Project Euler Problem 42

Problem 42

The n^th term of the sequence of triangle numbers is given by, t_n = ¹/₂n(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(right click and ‘Save Link/Target As…’), a 16K text file containing nearly two-thousand common English words, how many are triangle words?

三角形数序列的第n项由公式t_n = ¹/₂n(n+1)给出；因此前十个三角形数是：

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，我们可以计算出一个单词的值。例如，单词SKY的值就是 19 + 11 + 25 = 55 = t₁₀。如果一个单词的值是一个三角形数，我们就称这个单词为三角形单词。

在这个16K的文本文件words.txt （右击并选择“目标另存为……”）中包含有将近两千个常用英文单词，这其中有多少个三角形单词？

f = open('p042_words.txt', 'r')
name = f.read()
lst = name.split(',')
triangle_lst = [n*(n+1)/2 for n in range(1,30)]
count = 0
for name_str in lst:
    sumsub = 0
    for substr in name_str:
        if substr.isalpha():
            sumsub += (ord(substr) - 64)
    if sumsub in triangle_lst:
        count += 1
print(count)