Populating Next Right Pointers in Each Node

This challenge focuses on manipulating a binary tree structure where each node has an additional pointer, nextRight. The goal is to populate these nextRight pointers so that each node points to its immediate right neighbor on the same level within the tree. This problem is useful in scenarios where you need to traverse a binary tree level by level efficiently, without relying on queues or stacks.

Problem Description

You are given a perfect binary tree where each node has three pointers: left, right, and nextRight. The left and right pointers are standard binary tree pointers, while nextRight is the pointer you need to populate. Your task is to modify the tree such that each node's nextRight pointer points to its immediate right neighbor in the same level. If a node does not have a right neighbor (i.e., it's the rightmost node in its level), its nextRight pointer should be set to null. The tree is perfect, meaning every level is completely filled.

What needs to be achieved: Modify the given perfect binary tree in-place, setting the nextRight pointers for each node.

Key Requirements:

• The solution should be in-place, meaning you cannot create a new tree. You must modify the existing tree structure.
• The solution should work for perfect binary trees.
• The nextRight pointers should be populated correctly for each level.
• The rightmost node on each level should have its nextRight pointer set to null.

Expected Behavior:

After the function completes, traversing the tree level by level using the nextRight pointers should yield the nodes in the order they appear on each level.

Edge Cases to Consider:

• An empty tree (root is null).
• A tree with only one node (root).

Examples

Example 1:

Input:
      1
     / \
    2   3
   / \ / \
  4  5 6  7

Output:
      1 -> null
     / \
    2 -> 3 -> null
   / \ / \
  4  5 6  7 -> null

Explanation: The nextRight pointers are populated such that 1 points to null, 2 points to 3, 3 points to null, 4 points to 5, 5 points to 6, 6 points to 7, and 7 points to null.

Example 2:

Input:
      1
     / \
    2   3

Output:
      1 -> null
     / \
    2 -> 3 -> null

Explanation: The nextRight pointers are populated such that 1 points to null, 2 points to 3, and 3 points to null.

Example 3: (Single Node)

Input:
      1

Output:
      1 -> null

Explanation: The single node's nextRight pointer is set to null.

Constraints

• The tree is guaranteed to be a perfect binary tree.
• The number of nodes in the tree will be between 1 and 10000.
• The values of the nodes are not relevant to the solution; only the structure and pointer manipulation matter.
• The solution should have a time complexity of O(N), where N is the number of nodes in the tree.
• The solution should have a space complexity of O(1) (excluding the space used by the tree itself).

Notes

A level-order traversal approach is generally effective for this problem. Consider how you can iterate through the tree level by level, maintaining a pointer to the "head" of each level. You can use the nextRight pointer of the last node in a level to find the head of the next level. Think about how to update the nextRight pointers while traversing each level. The perfect binary tree property simplifies the logic significantly.