Median of All Values Across Several Sorted Integer Arrays

You are given several integer arrays, each sorted in non-decreasing order. Return the median of all of their elements taken together. The question was first asked for exactly two sorted arrays, and the follow-up asked for the same result when there are many input arrays. Implement the general version: the function receives any number of arrays, and two arrays is the original question. ### Function Signature ```python def median_of_sorted_arrays(arrays: list[list[int]]) -> float: ``` ### Rules - Let `N` be the total number of elements across all arrays, and let `merged` be all of those elements in sorted order, with duplicates kept. - If `N` is odd, the median is `merged[N // 2]`. If `N` is even, the median is `(merged[N // 2 - 1] + merged[N // 2]) / 2`. - Return the median as a float, for example `3.0` rather than `3`. Every possible median is an integer or an integer plus one half, so the result is exact. - Any individual array may be empty, but there is at least one element in total. ### Constraints - `1 <= len(arrays) <= 10^4` - `0 <= len(arrays[i])` for every `i`, and `1 <= N <= 2 * 10^5` - Each `arrays[i]` is sorted in non-decreasing order. - `-10^9 <= arrays[i][j] <= 10^9` ### Examples **Example 1** ```text Input: arrays = [[1, 4], [2, 9]] Output: 3.0 ``` All elements in order are `[1, 2, 4, 9]`. `N = 4` is even, so the median is the average of `2` and `4`. **Example 2** ```text Input: arrays = [[-3, 5, 5], [0]] Output: 2.5 ``` All elements in order are `[-3, 0, 5, 5]`, and the average of `0` and `5` is `2.5`. **Example 3** ```text Input: arrays = [[-5, 0, 7], [], [2, 2, 9], [4, 10, 11]] Output: 4.0 ``` All elements in order are `[-5, 0, 2, 2, 4, 7, 9, 10, 11]`. `N = 9` is odd, so the median is the element at index `4`, which is `4`. The empty array contributes nothing.