Valid Square
<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>
Geometry; Math
class Solution {
public:
    bool validSquare(vector<int>& p1, vector<int>& p2, vector<int>& p3, vector<int>& p4) {
        return check(p1, p2, p3) && check(p1, p3, p4) && check(p1, p2, p4) && check(p2, p3, p4);
    }

    bool check(vector<int>& a, vector<int>& b, vector<int>& c) {
        int x1 = a[0], y1 = a[1];
        int x2 = b[0], y2 = b[1];
        int x3 = c[0], y3 = c[1];
        int d1 = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
        int d2 = (x1 - x3) * (x1 - x3) + (y1 - y3) * (y1 - y3);
        int d3 = (x2 - x3) * (x2 - x3) + (y2 - y3) * (y2 - y3);
        if (d1 == d2 && d1 + d2 == d3 && d1 > 0) return true;
        if (d1 == d3 && d1 + d3 == d2 && d1 > 0) return true;
        if (d2 == d3 && d2 + d3 == d1 && d2 > 0) return true;
        return false;
    }
};