Choose a spanning tree and optionally upgrade edge weights to maximize the tree's total stability value.
You are given an undirected connected graph with n nodes and weighted edges. You may select a spanning tree of the graph. Some edges can be upgraded before or during selection according to the problem rules, which increases their effective weight.
Your goal is to build a spanning tree with the maximum possible total stability after applying upgrades optimally.
Return the best achievable stability value.
n - 1 edges and contains no cycles.This is an algorithmic interview problem. The exact input format may vary by platform wrapper; the core task is to compute the optimal spanning tree value under upgrade constraints.
n for the number of vertices.1 <= nn - 1 edges.Example 1
Input
n = 4 edges = [[1,2,4],[2,3,1],[3,4,3],[1,4,2],[1,3,5]] upgrades = [[2,3,4]]
Output
12
Explanation
If edge (2,3) can be upgraded from 1 to 4, the best spanning tree can use edges (1,3)=5, (1,2)=4, and (2,3)=4 for a total of 12.
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