# 593. Valid Square """ given the coordinates of four points in a 2d space 'p1 .. p4', return true if the four points oncstruct a square. the coordinate of a point 'p_i' is represented as '[x_i, y_i]'. the input is not given in any order. a valid square has four equal sides with positive length and four equal angles (90-degree angles) """ class Solution(object): def validSquare(self, p1, p2, p3, p4): """ :type p1: List[int] :type p2: List[int] :type p3: List[int] :type p4: List[int] :rtype: bool """ def dist(p, q): return (p[0] - q[0]) ** 2 + (p[1] - q[1]) ** 2 def check(p1, p2, p3, p4): if p1[0] + p2[0] != p3[0] + p4[0] or p1[1] + p2[1] != p3[1] + p4[1]: return False if dist(p1, p2) != dist(p3, p4) or dist(p1, p4) != dist(p2, p4): return False if p1 == p2: return False return True return check(p1, p2, p3, p4) or check(p1, p3, p2, p4) or check(p1, p4, p2, p3) if __name__ == "__main__": obj = Solution() print(obj.validSquare(p1=[0, 0], p2=[1, 1], p3=[1, 0], p4=[0, 1])) print(obj.validSquare(p1=[0, 0], p2=[1, 1], p3=[1, 0], p4=[0, 12])) print(obj.validSquare(p1=[1, 0], p2=[-1, 0], p3=[0, 1], p4=[0, -1]))