I'm working on problem 66 at project euler and this is my solution so
far. It calculates the minimum "x"s just fine but takes almost a
minute when I turn limit up to 20. It's not going to solve the
problem fast enough but what I find strange it that if I set the limit
to 20 then nothing happens for a while and then the minimum "x"s are
quickly spit out. Basically, it seems like the sequence in the loop
isn't lazy and I don't understand why.
Algorithm: For each D iterate over the squares. The minimum x will
be the first square for which decrementing it and dividing by D is
another square.
(time (let [limit 10
sqrt (fn [n] (if (zero? n)
0
(loop [guess (- n (/ (- (* n n) n) (* 2 n)))
last-guess n]
(if (< (- last-guess guess) 1/10)
(let [dec-guess (long guess)
inc-guess (inc dec-guess)]
(condp = n
(* dec-guess dec-guess) dec-guess
(* inc-guess inc-guess) inc-guess
guess))
(recur (- guess (/ (- (* guess guess) n) (* 2
guess)))
guess)))))]
(loop [x (for [D (range (inc limit))
:when (not (integer? (sqrt D)))]
(sqrt (first (filter (comp integer? #(sqrt (/ (dec %) D)))
(map #(* % %) (range 2
Double/POSITIVE_INFINITY))))))]
(when (first x)
(println (first x))
(recur (rest x))))))
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