Tree Node Relationship — Sibling / Cousin / Other

Given an arbitrary tree and two of its nodes, classify their relationship as `sibling`, `cousin`, or `other`. Requirements Input: the tree root plus two node references (or values) a and b. Output one of sibling (same parent), cousin (same depth, different parent), or other (everything else — ancestor / descendant / different depths). The interview prompt left tree arity (binary vs n-ary) open; clarify before coding. Notes The canonical solve is a single BFS / DFS that records (parent, depth) for both targets, then compares: same parent → sibling; same depth + different parent → cousin; otherwise other. Bail out as soon as both targets are seen so large trees stay O(n) worst-case with early termination. Edge cases worth raising up front: a == b (same node), one node missing from the tree, root involved (root has no parent, so it can never be a sibling or cousin). Preparation Drill LC 993 "Cousins in Binary Tree" first, then extend the same scan to also report the sibling vs other branches. Write both BFS and recursive-DFS variants — the interviewer in this loop pushed for the iterative version after the recursion was working. Pre-define an Info(parent, depth, found) carrier so the classification step reads as a clean three-way if instead of nested boolean logic.