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

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/03/rec1.JPG" style="width: 500px; height: 447px;" />
<pre>
<strong>Input:</strong> points = [[1,1],[1,3],[3,1],[3,3],[2,2]]
<strong>Output:</strong> 4
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/03/rec2.JPG" style="width: 500px; height: 477px;" />
<pre>
<strong>Input:</strong> points = [[1,1],[1,3],[3,1],[3,3],[4,1],[4,3]]
<strong>Output:</strong> 2
</pre>

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

<ul>
	<li><code>1 &lt;= points.length &lt;= 500</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>

class Solution:
    def minAreaRect(self, points: List[List[int]]) -> int:
        x_loc = dict()
        y_loc = dict()
        all_loc = dict()

        for idx, (x, y) in enumerate(points):
            x_loc[x] = x_loc.get(x, set())
            y_loc[y] = y_loc.get(y, set())
            x_loc[x].add((idx, y))
            y_loc[y].add((idx, x))
            all_loc[(x, y)] = idx

        self.ans = float("inf")
        def helper(idx, direct, w=None, h=None):
           # print(idx, direct, w, h)
            if direct == 4:
                self.ans = min(self.ans, w*h)
                return 

            x, y = points[idx]
           # print(idx, direct, x, y, w, h)
            next_loc_p = y_loc[y] if direct in [0, 2] else x_loc[x]
            if direct in [0, 1]:
                for next_idx, next_loc in next_loc_p:
                    if direct == 0:
                        if next_loc > x:
                            helper(next_idx, 1, next_loc-x, h)
                    elif direct == 1:
                        if next_loc < y:
                            helper(next_idx, 2, w, y-next_loc)
            elif direct==2:
                if (x-w, y) in all_loc:
                    helper(all_loc[(x-w, y)], 3, w, h)
            else:
                if (x, y+h) in all_loc:
                    helper(all_loc[(x, y+h)], 4, w, h)

        for i in range(len(points)):
           # print('===')
            helper(i, 0)
        return self.ans if self.ans != float('inf') else 0
17900