## DEV Community

Abhishek Chaudhary

Posted on

# Valid Square

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
``````