Problem 42

Coded Triangle Numbers

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

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 t_n = 0.5n(n+1) 给出。前十个三角形数是：

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？

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