Solve median extremes and segment flips

Part A — Sliding-window median extremes: - Input: an integer k (1 ≤ k ≤ n) and an array nums of length n. - For every contiguous subarray of length k, compute its median (for even k, use the lower median). - Output: the maximum and the minimum among these medians. - Design an algorithm that runs in O(n log k) time and O(k) space, and describe the data structures used. Part B — Even-length uniform segmenting with minimal flips: - Input: a binary array frames of length n. - You may flip any bits (0↔ 1). - After flipping, the array must be partitionable into contiguous segments, each of even length and containing identical values (all 0s or all 1s). - Objective: minimize the number of segments; subject to that minimum, minimize the total number of flips. - Output: the minimal number of segments and the minimal flips needed to achieve it. - Describe an algorithm and provide its time and space complexity.