime factor, divide the input number by this factor. Do this several times if the factor occurs in a higher power than 1. Dividing will make the test number smaller and subsequent tests faster (assuming your input is larger than standard 32-bit integers).

    (4) repeat with the next largest prime, up to the largest prime smaller than the square root.

    (5) if you don't find a prime factor smaller than the square root, then the input number is a prime.
     
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