Python Implementation of Problem 42
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Includes
Problem Solution
Project Euler Problem 42
The nth term of the sequence of triangle numbers is given by, tn = ½n(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?
1"""
2Project Euler Problem 42
3
4The nth term of the sequence of triangle numbers is given by, tn = ½n(n+1); so the first ten triangle numbers are:
5
61, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
7
8By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we
9form a word value. For example, the word value for SKY is 19 + 11 + 25 = 55 = t10. If the word value is a triangle
10number then we shall call the word a triangle word.
11
12Using words.txt (right click and 'Save Link/Target As...'), a 16K text file containing nearly two-thousand common
13English words, how many are triangle words?
14"""
15from typing import Set
16
17from .lib.math import triangle
18from .lib.utils import get_data_file
19
20
21def main() -> int:
22 answer = 0
23 words = get_data_file('p0042_words.txt', 'rb').replace(b'"', b'').split(b',')
24 max_cached_idx: int = 0
25 max_cached: int = 0
26 cache: Set[int] = set()
27 for word in words:
28 n = sum(x - 0x40 for x in word)
29 while n > max_cached:
30 max_cached_idx += 1
31 max_cached = triangle(max_cached_idx)
32 cache.add(max_cached)
33 if n in cache:
34 answer += 1
35 return answer