Question
You are laying fiber to connect n data centers (0..n-1). You are given a list of candidate `edges` `[u, v, cost]` and one `required` edge `[u, v, cost]` that policy forces you to build (e.g. a regulated backbone link). Return the minimum total cost to connect all n data centers into one network that includes the required edge, or -1 if full connectivity is impossible. The required edge may or may not appear in the candidate list.
min_network_cost(n: int, edges: list[list[int]], required: list[int]) → int[4,[[0,1,1],[1,2,2],[2,3,3],[0,3,4]],[0,3,10]]out13State your approach and its time/space complexity out loud before you optimize. Handle the edge cases (empty input, duplicates, overflow), and say why you chose this over the brute force. Green tests are the floor, not the grade.
Vibe coding: describe the solution in plain language (or narrate it) and the coach grades your approach. Generating runnable code from your description is coming next.