Consider the tree: root , left , right . Node has children and . Target is , k = 2.
After DFS, parent map: {5: 3, 1: 3, 6: 5, 2: 5}.
BFS from . Level : [5]. Level : expand to , , and parent . Level : from (no children, parent visited), from (its children if any), from (expand to , parent null). Result at level includes and any children of .
You visit every node at most once in DFS and once in BFS. That's time and space for the parent map and BFS queue.