Project Euler 42

题目

Coded triangle numbers

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

解决方案

先将三角形数直接添加到集合，然后计算每个单词的分值，再判断分值是否在集合中。

代码

ls = [s[1:-1] for s in open('p042_words.txt', 'r').readlines()[0].split(',')]
st = set()
for i in range(1, 41):
    st.add(i * (i + 1) // 2)
ans = 0
for s in ls:
    sum = 0
    for c in s:
        sum += ord(c) - ord('A') + 1
    if sum in st:
        ans += 1
print(ans)