Just had some fun using the new math library to solve ProjectEuler problems
#108 and #110.
Here's one of my functions:
; function which solves for the lowest number which has more than the
passed number of diophantine reciprocals
; n is multiplied by 2 to account for symmetrical (equivalent) solutions
(define (min-diophantine-recip n)
(define limit (* 2 n))
(define (findmax) ; find the largest candidate that meets the criteria
(let maxlp ([p 2] [prod 1])
(if (> (num-diophantine-reciprocals (factorize prod)) limit) prod
(maxlp (next-prime p) (* p prod)))))
(let lp ([max (findmax)]) ; strip off highest prime factor then search
for a smaller possibility
(let* ([lst (factorize max)] [l (take lst (sub1 (length lst)))]
[multlim (first (last lst))])
(let inclp ([cmult 2])
(if (>= cmult multlim) max ; found the answer
(let ([newmax (* cmult (defactorize l))])
(if (> (num-diophantine-reciprocals (factorize newmax)) limit)
(lp newmax) ; found a smaller answer, iterate
(inclp (add1 cmult)))))))))
It utilizes factorize and defactorize from the math library - very useful.
I absolutely love writing racket code, the named let especially allows so
much freedom of expression. Do functional purists find it easier to use
helper functions? Maybe because I come from an "imperative" background,
the named let feels more natural to me.
In case you want to try out the problem, I'll let you write
(num-diophantine-reciprocals lst) yourself, good luck, it's a bit of a
challenge.
-joe
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