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
func minAreaFreeRect(points [][]int) float64 {
	n := len(points)
	f := func(x, y int) int {
		return x*40001 + y
	}
	s := map[int]bool{}
	for _, p := range points {
		s[f(p[0], p[1])] = true
	}
	ans := 1e20
	for i := 0; i < n; i++ {
		x1, y1 := points[i][0], points[i][1]
		for j := 0; j < n; j++ {
			if j != i {
				x2, y2 := points[j][0], points[j][1]
				for k := j + 1; k < n; k++ {
					if k != i {
						x3, y3 := points[k][0], points[k][1]
						x4, y4 := x2-x1+x3, y2-y1+y3
						if s[f(x4, y4)] {
							if (x2-x1)*(x3-x1)+(y2-y1)*(y3-y1) == 0 {
								ww := (x2-x1)*(x2-x1) + (y2-y1)*(y2-y1)
								hh := (x3-x1)*(x3-x1) + (y3-y1)*(y3-y1)
								ans = math.Min(ans, math.Sqrt(float64(ww*hh)))
							}
						}
					}
				}
			}
		}
	}
	if ans == 1e20 {
		return 0
	}
	return ans
}