Minimum Area Rectangle II
<p>You are given an array of points in the <strong>X-Y</strong> plane <code>points</code> where <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code>.</p>

<p>Return <em>the minimum area of any rectangle formed from these points, with sides <strong>not necessarily parallel</strong> to the X and Y axes</em>. If there is not any such rectangle, return <code>0</code>.</p>

<p>Answers within <code>10<sup>-5</sup></code> of the actual answer will be accepted.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0900-0999/0963.Minimum%20Area%20Rectangle%20II/images/1a.png" style="width: 398px; height: 400px;" />
<pre>
<strong>Input:</strong> points = [[1,2],[2,1],[1,0],[0,1]]
<strong>Output:</strong> 2.00000
<strong>Explanation:</strong> The minimum area rectangle occurs at [1,2],[2,1],[1,0],[0,1], with an area of 2.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0900-0999/0963.Minimum%20Area%20Rectangle%20II/images/2.png" style="width: 400px; height: 251px;" />
<pre>
<strong>Input:</strong> points = [[0,1],[2,1],[1,1],[1,0],[2,0]]
<strong>Output:</strong> 1.00000
<strong>Explanation:</strong> The minimum area rectangle occurs at [1,0],[1,1],[2,1],[2,0], with an area of 1.
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0900-0999/0963.Minimum%20Area%20Rectangle%20II/images/3.png" style="width: 383px; height: 400px;" />
<pre>
<strong>Input:</strong> points = [[0,3],[1,2],[3,1],[1,3],[2,1]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> There is no possible rectangle to form from these points.
</pre>

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

<ul>
	<li><code>1 &lt;= points.length &lt;= 50</code></li>
	<li><code>points[i].length == 2</code></li>
	<li><code>0 &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 4 * 10<sup>4</sup></code></li>
	<li>All the given points are <strong>unique</strong>.</li>
</ul>
Geometry; Array; Hash Table; Math
function minAreaFreeRect(points: number[][]): number {
    const n = points.length;
    const f = (x: number, y: number): number => x * 40001 + y;
    const s: Set<number> = new Set();
    for (const [x, y] of points) {
        s.add(f(x, y));
    }
    let ans = Number.MAX_VALUE;
    for (let i = 0; i < n; ++i) {
        const [x1, y1] = points[i];
        for (let j = 0; j < n; ++j) {
            if (j !== i) {
                const [x2, y2] = points[j];
                for (let k = j + 1; k < n; ++k) {
                    if (k !== i) {
                        const [x3, y3] = points[k];
                        const x4 = x2 - x1 + x3;
                        const y4 = y2 - y1 + y3;
                        if (s.has(f(x4, y4))) {
                            if ((x2 - x1) * (x3 - x1) + (y2 - y1) * (y3 - y1) === 0) {
                                const ww = (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
                                const hh = (x3 - x1) * (x3 - x1) + (y3 - y1) * (y3 - y1);
                                ans = Math.min(ans, Math.sqrt(ww * hh));
                            }
                        }
                    }
                }
            }
        }
    }
    return ans === Number.MAX_VALUE ? 0 : ans;
}
