2013. 检测正方形

from collections import defaultdict
from itertools import product
from typing import List


class DetectSquares:

    def __init__(self):
        self.points = defaultdict(int)  # point -> count
        self.x_lookup = defaultdict(set)
        self.y_lookup = defaultdict(set)

    def add(self, point: List[int]) -> None:
        x, y = point
        self.points[(x, y)] += 1
        self.x_lookup[x].add(y)
        self.y_lookup[y].add(x)

    def count(self, point: List[int]) -> int:
        px, py = point
        if len(self.points) < 3 or len(self.x_lookup[px]) == 0 or len(self.y_lookup[py]) == 0:
            return 0

        return sum(
            self.points[(px + dx, py)] * self.points[(px, py + dy)] * self.points[(px + dx, py + dy)] for dx, dy in
            product((x - px for x in self.y_lookup[py]), (y - py for y in self.x_lookup[px])) if dx == dy != 0)

# Your DetectSquares object will be instantiated and called as such:
# obj = DetectSquares()
# obj.add(point)
# param_2 = obj.count(point)