A Gaussian Prime is a gaussian integer that cannot be decomposed as product of two non-unit gaussian integers (the complex units being: 1, 
, i and 
). We say that a gaussian prime 
, is positive, if 
and 
.
, i and ). We say that a gaussian prime , is positive, if and . Write a function that counts the number of elements of set, 
,of all positive gaussian primes , such that p and q are both 
.
,of all positive gaussian primes , such that p and q are both .For example, for 
, the complete set of positive gaussian primes are as follows:
, the complete set of positive gaussian primes are as follows: 
Therefore, for the function should return 
.
the function should return .Solution Stats
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I have a solution that works and the entire test suite can run in 18 seconds on my laptop, but takes a little over 45 seconds to run on the server, so the server times out on the test cases.
I'm stumped trying to figure out how I can optimize this code any further.
I just re-ran the solution and this time it worked. I must have gotten a slow core the first time I ran it. ;-)
Michael Sisco and I have the same solutions, except that I skipped one check for primes (saved little or no time, as it turns out), and made it purely functional (no internal variables needed).