<p>You are given an array of non-overlapping axis-aligned rectangles <code>rects</code> where <code>rects[i] = [a<sub>i</sub>, b<sub>i</sub>, x<sub>i</sub>, y<sub>i</sub>]</code> indicates that <code>(a<sub>i</sub>, b<sub>i</sub>)</code> is the bottom-left corner point of the <code>i<sup>th</sup></code> rectangle and <code>(x<sub>i</sub>, y<sub>i</sub>)</code> is the top-right corner point of the <code>i<sup>th</sup></code> rectangle. Design an algorithm to pick a random integer point inside the space covered by one of the given rectangles. A point on the perimeter of a rectangle is included in the space covered by the rectangle.</p>

<p>Any integer point inside the space covered by one of the given rectangles should be equally likely to be returned.</p>

<p><strong>Note</strong> that an integer point is a point that has integer coordinates.</p>

<p>Implement the <code>Solution</code> class:</p>

<ul>
	<li><code>Solution(int[][] rects)</code> Initializes the object with the given rectangles <code>rects</code>.</li>
	<li><code>int[] pick()</code> Returns a random integer point <code>[u, v]</code> inside the space covered by one of the given rectangles.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/24/lc-pickrandomrec.jpg" style="width: 419px; height: 539px;" />
<pre>
<strong>Input</strong>
[&quot;Solution&quot;, &quot;pick&quot;, &quot;pick&quot;, &quot;pick&quot;, &quot;pick&quot;, &quot;pick&quot;]
[[[[-2, -2, 1, 1], [2, 2, 4, 6]]], [], [], [], [], []]
<strong>Output</strong>
[null, [1, -2], [1, -1], [-1, -2], [-2, -2], [0, 0]]

<strong>Explanation</strong>
Solution solution = new Solution([[-2, -2, 1, 1], [2, 2, 4, 6]]);
solution.pick(); // return [1, -2]
solution.pick(); // return [1, -1]
solution.pick(); // return [-1, -2]
solution.pick(); // return [-2, -2]
solution.pick(); // return [0, 0]
</pre>

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

<ul>
	<li><code>1 &lt;= rects.length &lt;= 100</code></li>
	<li><code>rects[i].length == 4</code></li>
	<li><code>-10<sup>9</sup> &lt;= a<sub>i</sub> &lt; x<sub>i</sub> &lt;= 10<sup>9</sup></code></li>
	<li><code>-10<sup>9</sup> &lt;= b<sub>i</sub> &lt; y<sub>i</sub> &lt;= 10<sup>9</sup></code></li>
	<li><code>x<sub>i</sub> - a<sub>i</sub> &lt;= 2000</code></li>
	<li><code>y<sub>i</sub> - b<sub>i</sub> &lt;= 2000</code></li>
	<li>All the rectangles do not overlap.</li>
	<li>At most <code>10<sup>4</sup></code> calls will be made to <code>pick</code>.</li>
</ul>

import random
from typing import List

class Solution:

    def __init__(self, rects: List[List[int]]):
        self.rects = rects
        self.areas = []
        total_area = 0
        
        for rect in rects:
            a, b, x, y = rect
            rect_area = (x - a + 1) * (y - b + 1)  # +1 to include both endpoints
            total_area += rect_area
            self.areas.append(total_area)
        
        self.total_area = total_area

    def pick(self) -> List[int]:
        # Randomly select a rectangle based on its area
        rand_area = random.randint(1, self.total_area)
        rect_index = next(i for i, area in enumerate(self.areas) if rand_area <= area)
        
        # Get the selected rectangle
        rect = self.rects[rect_index]
        a, b, x, y = rect
        
        # Generate random coordinates within the selected rectangle
        rand_x = random.randint(a, x)
        rand_y = random.randint(b, y)
        
        return [rand_x, rand_y]

# Your Solution object will be instantiated and called as such:
# obj = Solution(rects)
# param_1 = obj.pick()
20200