[Coco] Project Euler and the Coco

[Arthur Flexser]

Mark,

While I agree that b > (500-a), (and nice work to you, too), b must also be
greater than or equal to a.  So, for maximum efficiency, the lower bound of b
should be either a or (500-a), whichever is greater.  That is, use a as the
lower bound if a > 250, and (500-a) as the lower bound otherwise, to save yet
more iterations when a is between 250 and 333.

Art


On Sat, 15 Nov 2008, Mark McDougall wrote:

> Arthur Flexser wrote:
> 
> > The ascending length requirement means that B must
> > take up no more than half of the remaining board, or (1000-A)/2.  
> 
> (a^2 + b^2)= c^2
> (a^2 + b^2) = (a+b)^2 - 2ab = c^2
> therefore, a+b > c
> a + b > (1000 - a - b)
> 2a + 2b > 1000
> (a+b) > 500
> ie, b > (500-a)
> 
> and using Arthur's observation (nice work)
> 
> FOR B=500-A TO (1000-A)/2
> 
> reduces the number of iterations to find the solution to 10,174 from the 
> original 66,174 iterations - a massive 85% reduction!
> 
> Regards,
> 
> -- 
> |              Mark McDougall                | "Electrical Engineers do it
> |  <http://members.iinet.net.au/~msmcdoug>   |   with less resistance!"
> 
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