----------------------------------- Insectoid Thu Apr 15, 2010 4:51 pm Seive of Eratosthenes optimizing ----------------------------------- I found the Sieve of Eratosthenes algorithm, and decided to write one myself. It works, but it's really, really slow calculating primes up to anything higher than 100000. I want to make it as fast as possible. Anyway, here's my code: #Seive of Eratosthenes #Finds Prime Numbers print "Enter the last number to check (greater than 1): " max_int = gets.to_i list = (2..max_int).to_a #(2..Math.sqrt(max_int).to_i).to_a.each do |n| list.each do |n| #n will only ever be a prime number puts "Prime Found: #{n}\n Deleting multiples of #{n}..." if n**2 > max_int then #Quits once n squared is greater than max_int (only primes will be left) puts "Sieve complete..." break end list.each_index do |i| if (list % n == 0) && (list I figure, if I can change +1 (all previous elements are prime) I can drop the 2nd condition out of [code]if (list[i] % n == 0) && (list[i] != n) then[/code] Which should significantly speed up the script (that conditional is run 849117 of times when max_int = 100000, whereas that loop is only tested 65 times) I tried changing the loop to [code]list.slice(1..-1).each_index do |i|[/code] but that causes a syntax error (dunno if -1 is valid in that scenario...). I also tried [code]list.slice(1..list.length-1).each_index do |i|[/code] but that throws the same error. If anyone could help me execute that loop without passing the first element in list (in a non-hackish manner), please do! ----------------------------------- Brightguy Thu Apr 15, 2010 6:55 pm Re: Seive of Eratosthenes optimizing ----------------------------------- Which should significantly speed up the script (that conditional is run 849117 of times when max_int = 100000, whereas that loop is only tested 65 times) That conditional isn't of much concern: it's only O(1). (And BTW, you could actually use a list condition). If you want to be efficient, don't use Ruby's split inside the loop! Have you seen the code for even delete_at? It's O(N)! Also checking every element in the list for divisibility is quite needlessly inefficient. ----------------------------------- Tony Thu Apr 15, 2010 7:06 pm RE:Seive of Eratosthenes optimizing ----------------------------------- list.each_index do |i| if (list There's a _much faster_ way of getting the same list of values, without doing any comparisons. (modulo is expensive in a loop) list.slice!(i) #deletes list There's a _much faster_ way to mark a number as prime or not, than taking it out of a list. Currently, your list.include? is O(N). You want to be able to check if the number is prime in O(1), once you build that list. ----------------------------------- Insectoid Thu Apr 15, 2010 7:13 pm RE:Seive of Eratosthenes optimizing ----------------------------------- Brightguy, I did try delete_at after posting this, but figured out something else that might be faster, which your post moots anyway. So delete_at might be the thing. Tony, I don't see what you're getting at. I'll take your bolded 'mark' as a hint. ----------------------------------- Brightguy Thu Apr 15, 2010 7:29 pm Re: RE:Seive of Eratosthenes optimizing ----------------------------------- Brightguy, I did try delete_at after posting this, but figured out something else that might be faster, which your post moots anyway. So delete_at might be the thing. :!: I was pointing out how bad it is. The O(N) call inside your loop is terrible to your efficiency. ----------------------------------- Insectoid Thu Apr 15, 2010 7:30 pm RE:Seive of Eratosthenes optimizing ----------------------------------- ah, heh. *Insectoid hasn't looked up Big-O notation and so is just assuming that O(N) is significantly worse than O(1). ----------------------------------- chrisbrown Thu Apr 15, 2010 7:51 pm RE:Seive of Eratosthenes optimizing ----------------------------------- To put it loosely, if N is the size of your input, runtime can be estimated by counting the number of operations as a function of N. O(1) means as N grows large, the time it takes to perform whatever you're looking at is constant - a good thing. O(N) is a linear relationship. O(N^2) gets large faster than O(N), so it is worse and is very poor for large inputs. ----------------------------------- Brightguy Thu Apr 15, 2010 7:51 pm Re: RE:Seive of Eratosthenes optimizing ----------------------------------- This is abusing the notation, but if you want a better feeling than "significantly worse", here it means that computing the primes to 100,000 takes you about 100,000 times longer. ----------------------------------- Insectoid Thu Apr 15, 2010 7:57 pm RE:Seive of Eratosthenes optimizing ----------------------------------- Ah. Well. That makes sense. I did notice incredible slowdowns at higher numbers (500 000 took over 100 times as long as 100 000). Damn.