# Solution Alignment The prompt asks for an implementation-level answer. The safest way to present it is to define the state, maintain clear invariants, then walk through complexity and tests. ## Problem Restatement You're given a short written specification for a small service class (no external dependencies). Implement the class using clear control flow (primarily if/else) and robust input validation. The exercise has three parts: ( 1) implement the core logic; ( 2) extend it with an additional requirement based on clarified assumptions; ( 3) write unit tests that cover happy paths, edge cases, and error handling for both parts. State all assumptions explicitly and provide method signatures and representative test cases. ## Recommended Approach Model the states explicitly and use BFS for unweighted shortest paths, Dijkstra for weighted non-negative paths, or topological DP for DAGs. Track visited states at the right granularity so cycles do not cause repeated work. ## Correctness The implementation should maintain an invariant after each loop or operation that directly matches the problem statement. At termination, that invariant implies the returned value has considered every valid candidate exactly once, or has preserved the required data-structure state after every API call. ## Complexity BFS is O(V + E) time and O(V) space for a standard graph. Expanded-state problems multiply those bounds by the number of state dimensions. ## Edge Cases and Tests Disconnected graph, source equals target, cycles, duplicate edges, unreachable target, and whether the answer counts nodes, edges, moves, or transfers.