project_euler.problem_009.sol4
==============================

.. py:module:: project_euler.problem_009.sol4

.. autoapi-nested-parse::

   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 abc.

   References:
       - https://en.wikipedia.org/wiki/Pythagorean_triple



Functions
---------

.. autoapisummary::

   project_euler.problem_009.sol4.get_squares
   project_euler.problem_009.sol4.solution


Module Contents
---------------

.. py:function:: get_squares(n: int) -> list[int]

   >>> get_squares(0)
   []
   >>> get_squares(1)
   [0]
   >>> get_squares(2)
   [0, 1]
   >>> get_squares(3)
   [0, 1, 4]
   >>> get_squares(4)
   [0, 1, 4, 9]


.. py:function:: solution(n: int = 1000) -> int

   Precomputing squares and checking if a^2 + b^2 is the square by set look-up.

   >>> solution(12)
   60
   >>> solution(36)
   1620