mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-18 09:10:16 +00:00
765be4581e
* Improve solution
* updating DIRECTORY.md
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
58 lines
1.2 KiB
Python
58 lines
1.2 KiB
Python
"""
|
|
Highly divisible triangular numbers
|
|
Problem 12
|
|
The sequence of triangle numbers is generated by adding the natural numbers. So
|
|
the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten
|
|
terms would be:
|
|
|
|
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
|
|
|
|
Let us list the factors of the first seven triangle numbers:
|
|
|
|
1: 1
|
|
3: 1,3
|
|
6: 1,2,3,6
|
|
10: 1,2,5,10
|
|
15: 1,3,5,15
|
|
21: 1,3,7,21
|
|
28: 1,2,4,7,14,28
|
|
We can see that 28 is the first triangle number to have over five divisors.
|
|
|
|
What is the value of the first triangle number to have over five hundred
|
|
divisors?
|
|
"""
|
|
|
|
|
|
def triangle_number_generator():
|
|
for n in range(1, 1000000):
|
|
yield n * (n + 1) // 2
|
|
|
|
|
|
def count_divisors(n):
|
|
divisors_count = 1
|
|
i = 2
|
|
while i * i <= n:
|
|
multiplicity = 0
|
|
while n % i == 0:
|
|
n //= i
|
|
multiplicity += 1
|
|
divisors_count *= multiplicity + 1
|
|
i += 1
|
|
if n > 1:
|
|
divisors_count *= 2
|
|
return divisors_count
|
|
|
|
|
|
def solution():
|
|
"""Returns the value of the first triangle number to have over five hundred
|
|
divisors.
|
|
|
|
>>> solution()
|
|
76576500
|
|
"""
|
|
return next(i for i in triangle_number_generator() if count_divisors(i) > 500)
|
|
|
|
|
|
if __name__ == "__main__":
|
|
print(solution())
|