mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 13:31:07 +00:00
98e9d6bdb6
* Fix style of the first ten solutions for Project Euler - Unify the header docstring, and add reference URLs to wikipedia or similar - Fix docstrings to be properly multilined - Add newlines where appropriate - Add doctests where they were missing - Remove doctests that test for the correct solution - fix obvious spelling or grammar mistakes in comments and exception messages - Fix line endings to be UNIX. This makes two of the files seem to have changed completely - no functional changes in any of the solutions were done (except for the spelling fixes mentioned above) * Fix docstrings and main function as per Style Guide
49 lines
1.1 KiB
Python
49 lines
1.1 KiB
Python
"""
|
|
Project Euler Problem 9: https://projecteuler.net/problem=9
|
|
|
|
Special Pythagorean triplet
|
|
|
|
A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
|
|
|
|
a^2 + b^2 = c^2
|
|
|
|
For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
|
|
|
|
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
|
|
Find the product a*b*c.
|
|
|
|
References:
|
|
- https://en.wikipedia.org/wiki/Pythagorean_triple
|
|
"""
|
|
|
|
|
|
def solution(n: int = 1000) -> int:
|
|
"""
|
|
Return the product of a,b,c which are Pythagorean Triplet that satisfies
|
|
the following:
|
|
1. a < b < c
|
|
2. a**2 + b**2 = c**2
|
|
3. a + b + c = n
|
|
|
|
>>> solution(36)
|
|
1620
|
|
>>> solution(126)
|
|
66780
|
|
"""
|
|
|
|
product = -1
|
|
candidate = 0
|
|
for a in range(1, n // 3):
|
|
# Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
|
|
b = (n * n - 2 * a * n) // (2 * n - 2 * a)
|
|
c = n - a - b
|
|
if c * c == (a * a + b * b):
|
|
candidate = a * b * c
|
|
if candidate >= product:
|
|
product = candidate
|
|
return product
|
|
|
|
|
|
if __name__ == "__main__":
|
|
print(f"{solution() = }")
|