593. 有效的正方形 改善醜陋的代碼

給定2D空間中四個點的坐标 p1, p2, p3 和 p4，如果這四個點構成一個正方形，則傳回 true 。

點的坐标 pi 表示為 [xi, yi] 。輸入 不是 按任何順序給出的。

一個 有效的正方形 有四條等邊和四個等角(90度角)。

from typing import List


class Solution:
    @staticmethod
    def distance2(p1, p2):
        return (p1[0] - p2[0]) ** 2 + (p1[1] - p2[1]) ** 2

    def validSquare(self, p1: List[int], p2: List[int], p3: List[int], p4: List[int]) -> bool:
        p_list = [p1,p2,p3,p4]
        sorted_p_list = sorted(p_list)
        if  sorted_p_list[0] == sorted_p_list[1] or  sorted_p_list[2] == sorted_p_list[3]:
            return False

        distance2s  = [ self.distance2(p1, point) for point in p_list ]
        # 找四條等邊
        fourEqualEdge = False
        fourEqualAngle = False
        for point in p_list:
            if point == p1 :
                continue
            if self.distance2(p1, point) == max(distance2s):
                # point 是對點
                other_points = [p  for p in p_list if p != point and p != p1]
                distance2s_p2 = [self.distance2(p, point) for p in other_points]
                distance2s_p1 = [self.distance2(p, p1) for p in other_points]
                edges = distance2s_p1
                edges.extend(distance2s_p2)
                #print(f"edges={edges}")
                if all( x == edges[0] for x in edges):
                    fourEqualEdge = True
                if 2*edges[0] == max(distance2s):
                    fourEqualAngle = True
                return  fourEqualEdge and fourEqualAngle
           

from typing import List


class Solution:
    @staticmethod
    def distance(point1, point2):
        """point1和point2距離的平方"""
        return (point1[0] - point2[0]) ** 2 + (point1[1] - point2[1]) ** 2

    def validSquare(self, p1: List[int], p2: List[int], p3: List[int], p4: List[int]) -> bool:
        sorted_p_list = sorted([p1, p2, p3, p4])
        # 如果有重複的點，則傳回False
        if any(sorted_p_list[i]==sorted_p_list[i+1] for i in range(3)) :
            return False

        max_distance = max([self.distance(p1, point) for point in sorted_p_list])
        for point in sorted_p_list:
            if self.distance(p1, point) == max_distance:
                # point 是對角點
                other_points = [p for p in sorted_p_list if p != point and p != p1]
                distance2s_p2 = [self.distance(p, point) for p in other_points]
                distance2s_p1 = [self.distance(p, p1) for p in other_points]
                distance2s_p1.extend(distance2s_p2)
                edges = distance2s_p1
                if all(x == edges[0] for x in edges) and 2 * edges[0] == max_distance:
                    return True
                return False