EularProject 42：单词解码出来的三角形数

Coded triangle numbers

Problem 42

The nth term of the sequence of triangle numbers is given by, tn = ?n(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?

Answer:

162

Completed on Thu, 30 Jul 2015, 09:06

from math import sqrt

def IsTriangleNumber(word):
    data=0
    for i in word:
        data+=ord(i)-ord(‘A‘)+1
    k=int(sqrt(data*2))
    if data*2==k*(k+1):
        return 1
    else:
        return 0

count=0
for line in open(‘p042_words.txt‘,‘r‘):
    line=line.strip(‘\n‘).split(",")
    for word in line:
        word=word.strip("\"")
        count+=IsTriangleNumber(word)

print(count)