Compute Minimum Broadcast Latencies Between Cities

## Problem Cities are connected by bidirectional network links with positive ping times. Starting from one city, compute the minimum total ping needed to reach every city. Unreachable cities should be reported as `-1`. ### Function Contract Implement `minimum_broadcast_latencies(n, links, source) -> list[int]`. Each link is `[u, v, ping]`; the returned list is indexed by city. ### Constraints - `1 <= n <= 200000` and `0 <= len(links) <= 300000`. - `1 <= ping <= 10^9`; parallel links are allowed. - `0 <= source < n`. - Distances can exceed a 32-bit signed integer. ### Examples - For `n = 4`, links `[[0,1,5],[0,2,2],[2,1,1],[1,3,3]]`, and source `0`, return `[0,3,2,6]`. - With no links and source `1` in a three-city graph, return `[-1,0,-1]`. ```hint Finalize the nearest frontier A min-priority queue lets the smallest known unsettled distance become final before longer alternatives are expanded. ``` ```hint Treat changing pings separately If link weights update continuously, identify whether queries justify recomputing or require a dynamic shortest-path structure. ``` ### Edge Cases - The source city always has distance zero. - The graph may be disconnected. - A later path can improve a distance discovered through a direct link.