## Problem A network of `n` nodes is represented as a directed weighted graph where `edges[i] = (u, v, latency_ms)`. A message is broadcast from a source node `src`. Compute the minimum time (in ms) for the message to reach every node. If any node is unreachable, return `-1`. ```python def min_broadcast_time( n: int, edges: list[tuple[int, int, int]], src: int ) -> int: ``` ## Example ``` n=4, edges=[(0,1,1),(0,2,4),(1,2,2),(1,3,5),(2,3,1)], src=0 Shortest paths from 0: {0:0, 1:1, 2:3, 3:4} Output: 4 (time until last node receives message) ``` This is equivalent to LeetCode 743 (Network Delay Time). ## Follow-ups 1. What algorithm did you use, and what is its time complexity for a dense graph? 2. How would you identify which nodes are the bottleneck (critical path) in the broadcast? 3. If up to `k` edges can be removed to reduce broadcast time, how would you approach that? 4. Extend to bidirectional edges -- does the algorithm change?

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Message Broadcast - Minimum Time to Reach All Nodes in Network

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Problem A network of n nodes is represented as a directed weighted graph where edges[i] = (u, v, latency_ms). A message is broadcast from a source node src. Compute the minimum time (in ms) for the message to reach every node. If any node is unreacha…

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