project_euler.problem_091.sol1

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

is_right(→ bool)

Check if the triangle described by P(x1,y1), Q(x2,y2) and O(0,0) is right-angled.

solution(→ int)

Return the number of right triangles OPQ that can be formed by two points P, Q

Module Contents

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