Is it possible to get some optimization on any algorithm used for getting the gcd of numbers in an array if the array is sorted? Thanks!
So, let's see. The general method of finding the GCD of an array of numbers is:
result = a[0]
for i = 1 to length(a)-1
result = gcd(result, a[i])
So what's the complexity of the gcd algorithm? Well, that's a rather involved question. See, for example, Time complexity of Euclid's Algorithm
If we pretend, as posited in the accepted answer, that the GCD algorithm is constant time (i.e. O(1)), then the complexity of the loop above is O(n). That's a reasonable assumption for numbers that fit into computer registers. And if that's the case then spending O(n log n) time to sort the array would almost certainly be a loser.
But in reality the GCD calculation is linear in the number of digits in the two numbers. If your input data consists of lots of large numbers, it's possible that sorting the array first will give you an advantage. The reasoning is that the result of gcd(a, b) will by definition give you a number that's no larger than min(a,b). So by getting the GCD of the two smallest numbers first, you limit the number of digits you have to deal with. Whether that limiting will overcome the cost of sorting the array is unclear.
If the numbers are larger than will fit into a computer register (hundreds of digits), then the GCD calculation is more expensive. But then again, so is sorting.
So the answer to your question is that sorting will almost certainly increase the speed of calculating the GCD of an array of numbers, but whether the performance improvement will offset the cost of sorting is unclear.
I think the only way you'll know for sure is to test it with representative data.