Clarify and Find Common Ancestors in a Graph

Explain how you would find common ancestors in a graph. Begin by clarifying the edge direction, graph structure, queried vertices, and whether the result should contain every common ancestor or only a nearest or lowest one. ### Constraints The graph representation, acyclicity, number of parents, self-ancestor convention, and output rule are unspecified. Do not silently turn the task into a binary-tree lowest-common-ancestor problem. Use a clearly labeled hypothetical interpretation to explain an algorithm, then discuss how a different output rule changes it. ### Clarifying Questions - Do edges point from parent to child, and can a vertex have several parents? - Is the graph a tree, a directed acyclic graph, or a general directed graph? - Is a queried vertex its own ancestor? - Are we returning all common ancestors, a Boolean, or one or more lowest ancestors? ```hint Reverse the reachability direction When edges point from parent to child, walking incoming edges from a queried vertex reveals its ancestors. ``` ### What a Strong Answer Covers - Explicit graph and ancestor semantics before choosing an algorithm. - Reachability sets, intersection, visited-state handling, and complexity. - The distinction between all common ancestors and a potentially nonunique lowest result in a DAG. ### Follow-up Questions - How would repeated queries on an unchanged graph affect preprocessing choices? - Can two vertices in a DAG have several incomparable lowest common ancestors?