Populating Next Right Pointers in Each Node

Populating Next Right Pointers in Each Node

What is this problem about?

The Populating Next Right Pointers in Each Node problem asks you to populate each node's next pointer to point to the next node on the same level (or null if none). The tree is a perfect binary tree. This coding problem uses level-order traversal or a clever O(1)-space linked pointer approach. The linked list, BFS, DFS, binary tree, and tree interview pattern is the core.

Why is this asked in interviews?

Microsoft, Meta, Amazon, Google, Bloomberg, and Walmart Labs ask this because the O(1)-space solution — using already-established next pointers to traverse the level — is an elegant technique demonstrating mastery of tree pointer manipulation.

Algorithmic pattern used

O(1) space level-by-level pointer setting. For each level: use node.next pointers already set at this level to traverse it. For each node on the current level: set node.left.next = node.right and node.right.next = node.next?.left. After connecting all children, move to the first node of the next level (leftmost child).

Example explanation

Tree: root=1, level 2: 2,3, level 3: 4,5,6,7. Level 1: connect root.next=null (default). Level 2: root.left.next = root.right (2.next=3). root.right.next = null (3.next=null). Level 3: node 2's children: 4.next=5. node 2's right-to-3's left: 5.next=6. node 3's children: 6.next=7. 7.next=null. All next pointers set in O(1) space.

Common mistakes candidates make

• Using a queue (BFS) — O(n) space, acceptable but not optimal for perfect binary trees.
• Not leveraging already-established next pointers for traversal.
• Off-by-one: connecting right.next to next.left requires checking if next is null.
• Not advancing to the leftmost child of the next level.

Interview preparation tip

The O(1) space solution is the key differentiator. For perfect binary trees, the next pointers from the current level enable traversal without a queue. Practice this level-by-level pointer approach: it's used in "right side view," "level sum," and many tree problems. Populating Next Right Pointers I (perfect tree) and II (general tree) test progressively harder O(1)-space solutions.