Given the coordinates of four points in 2D space p1, p2, p3 and p4, return true if the four points construct a square.
The coordinate of a point pi is represented as [xi, yi]. 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).
Example 1:
Input: p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,1]
Output: true
Example 2:
Input: p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,12]
Output: false
Example 3:
Input: p1 = [1,0], p2 = [-1,0], p3 = [0,1], p4 = [0,-1]
Output: true
Constraints:
-
p1.length == p2.length == p3.length == p4.length == 2 -
-104 <= xi, yi <= 104
SOLUTION:
class Solution:
def dist(self, a, b):
return (a[0] - b[0]) * (a[0] - b[0]) + (a[1] - b[1]) * (a[1] - b[1])
def isPerpendicular(self, a, b, c, d):
return (b[1] - a[1]) * (d[1] - c[1]) == (b[0] - a[0]) * (c[0] - d[0])
def midPoint(self, a, b):
return (a[0] + b[0], a[1] + b[1])
def validSquare(self, p1: List[int], p2: List[int], p3: List[int], p4: List[int]) -> bool:
plist = [p1, p2, p3, p4]
points = [[(0, 1), (2, 3)], [(0, 2), (1, 3)], [(0, 3), (1, 2)]]
for diag in points:
a, b = [plist[d] for d in diag[0]]
c, d = [plist[d] for d in diag[1]]
isBisector = self.midPoint(a, b) == self.midPoint(c, d)
if not isBisector:
continue
d1, d2 = self.dist(a, b), self.dist(c, d)
if d1 != d2 or d1 == 0:
continue
if self.isPerpendicular(a, b, c, d):
return True
return False
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