Solve meeting-room scheduling and shortest paths

You are asked to solve two algorithmic problems. ## Part A: Meeting-room scheduling (intervals) You are given an array of meeting time intervals `intervals`, where each interval is `[start, end)` with `0 <= start < end`. 1. **Attend-all check**: Return `true` if a single person can attend all meetings (i.e., no overlaps), else `false`. 2. **Minimum rooms**: Return the minimum number of conference rooms required to host all meetings. 3. **Room assignment / most-used room (optional extension)**: You have `n` rooms labeled `0..n-1`. Schedule meetings in start-time order using the lowest-index available room; if none are available at a meeting’s start, delay the meeting until the earliest room becomes free (preserving meeting duration). Return the room index that hosted the most meetings (tie → smallest index). ### Constraints (assume) - `1 <= intervals.length <= 2e5` - Times are integers up to `1e9` ## Part B: Shortest path in a weighted directed graph Given a weighted **directed** graph with `V` nodes labeled `0..V-1` and `E` edges. Each edge is `(u, v, w)` with `w > 0`. - Input: `V`, edge list, `source s`, `target t`. - Output: the shortest distance from `s` to `t` (and optionally the actual path). If `t` is unreachable, return `-1`. ### Constraints (assume) - `1 <= V <= 2e5`, `0 <= E <= 2e5` - Weights are positive integers.