Compute distance of each node to a cycle

## Problem You are given an **undirected** graph with `n` nodes labeled `0..n-1` and a list of edges. The graph is connected and contains **exactly one simple cycle** (i.e., it is a *unicyclic* graph). For each node `i`, return `dist[i]` = the **minimum number of edges** from node `i` to **any node on the cycle**. - Nodes that are on the cycle have distance `0`. ### Example (illustrative) If nodes `{2,3,4}` form the only cycle, then `dist[2]=dist[3]=dist[4]=0`, and nodes in trees attached to the cycle have distance equal to their shortest path length to any of `{2,3,4}`. ### Input / Output - Input: - integer `n` - edges: list of pairs `(u, v)` - Output: integer array `dist` of length `n` ### Constraints (assume) - `2 ≤ n ≤ 2 * 10^5` - `edges.length = n` (connected unicyclic graph) - `0 ≤ u, v < n`, `u != v` ### Notes A linear-time approach is expected. (A common approach involves pruning leaves to identify cycle nodes, then multi-source BFS from the cycle.)