My first instinct was to just simulate BFS for each query and check, which works but blows up when q is large.
Root the tree at the first node of the permutation and verify that the permutation respects BFS level order and parent-child constraints. For each node, its parent must appear earlier, and all nodes at the same depth must appear before any node at the next depth. Additionally, the set of children of each node must appear as a contiguous block in the permutation.
Pro tip: Clarify that the tree is undirected and that BFS can start from any node, but the permutation fixes the start. Mention that the problem reduces to checking if the permutation is a valid BFS order for some ordering of neighbors, which can be done in O(n) time with a queue simulation.
Since the permutation starts with some node, treat that node as the root of the BFS tree. Build adjacency lists and compute parent-child relationships via BFS from that root.
Ensure that nodes appear in non-decreasing order of depth. Compute the depth of each node from the root and verify that the permutation is sorted by depth.
For each node, its children in the BFS tree must appear as a contiguous block in the permutation, and all children must appear after the parent. Use a queue to simulate BFS and check that the order of children matches the permutation.
Process nodes in the given permutation order. Maintain a queue of nodes whose children have not been fully processed. For each node in the permutation, it must be the next expected child of the front of the queue. If not, the permutation is invalid.
Consider cases like n=1, star graphs, and paths. Ensure the algorithm runs in O(n) per query, and discuss how to handle multiple queries efficiently if needed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.