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Re: Re: Factorial algorithm execution time

by gri6507 (Deacon)
on Oct 18, 2002 at 17:31 UTC ( [id://206372]=note: print w/replies, xml ) Need Help??


in reply to Re: Factorial algorithm execution time
in thread Factorial algorithm execution time

I thought about this one also. But your implementation can be improved still. Let's look at 6!:

2 * 3 * 4 * 5 * 6 = | | | | | +-------+ | +---------------+ 4 * 12 * 15 = | | +---------+ 12 * 60 = 120
There are a couple of changes. First, there is no need to multiply by 1. The answer is not going to change :-). Second, you are correct in saying that it's best to multiply the smallest number by the largest first. So, in this case, the left over "4" from the first step should be the first number in the second step. These are implemented in fact8(). If you run it, you'll see that it run's just abit faster.

sub fact8{ #divide and conquer without recursion my @N = (2 .. shift); my @M; my $tmp; while ($#N){ while(@N){ $tmp = pop(@N); if (($_ = shift(@N))){push(@M,Math::BigInt->new($tmp)->bmul($_)) +} else {unshift(@M,$tmp)} } while(@M){ $tmp = pop(@M); if (($_ = shift(@M))){push(@N,Math::BigInt->new($tmp)->bmul($_)) +} else {unshift(@N,$tmp)} } } return @N; } perl fact.pl 5000 Method 8 (new func): 28 wallclock secs (28.65 usr + 0.00 sys = 28.65 +CPU) Method 7 (your func): 30 wallclock secs (29.06 usr + 0.00 sys = 29.06 + CPU)

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Re^3: Factorial algorithm execution time
by Aristotle (Chancellor) on Oct 18, 2002 at 17:41 UTC
    You're right. But why so much work? A trivial modification to my code will do that.
    sub fact7b { my @factor = map Math::BigInt->new($_), (2 .. shift); while(@factor > 1) { my @pair = splice @factor, 0, @factor / 2; $_ = $_ * pop @pair for @factor[0..$#pair]; } return shift @factor; }
    Update: doh, fixed overly clever, broken code. (s{1 + $#factor / 2}{@factor / 2})

    Makeshifts last the longest.

      Did you test that code?

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