# Detect a Reachable Negative Cycle Given a directed weighted graph, determine whether a negative-weight cycle is reachable from a specified start vertex. A cycle is negative when the sum of its edge weights is less than zero. Implement: ```python def has_reachable_negative_cycle( vertex_count: int, edges: list[tuple[int, int, int]], start: int, ) -> bool: ... ``` Each edge is `(source, destination, weight)`, vertices are numbered `0` through `vertex_count - 1`, and parallel edges and self-loops are allowed. ## Constraints and Clarifications - A negative cycle in a disconnected component that cannot be reached from `start` does not count. - Edge weights may be positive, zero, or negative. - An unreachable distance must never participate in arithmetic relaxation. - Return only a boolean, but be prepared to explain how to recover one witness cycle. - Analyze time and space complexity in terms of vertices and edges. ## Hints - Ask how many edge-relaxation rounds can improve a shortest simple path when no reachable negative cycle exists. - Track whether any relevant value still changes after that bound. - Test a negative self-loop, an unreachable negative cycle, and a graph with negative edges but no negative cycle.