The challenge

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 p<sub>i</sub> is represented as [x<sub>i</sub>, y<sub>i</sub>]. 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
  • -10<sup>4</sup>&nbsp;<= x<sub>i</sub>, y<sub>i</sub>&nbsp;<= 10<sup>4</sup>

The solution in Java code

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class Solution {
    
    public double dist(int[] p1, int[] p2) {
        return (p2[1] - p1[1]) * (p2[1] - p1[1]) + (p2[0] - p1[0]) * (p2[0] - p1[0]);
    }
    
    public boolean validSquare(int[] p1, int[] p2, int[] p3, int[] p4) {
        int[][] p={p1,p2,p3,p4};
        Arrays.sort(p, (l1, l2) -> l2[0] == l1[0] ? l1[1] - l2[1] : l1[0] - l2[0]);
        return dist(p[0], p[1]) != 0 && dist(p[0], p[1]) == dist(p[1], p[3]) && dist(p[1], p[3]) == dist(p[3], p[2]) && dist(p[3], p[2]) == dist(p[2], p[0])   && dist(p[0],p[3])==dist(p[1],p[2]);
    }
    
}