The naive BFS solution comes to mind immediately but they pushed back on the space usage right away.
Start by clarifying the problem and constraints, then propose a level-by-level traversal using already established next pointers to avoid queues or recursion. Emphasize the O(1) space requirement by leveraging the tree structure and parent-level connections.
Pro tip: Mention that this approach works because the tree is perfect; for a general binary tree, O(1) space is not possible without parent pointers or additional data structures. This shows you understand the problem's boundaries.
Confirm that the tree is perfect, that we need to set next pointers for all nodes, and that O(1) extra space means no queues or recursion stack.
Explain that we can traverse each level using the next pointers already set for the parent level, starting from the leftmost node of each level.
For each node, set its left child's next to its right child, and if the node has a next, set its right child's next to the next node's left child.
After processing a level, move to the next level by following the left child of the leftmost node, and repeat until all levels are processed.
State that time complexity is O(n) and space is O(1). Discuss edge cases like empty tree or single node.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.