How many integer points within the three points forming a triangle?

Question

Actually this is a classic problem as SO user Victor put it (in another SO question regarding which tasks to ask during an interview).

I couldn\'t do it in an hour

Answer 1

Here is a Python implementation of @Prabhala's solution:

from collections import namedtuple
from fractions import gcd


def get_points(vertices):
    Point = namedtuple('Point', 'x,y')
    vertices = [Point(x, y) for x, y in vertices]

    a, b, c = vertices

    triangle_area = abs((a.x - b.x) * (a.y + b.y) + (b.x - c.x) * (b.y + c.y) + (c.x - a.x) * (c.y + a.y))
    triangle_area /= 2
    triangle_area += 1

    interior = abs(gcd(a.x - b.x, a.y - b.y)) + abs(gcd(b.x - c.x, b.y - c.y)) + abs(gcd(c.x - a.x, c.y - a.y))
    interior /= 2

    return triangle_area - interior

Usage:

print(get_points([(-1, -1), (1, 0), (0, 1)]))  # 1
print(get_points([[2, 3], [6, 9], [10, 160]]))  # 289