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Problem 42

1. Problem

Coded Triangle Numbers

The nth term of the sequence of triangle numbers is given by, tn = 0.5n(n+1); so the first ten triangle numbers are:

1,3,6,10,15,21,28,36,45,55,…

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 = t10. If the word value is a triangle number then we shall call the word a triangle word.

Using words.txt 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?

编码三角形数

三角形数序列的第 n 项由公式 tn = 0.5n(n+1) 给出。前十个三角形数是:

1,3,6,10,15,21,28,36,45,55,…

将一个单词的每个字母分别转化为其在字母表中的顺序并相加,所得结果即为这个单词的价值。例如,单词 SKY 的价值是 19 + 11 + 25 = 55 = t10。如果一个单词的价值是一个三角形数,称这个单词为三角形单词。

在文本文件 words.txt 中包含有将近两千个常用英文单词,其中有多少个三角形单词?

2. Solution

首先使用如下代码获取并处理来自文本的单词:

(defun eu42-get-names ()
  (with-current-buffer
      (url-retrieve-synchronously
       "https://projecteuler.net/resources/documents/0042_words.txt")
    (goto-char (point-min))
    (search-forward "\"A\"")
    (move-beginning-of-line 1)
    (insert "(")
    (replace-string "," " ")
    (goto-char (point-max))
    (insert ")")
    (goto-char (point-min))
    (search-forward "\"A\"")
    (move-beginning-of-line 1)
    (prog1 (read (current-buffer))
      (kill-buffer))))

(setq eu42-wordls (eu42-get-names))

然后直接无脑算就行了:

(defun eu42-word2num (str)
  (cl-reduce (lambda (s a)
               (+ s 1 (- a ?A)))
             str
             :initial-value 0))

(let ((tri-tbl (cl-loop for n from 1 to 100
                        collect (/ (* n (1+ n)) 2))))
  (cl-loop for a in (mapcar 'eu42-word2num eu42-wordls)
           count (member a tri-tbl)))
=> 162