79 lines
2.1 KiB
Python
79 lines
2.1 KiB
Python
"""
|
||
The nth term of the sequence of triangle numbers is given by, $t_n = \frac{n(n+1)}{2}$ ;
|
||
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 = 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?
|
||
"""
|
||
|
||
import time
|
||
from pathlib import Path
|
||
|
||
|
||
def timer(func):
|
||
def wrapper(*args, **kwargs):
|
||
start_time = time.perf_counter()
|
||
result = func(*args, **kwargs)
|
||
end_time = time.perf_counter()
|
||
print(f"Time taken by {func.__name__}: {end_time - start_time:.8f} seconds")
|
||
return result
|
||
|
||
return wrapper
|
||
|
||
|
||
def word_to_num(txt: str) -> int:
|
||
"""
|
||
将单词转换为数字，每个字母对应其在字母表中的位置（A=1, B=2, ..., Z=26）
|
||
|
||
参数:
|
||
txt: 要转换的单词
|
||
|
||
返回:
|
||
单词的数字表示
|
||
|
||
示例:
|
||
>>> word_to_num("SKY")
|
||
55
|
||
"""
|
||
return sum(ord(c) - ord("A") + 1 for c in txt)
|
||
|
||
|
||
def is_triangle_number(n: int) -> bool:
|
||
"""
|
||
判断一个数是否为三角形数
|
||
|
||
参数:
|
||
n: 要判断的数
|
||
|
||
返回:
|
||
True 如果 n 是三角形数，否则 False
|
||
|
||
示例:
|
||
>>> is_triangle_number(10)
|
||
True
|
||
>>> is_triangle_number(11)
|
||
False
|
||
"""
|
||
# 使用二次方程求解，如果结果是整数则为三角形数
|
||
# 三角形数公式：n = k(k+1)/2
|
||
# 解得 k = (-1 + sqrt(1 + 8n)) / 2
|
||
k = (-1 + (1 + 8 * n) ** 0.5) / 2
|
||
return k.is_integer()
|
||
|
||
|
||
@timer
|
||
def main() -> None:
|
||
with open(Path(__file__).parent / "0042_words.txt", "r") as file:
|
||
words = file.read().replace('"', "").split(",")
|
||
|
||
triangle_words = [word for word in words if is_triangle_number(word_to_num(word))]
|
||
print(f"Number of triangle words: {len(triangle_words)}")
|
||
|
||
|
||
if __name__ == "__main__":
|
||
main()
|