euler/python/e091.py

from collections import namedtuple

Point = namedtuple("P", ["x", "y"])
Vector = namedtuple("V", ["x", "y"])

def generate_triangles(n):
    all_points = [Point(x, y)
        for x in range(0, n + 1)
        for y in range(0, n + 1)
    ]
    all_points = all_points[1:]  # remove (0, 0)
    all_pairs = []

    for i in range(len(all_points)):
        for j in range(i + 1, len(all_points)):
            p = (all_points[i], all_points[j])
            yield p


def vector(p1, p2):
    return Vector(p2.x - p1.x, p2.y - p1.y)


def dot_product(v1, v2):
    return v1.x * v2.x + v1.y * v2.y


def has_right_angle(p, q):
    o = Point(0, 0)
    oq = vector(o, q)
    op = vector(o, p)
    qp = vector(q, p)

    if dot_product(oq, op) == 0:
        return True
    elif dot_product(oq, qp) == 0:
        return True
    elif dot_product(op, qp) == 0:
        return True
    return False

def euler_091():
    count = 0
    ts = generate_triangles(50)
    for t in ts:
        if has_right_angle(*t):
            count += 1
    return count


if __name__ == "__main__":
    solution = euler_091()
    print("e091.py: " + str(solution))
    assert(solution == 14234)