Project Euler

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# [[Problem 39]]

## Integer Right Triangles

If $p$ is the perimeter of a right angle triangle with integral length sides, $\{a, b, c\}$, there are exactly three solutions for $p = 120$.

$\{20,48,52\}$, $\{24,45,51\}$, $\{30,40,50\}$

For which value of $p \le 1000$, is the number of solutions maximised?

## 整数の直角三角形

辺の長さが整数の3つ組{a,b,c}である直角三角形を考え, その周囲の長さを p とする. p = 120のときには3つの解が存在する:

{20,48,52}, {24,45,51}, {30,40,50}

p ≤ 1000 のとき解の個数が最大になる p はいくつか?

```scheme

(import (scheme base)

        (gauche base))

(define triangle-list

  (let loop1 ([p 3] [result '()])

    (if (< 1000 p)

      result

      (let ([a-max (div p 3)])

        (let loop2 ([a 1]

                    [result result]

                    [temp-result '()])

          (if (< a-max a)

            (loop1 (+ p 1)

                   (if (null? temp-result)

                     result

                     (cons temp-result result)))

            (let loop3 ([b a]

                        [result result]

                        [temp-result temp-result])

              (let ([c (- p a b)])

                (if (< c b)

                  (loop2 (+ a 1) result temp-result)

                  (if (= (+ (* a a)

                            (* b b))

                         (* c c))

                    (loop3 (+ b 1)

                           result

                           (cons `(,a ,b . ,c) temp-result))

                    (loop3 (+ b 1)

                           result

                           temp-result)))))))))))

(define count-triangle

  (map (^[lis]

         (let* ([current (car lis)]

                [a (car current)]

                [b (cadr current)]

                [c (cddr current)])

           `(,(+ a b c) . ,(length lis))))

       triangle-list))

(define max-count-triangle

  (fold (^[c max-lis]

          (if (< (cdr max-lis) (cdr c))

            c

            max-lis))

        '(0 . 0)

        count-triangle))

(define answer-39

  (car max-count-triangle))

(format #t "39: ~d~%" answer-39)

```