Resolve Inherited Allow and Deny Permissions in a DAG

## Problem You are given a directed acyclic graph of inheritance edges `parent -> child`, an allow list, and a deny list. A node inherits every explicit decision reachable from its ancestors, including itself. Resolve one Boolean permission for every node using these rules: - If the node or any ancestor is in the deny list, the final permission is denied. - Otherwise, if the node or any ancestor is in the allow list, the final permission is allowed. - Otherwise, the final permission is denied by default. Return results in the same order as the input node list. ### Function Contract Implement `resolveInheritedPermission(nodes, edges, allow, deny)` and return a Boolean array. ### Constraints & Assumptions - `1 <= len(nodes) <= 200,000` and node names are unique nonempty ASCII strings. - Every edge endpoint and every ACL entry names an input node. - The graph is acyclic but may have multiple roots and multiple parents per node. - Deny overrides allow regardless of inheritance distance. - Duplicate edges and duplicate ACL entries do not change the result. ### Clarifying Questions to Ask - Which direction does permission flow? From parent to child. - Does a nearer allow override a farther deny? No; any inherited deny wins. - What is the default when no decision is inherited? Deny. - Can a node have several parents? Yes. ```hint Propagate two independent facts In topological order, each node needs only `hasInheritedAllow` and `hasInheritedDeny`. OR those facts into every child, then apply deny precedence. ``` ### Example ```text nodes = ["root","teamA","teamB","service"] edges = [["root","teamA"], ["root","teamB"], ["teamA","service"], ["teamB","service"]] allow = ["root"] deny = ["teamB"] result = [true, true, false, false] ``` ### Evaluation Focus - Handles multiple inheritance paths and deny precedence. - Includes a node's own explicit entries. - Processes every component, including isolated nodes. - Uses topological traversal in `O(V + E)` time. ### Extensions to Discuss 1. How would you report invalid cyclic input? 2. What changes if a closer explicit rule overrides a farther one? 3. How would you update only affected descendants after one ACL change?