Algorithm: Perform arithmetic computations over a bidirectional graph

Given an undirected (bidirectional) graph, each edge (u, v) has a value w representing a transformation from u to v. Because the graph is bidirectional, a reverse transformation exists as well. Answer multiple queries: for each pair (s, t), return the composed result along some path from s to t. If s and t are disconnected, return -1. Implement: Input: n, m, then m lines u v w, then q, then q queries s t. Output: one result per query. Constraints: 1 <= n,m,q <= 2e5 Nodes labeled 0..n-1 w positive (integer or float; clarify in interview) Aim for near O((n+m+q) α(n)) (weighted DSU) or O((n+m) log n + q log n). You must clarify in the interview: The composition operator (multiply vs add) How to derive the reverse relation (reciprocal vs negation) Floating-point tolerance requirements.