# Time:  O(1)
# Space: O(1)

# Given the coordinates of four points in 2D space,
# return whether the four points could construct a square.
#
# The coordinate (x,y) of a point is represented by an integer array with two integers.
#
# Example:
# Input: p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,1]
# Output: True
# Note:
#
# All the input integers are in the range [-10000, 10000].
# A valid square has four equal sides with positive length
# and four equal angles (90-degree angles).
# Input points have no order.

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(p1, p2):
            return (p1[0] - p2[0]) ** 2 + (p1[1] - p2[1]) ** 2

        counter = collections.Counter([dist(p1, p2), dist(p1, p3),\
                                       dist(p1, p4), dist(p2, p3),\
                                       dist(p2, p4), dist(p3, p4)])
        return 0 not in counter and len(counter) == 2

Create valid-square.py