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# 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]))
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