Solve Three Algorithmic Tasks

You were asked three coding problems: 1. **Count events inside a time window** - You are given an initial collection of event timestamps in `HH:MM:SS` format. - The timestamps may be unsorted and may contain duplicates. - Design a data structure that supports preprocessing and a query function: - `build(events)`: preprocess the events. - `query(start_time, end_time)`: return how many events fall within the inclusive range `[start_time, end_time]`. - Example: - `events = ["12:00:01", "01:02:02", "03:03:03"]` - `query("01:02:01", "01:02:03") -> 1` - `query("01:00:00", "04:00:00") -> 2` 2. **Form a target string from double-sided cards** - You are given cards where each card has one lowercase English letter on the front and one on the back. - Each card can be used at most once, and if used, you may choose only one side. - Determine whether the target string can be formed using the available cards. - Example: - `cards = [["a", "b"], ["c", "d"]]` - `target = "ac" -> true` - `target = "ab" -> false` because both `a` and `b` are on the same card. 3. **Merge multiple sorted lists** - You are given `N` sorted lists of integers. - Merge them into one fully sorted output list. - The goal is to do better than concatenating everything and sorting again.