Given a tic tac toe grid, determine if three points form a straight line. Better than hard-coding the solutions like a noob.

colinear.py

# -*- coding: utf-8 -*-
"""
There are a few algorithms for determining collinearity,
since we are in two dimensional space with limited neighbours
we can afford to use the simpler first difference one.
"""
from __future__ import print_function

from operator import itemgetter


def equal_differences(values):
    """
    Check if all values in the list of differences are the same

    """
    # print('Checking if all values are equal in {}'.format(values))
    first_element = values[0]
    num_matching = values.count(first_element)
    total_values = len(values)
    # print('{} occurs {} times out of a possible {}'.format(first_element, num_matching, total_values))

    return not values or num_matching == total_values


def first_difference(values):
    """
    A generator to get the first differences of a list of values

    """
    iterable = iter(values)
    previous_element = next(iterable)
    for current_element in iterable:
        yield current_element - previous_element
        previous_element = current_element


def are_colinear(points):
    """
    Determine if a set of points are colinear (on the same straight line)

    """
    if not points:
        return False

    sorted_points = sorted(points, key=itemgetter(0, 1))

    # print('Points: {}'.format(sorted_points))

    x, y = zip(*sorted_points)
    
    diff_x = list(first_difference(x))
    diff_y = list(first_difference(y))

    # print('X: {}'.format(x))
    # print('diff X: {}'.format(diff_x))

    # print('y: {}'.format(y))
    # print('diff y: {}'.format(diff_y))

    return all(map(equal_differences, [diff_x, diff_y]))


if __name__ == "__main__":

    all_points = [
        [
            (0, 2),
            (1, 1),
            (2, 0),
        ],
        [
            (0, 2),
            (1, 2),
            (2, 0),
        ],
        [
            (0, 2),
            (0, 1),
            (0, 0),
        ],
        [
            (2, 2),
            (2, 0),
            (2, 1),
        ],
        [
            (1, 1),
            (1, 1),
            (1, 1),
        ],
        []
    ]

    for points in all_points:
        print('Points {} are colinear: {}'.format(points, 'yes' if are_colinear(points) else 'no'))