Implement a Graph With Path and Cycle Detection

Problem Implement a directed graph supporting addNode, removeNode, addEdge, removeEdge, hasPath(a, b), and hasCycle().

Input / Output

• Input: a sequence of mutation and query calls.
• Output: hasPath(a,b) returns whether b is reachable from a; hasCycle() returns whether the graph has any directed cycle.

Constraints

• Directed graph; handle removal of nodes that still have incident edges.

Example

• addEdge(A,B); addEdge(B,C); hasPath(A,C) -> true; addEdge(C,A); hasCycle() -> true.