Python O(n) with approach
Intuition\n Describe your first thoughts on how to solve this problem. \nThe problem is asking us to pick a random point within a given list of rectangles. The 
# Intuition\n<!-- Describe your first thoughts on how to solve this problem. -->\nThe problem is asking us to pick a random point within a given list of rectangles. The key to solving this problem is to understand the concept of weighting. We can assign a weight to each rectangle based on the number of points it contains, and then use a random number generator to pick a rectangle based on its weight.\n# Approach\n<!-- Describe your approach to solving the problem. -->\n- Create an instance variable weights that will store the weights of each rectangle.\n- For each rectangle in the input list, calculate the number of points it contains and store it in weights.\n- Calculate the total number of points in all rectangles and store it in the total variable.\n- Create a prefix sum of weights to make it easier to pick a rectangle based on its weight.\n- In the pick() method, use a bisect function to find the index of the rectangle that the random number falls within.\n- Use a random number generator to pick a point within the selected rectangle.\n# Complexity\n- Time complexity: O(n) \n<!-- Add your time complexity here, e.g. $$O(n)$$ -->\nwhere n is the number of rectangles. We need to iterate through the rectangles once to calculate their weights and create the prefix sum.\n- Space complexity: O(n) \n<!-- Add your space complexity here, e.g. $$O(n)$$ -->\nwhere n is the number of rectangles. We need to store the weights of each rectangle in an array.\n# Code\n```\nclass Solution:\n\n    def __init__(self, rects: List[List[int]]):\n        self.rects = rects\n        self.weights = []\n        for rect in rects:\n            self.weights.append((rect[2] - rect[0] + 1) * (rect[3] - rect[1] + 1))\n        self.total = sum(self.weights)\n        for i in range(1, len(self.weights)):\n            self.weights[i] += self.weights[i - 1]\n        self.weights = [0] + self.weights\n        \n\n    def pick(self) -> List[int]:\n        index = bisect.bisect_left(self.weights, random.randint(1, self.total))\n        rect = self.rects[index - 1]\n        return [random.randint(rect[0], rect[2]), random.randint(rect[1], rect[3])]\n\n# Your Solution object will be instantiated and called as such:\n# obj = Solution(rects)\n# param_1 = obj.pick()\n```
['Python3']