Populating Next Right Pointers in Each Node II

Populating Next Right Pointers in Each Node II

What is this problem about?

The Populating Next Right Pointers in Each Node II extends the first problem to any binary tree (not just perfect). Each node may have 0, 1, or 2 children. The O(1)-space solution is more complex since you can't assume all nodes at a level have children. The linked list, BFS, DFS, binary tree, and tree interview pattern is demonstrated at an advanced level.

Why is this asked in interviews?

Citadel, Microsoft, Meta, Amazon, Google, and Bloomberg ask this as the harder variant. It tests whether candidates can extend the perfect-tree O(1) solution to handle missing children — requiring a "dummy head" trick for each level.

Algorithmic pattern used

Dummy head for each level + O(1) space. For each level: use a dummy node levelHead to build the next level's linked list as you traverse the current level. For each node traversed: if it has a left child, add to levelHead chain. If it has a right child, add to chain. After processing the current level, move to the next level's first real node (levelHead.next). Repeat.

Example explanation

Tree: root=1 (children: 2,3). Node 2 (children: 4,5). Node 3 (children: none,7). Level 1 processed: 1.next=null. Next level dummy → chain: 2→3. Level 2 processed (using next pointers 2→3): node 2's children: dummy→4→5. node 3's children: dummy→...→7. Chain: 4→5→7. Level 3 processed: 4.next=5, 5.next=7, 7.next=null.

Common mistakes candidates make

• Using BFS queue (works but O(n) space — missing the O(1) insight).
• Not using a dummy head (null checks become messy without it).
• Forgetting to advance to the next level after completing a level.
• Handling single-child nodes incorrectly.

Interview preparation tip

The dummy head trick for linked list level building is elegant: dummy = ListNode(0); tail = dummy. As you add children to the next level, extend the tail. After processing a level, next_level_head = dummy.next. This pattern generalizes to any "build next level as linked list" tree problem. Practice both variants I and II until the O(1)-space approach feels natural.