How to count the squares on a lined page?

Question

Images

Actually, the squares must be calculated here:

Maybe there is an algorithm or an approach or a pattern.
Thanks in advance.

Answer 1

from collections import Counter
from itertools import combinations


def HowManySquares(xx, yy):
    """
    :param xx: отсортированые x-координаты вертикалей
    :param yy: отсортированые y-координаты горизонталей
    """
    ww = Counter(b - a for a, b in combinations(xx, 2))
    hh = Counter(b - a for a, b in combinations(yy, 2))
    return sum(c * hh[w] for w, c in ww.items())


print(HowManySquares([0, 2, 3, 4, 5, 6], [0, 2, 3, 4, 6]))  # 31