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.