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project_euler/problem_012/sol2.py
57 строк
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Maxim Smolskiy
Improve Project Euler problem 012 solution 2 (#5760)
03 ноя 2021, 23:32
Не верифицирован
03 ноя 2021, 23:32
765be45
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""" 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())