Problem Description

You are given an undirected graph representing professional connections. The graph consists of n people, labeled 0 to n-1, and a list of undirected edges called connections, where an edge (a, b) signifies that person a and person b are directly connected (a 1st-degree connection).

Given two specific people, src (source) and dst (destination), your task is to find and return the minimum number of connections (degrees) required to reach dst from src.

Return Values

• Return 0 if src is the same as dst.
• Return 1 if src and dst are directly connected.
• Return 2 if src and dst are connected via one intermediate person, and so on for higher degrees.
• Return -1 if dst is not reachable from src.

Optional Requirement

If explicitly asked, also return one shortest path (the sequence of people) from src to dst.

Constraints

• 1 ≤ n ≤ 1e5 (number of people)
• 0 ≤ |connections| ≤ 2e5 (number of direct connections)
• The solution must be efficient.