[plt-scheme] Project Euler was Hash Table implementation

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