Connect next pointers for each tree level
Company: Meta
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: hard
Interview Round: Technical Screen
You are given the root of a binary tree where each node has fields `left`, `right`, and `next` (initially `null`). For every node, set its `next` pointer to the node immediately to its right on the same level. If there is no node to the right, set `next = null`.
Constraints/requirements:
- The tree is not necessarily perfect or complete.
- Aim for O(n) time.
- Use O(1) extra space beyond the recursion/iteration variables (i.e., do not use a queue for BFS).
Return the root after populating all `next` pointers.
Quick Answer: Evaluates understanding of binary tree traversal, in-place pointer manipulation, and time-space trade-offs by requiring population of sibling pointers across each level while meeting O(n) time and O(1) extra space constraints.
You are given a binary tree where every non-null node conceptually has four fields: `val`, `left`, `right`, and `next` (initially `null`). Set each node's `next` pointer to the node immediately to its right on the same level. If there is no such node, its `next` pointer should remain `null`.
The tree is not necessarily perfect or complete.
For this coding problem, the input tree is provided as a level-order array using heap-style indexing: for a node at index `i`, its left child is at `2*i + 1` and its right child is at `2*i + 2`. Missing nodes are represented by `None`.
Because pointer-based trees are hard to compare directly in automated tests, return a flat serialization of the tree *after* connecting `next` pointers. Serialize level by level by following only `next` pointers, and append the string `'#'` after each level.
Example:
- Input: `[1, 2, 3, 4, 5, None, 7]`
- After linking: `1 -> null`, `2 -> 3 -> null`, `4 -> 5 -> 7 -> null`
- Output: `[1, '#', 2, 3, '#', 4, 5, 7, '#']`
Aim for `O(n)` time and `O(1)` auxiliary space for the pointer-connection step.
Constraints
- 0 <= len(values) <= 100000
- -10^9 <= values[i] <= 10^9 for every non-None value
- The tree uses heap-style array indexing with `None` placeholders for missing nodes
- The linking step should run in O(n) time
- Do not use a BFS queue; use O(1) auxiliary space for connecting pointers
Examples
Input: []
Expected Output: []
Explanation: An empty tree has no levels, so the serialized result is empty.
Input: [1]
Expected Output: [1, '#']
Explanation: There is only one node, and it has no neighbor on its level.
Hints
- Once one level is connected, you can traverse that entire level using `next` pointers instead of a queue.
- While scanning the current level, build the next level's linked list using a dummy head and a moving tail pointer.