project_euler.problem_091.sol1
==============================

.. py:module:: project_euler.problem_091.sol1

.. autoapi-nested-parse::

   Project Euler Problem 91: https://projecteuler.net/problem=91

   The points P (x1, y1) and Q (x2, y2) are plotted at integer coordinates and
   are joined to the origin, O(0,0), to form ΔOPQ.
   
   There are exactly fourteen triangles containing a right angle that can be formed
   when each coordinate lies between 0 and 2 inclusive; that is,
   0 ≤ x1, y1, x2, y2 ≤ 2.
   
   Given that 0 ≤ x1, y1, x2, y2 ≤ 50, how many right triangles can be formed?



Functions
---------

.. autoapisummary::

   project_euler.problem_091.sol1.is_right
   project_euler.problem_091.sol1.solution


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

.. py:function:: is_right(x1: int, y1: int, x2: int, y2: int) -> bool

   Check if the triangle described by P(x1,y1), Q(x2,y2) and O(0,0) is right-angled.
   Note: this doesn't check if P and Q are equal, but that's handled by the use of
   itertools.combinations in the solution function.

   >>> is_right(0, 1, 2, 0)
   True
   >>> is_right(1, 0, 2, 2)
   False


.. py:function:: solution(limit: int = 50) -> int

   Return the number of right triangles OPQ that can be formed by two points P, Q
   which have both x- and y- coordinates between 0 and limit inclusive.

   >>> solution(2)
   14
   >>> solution(10)
   448