Compute decayed power levels in a graph

You are given an unweighted graph representing a network of wires. - The graph has **N nodes** labeled `0..N-1` and **M edges** (each edge is a bidirectional wire). - A subset of nodes are **torches**. - Each torch provides power level **16 at its own node**. - Power propagates through wires and **decays by 1 per wire traversed** (i.e., by graph distance in number of edges). - If multiple torches can reach a node, the node receives the **maximum** power among them. - Power cannot be negative. For every node `v`, define: - `dist(v) =` the length (in edges) of the shortest path from `v` to any torch (∞ if unreachable) - `power(v) = max(0, 16 - dist(v))` (and `power(v)=0` if unreachable) ### Task Given `N`, the edge list, and the list of torch nodes, compute `power(v)` for all nodes. ### Input (one possible format) - `N` (number of nodes) - `edges`: list of pairs `(u, v)` - `torches`: list of torch node indices ### Output - Array `power[0..N-1]`. ### Notes / constraints - Assume `N` can be large (e.g., up to 10^5), so the solution should be near-linear in `N + M`. - Graph may be disconnected.