My first instinct was BFS and track depth plus parent for each node, which works fine.
Use a single traversal (BFS or DFS) to track each node's parent and depth. Then compare the parent and depth of x and y to classify their relationship.
Pro tip: Clarify edge cases upfront, such as x and y being the same node or not present in the tree, and discuss how to handle them. This shows attention to detail and robustness.
Confirm what 'siblings' and 'cousins' mean: siblings share the same parent; cousins have the same depth but different parents. Ask about edge cases like x == y, missing nodes, or duplicate values.
Decide between BFS (level-order) or DFS (pre-order) to record parent and depth for each node. BFS naturally processes nodes level by level, making depth tracking straightforward.
During traversal, maintain a map or variables to store the parent and depth of x and y. For BFS, enqueue children with their parent and depth; for DFS, pass parent and depth as parameters.
After traversal, compare the recorded parent and depth: if parents are equal, they are siblings; else if depths are equal, they are cousins; otherwise, neither.
State time and space complexity: O(n) time and O(n) space for the map, or O(h) space for DFS recursion. Discuss early termination if both nodes are found.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.