# [plt-scheme] Project Euler was Hash Table implementation

 From: David Einstein (deinst at gmail.com) Date: Sun Aug 5 19:38:31 EDT 2007 Previous message: [plt-scheme] Project Euler was Hash Table implementation Next message: [plt-scheme] OpenBSD build problems Messages sorted by: [date] [thread] [subject] [author]

```This is a very nice library.  I could have saved quite a bit of time
Looking at the hash table problem I noticed that mzscheme is built on
gmp, and gmp has a  good deal of the low level functions implemented,
extended gcd and modular exponentiation, for example.  Is there some
way of bringing them into mzscheme?

On 8/5/07, Jens Axel Søgaard <jensaxel at soegaard.net> wrote:
> Grant Rettke wrote:
> > On 8/3/07, Mark Engelberg <mark.engelberg at gmail.com> wrote:
> >> Anyone else want to comment on the relative strengths of languages for
> >> Project Euler?
>
> The numeric tower of R5RS is really shining when solving these problem.
>
> Here is how I find reals solution of a second degree equation:
>
>    (define (second-degree-solutions a b c)
>      ; return list of solutions to a a x^2 + b x + c = 0
>      (let ([d (- (* b b) (* 4 a c))])
>        (cond
>          [(< d 0)
>           '()]
>          [(= d 0)
>           (list (/ b (* -2 a)))]
>          [else
>           (let ([sqrt-d (sqrt d)])
>             (list (/ (- (- b) sqrt-d) (* 2 a))
>                   (/ (+ (- b) sqrt-d) (* 2 a))))])))
>
> For example the equation 2x^2-8=0 has the solutions -2 and 2:
>
>    > (second-degree-solutions 2 0 -8)
>    (-2 2)
>
> The thing to notice is that I get exact solutions, even
> though I used sqrt above.
>
> Finding *integer* solutions is now easy:
>
>   (define (second-degree-integer-solutions a b c)
>     ; return list of integer solutions to a x^2 + b x + c = 0
>     (filter integer? (second-degree-solutions a b c)))
>
> The tools I use to solve Project Euler problems are:
>
>   - the following library of number theory functions, released
>     through PLaneT today:
>        http://www.scheme.dk/blog/2007/08/number-theory.html
>
>   - Herman's memoize package (remember to use memoize*)
>
>   - Eager Comprehensions
>
> > It is a lot of fun to read everyone's solution to the problems on
> > project Euler.
>
> Sure is.
>
> --
> Jens Axel Søgaard
>
> _________________________________________________