<p>Given the coordinates of four points in 2D space <code>p1</code>, <code>p2</code>, <code>p3</code> and <code>p4</code>, return <code>true</code> <em>if the four points construct a square</em>.</p>

<p>The coordinate of a point <code>p<sub>i</sub></code> is represented as <code>[x<sub>i</sub>, y<sub>i</sub>]</code>. The input is <strong>not</strong> given in any order.</p>

<p>A <strong>valid square</strong> has four equal sides with positive length and four equal angles (90-degree angles).</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,1]
<strong>Output:</strong> true
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,12]
<strong>Output:</strong> false
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> p1 = [1,0], p2 = [-1,0], p3 = [0,1], p4 = [0,-1]
<strong>Output:</strong> true
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>p1.length == p2.length == p3.length == p4.length == 2</code></li>
	<li><code>-10<sup>4</sup> &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
    double findDistance(vector<int>& p1, vector<int>& p2){
        return sqrt(pow(p1[0]-p2[0],2) + pow(p1[1]-p2[1],2));
    }
    bool areAlmostEqual(double a, double b, double epsilon = 1e-9) {
        return fabs(a - b) < epsilon;
    }
public:
    bool validSquare(vector<int>& p1, vector<int>& p2, vector<int>& p3, vector<int>& p4) {
        double dist1 = findDistance(p1,p2);
        double dist2 = findDistance(p1,p3);
        double dist3 = findDistance(p1,p4);
        double dist4 = findDistance(p2,p3);
        double dist5 = findDistance(p2,p4);
        double dist6 = findDistance(p3,p4);

        double arr[6] = {dist1,dist2,dist3,dist4,dist5,dist6};
        sort(arr,arr+6);

        bool sidesEqual = arr[0]>0 && arr[4]>0 && areAlmostEqual(arr[0], arr[1]) && areAlmostEqual(arr[1], arr[2]) && areAlmostEqual(arr[2], arr[3]);
        
        // Check for diagonals being equal and correct
        bool diagonalsCorrect = areAlmostEqual(arr[4], arr[5]) && areAlmostEqual(arr[4], arr[0] * sqrt(2));
        return sidesEqual && diagonalsCorrect;
    }
};
29000