Valid Square

https://leetcode.com/problems/valid-square/

Question

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

Answer

Let's draw out our square.

There are 2 things to note here:

• These numbers do not have to be 0 or 1. They can be 500, 0 etc.

• A valid square has four equal sides with positive length and four equal angles (90-degree angles).

One way to do this is to calculate the number of unique distances. Let's visualise this.

The distance here is 1.

And here. This means for all 4 points, we have 1 unique distance (1 to each point) in this square.

But, if we include diagonals

We now have 2.

Using Pythagoras' Therom we can calculate the distance.

We then need to:

• Number of unique distances = 2

• We have 4 distances in total for our square

• We have 2 distances for our diagonals

class Solution(object):
    def validSquare(self, p1, p2, p3, p4):
        points = [p1, p2, p3, p4]
        
        dists = collections.Counter()
        for i in range(len(points)):
            for j in range(i+1, len(points)):
                dists[self.getDistance(points[i], points[j])] += 1
        
        return len(dists.values())==2 and 4 in dists.values() and 2 in dists.values()
        
    def getDistance(self, p1, p2):
        return (p1[0] - p2[0])**2 + (p1[1] - p2[1])**2