Project Euler

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# [[Problem 42]]

## Coded Triangle Numbers

The $n$<sup>th</sup> term of the sequence of triangle numbers is given by, $t_n = \frac12n(n+1)$; so the first ten triangle numbers are:

$$1, 3, 6, 10, 15, 21, 28, 36, 45, 55, \dots$$

By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form a word value. For example, the word value for SKY is $19 + 11 + 25 = 55 = t_{10}$. If the word value is a triangle number then we shall call the word a triangle word.

Using [words.txt](https://projecteuler.net/resources/documents/0042_words.txt) (right click and 'Save Link/Target As...'), a 16K text file containing nearly two-thousand common English words, how many are triangle words?

## 符号化三角数

三角数のn項は t<sub>n</sub> = n(n+1)/2で与えられる. 最初の10項は

$$1, 3, 6, 10, 15, 21, 28, 36, 45, 55, \dots$$

である.

単語中のアルファベットを数値に変換した後に和をとる. この和を「単語の値」と呼ぶことにする. 例えば SKY は 19 + 11 + 25 = 55 = t<sub>10</sub>である. 単語の値が三角数であるとき, その単語を三角語と呼ぶ.

16Kのテキストファイル [words.txt](https://projecteuler.net/resources/documents/0042_words.txt) 中に約2000語の英単語が記されている. 三角語はいくつあるか?

```scheme

(import (scheme base)

        (gauche base)

        (scheme file))

(define words (string-split

                (call-with-output-string

                  (^[string-port]

                    (format string-port

                            "~a"

                            (call-with-input-file

                              "words.txt"

                              (^[file-port]

                                (read-line file-port))

                              :element-type :character))))

                #[","] 'suffix #f 1))

(define (words-num words)

  (map (^s

         (fold (^[c n]

                 (+ n

                    (- (char->integer c)

                       (char->integer #\A)

                       -1)))

               0

               (string->list s)))

       words))

(define (triangle-num num)

  (let loop ([index 1] [lis '()])

    (let ([current (/ (* index

                         (+ index 1))

                      2)])

      (if (< num current)

        (reverse lis)

        (loop (+ index 1) (cons current lis))))))

(define (match-triangle-num words)

  (let* ([words-num-list (words-num words)]

         [triangle-num-list (triangle-num

                              (apply max words-num-list))])

    (filter (^n

              (find (cut = n <>)

                    triangle-num-list))

            words-num-list)))

(define answer-42

  (length (match-triangle-num words)))

(format #t "42: ~d~%" answer-42)

```