Populating Next Right Pointers in Each Node II

This challenge focuses on manipulating a multi-level linked list where each node has a next, child, and next_right pointer. The goal is to populate the next_right pointers to form a perfect binary tree structure, connecting nodes at the same level, even when the tree isn't a binary tree (i.e., nodes can have more than two children). This problem is useful for efficiently traversing and processing multi-level data structures.

Problem Description

You are given a multi-level linked list where each node has three pointers: next (points to the next node at the same level), child (points to the first child node), and next_right (points to the next node at the same level, which needs to be populated). Your task is to populate the next_right pointers for all nodes in the multi-level linked list such that the resulting structure represents a perfect binary tree. The next pointers should remain unchanged.

Specifically, you need to traverse the multi-level linked list level by level. For each level, connect the next_right pointers of the nodes in that level in the order they appear in the next pointers. If a node has a child, the child pointer should not be modified.

Key Requirements:

• Modify the next_right pointers in-place.
• The next pointers should remain unchanged.
• The resulting structure should be a perfect binary tree, where each node at a given level points to its immediate right neighbor via the next_right pointer.
• The last node at each level should have its next_right pointer set to null.

Expected Behavior:

The function should take the root node of the multi-level linked list as input and modify the next_right pointers in-place. The function should return the root node of the modified list.

Edge Cases to Consider:

• Empty list (root is null).
• Single-node list (root is the only node).
• Levels with varying numbers of nodes.
• Nodes with multiple children.
• The last node on a level.

Examples

Example 1:

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

(Represented as a linked list structure, but visualized as a tree for clarity)

Output:

     1 -> null
    /  \
   2 -> 3 -> null
  /  \    \
 4 -> 5    6 -> null

Explanation: The nodes 1, 2, and 3 are connected at the first level. Nodes 4, 5, and 6 are connected at the second level. The last nodes (3 and 6) have their next_right pointers set to null.

Example 2:

Input:
    1
   /
  2
 / \
3   4
 \
  5

Output:

    1 -> null
   /
  2 -> null
 / \
3   4 -> null
 \
  5 -> null

Explanation: The nodes 1 and 2 are connected at the first level. Nodes 3 and 4 are connected at the second level. Node 5 is the last node at its level and has its next_right pointer set to null.

Example 3: (Edge Case - Empty List)

Input: null
Output: null
Explanation: If the input is null, return null.

Constraints

• The number of nodes in the multi-level linked list can range from 0 to 1000.
• Each node has next, child, and next_right pointers.
• The tree is not necessarily a binary tree; nodes can have more than two children.
• The solution should have a time complexity of O(N), where N is the number of nodes in the multi-level linked list.
• The solution should have a space complexity of O(1) (constant space). No additional data structures that scale with the input size are allowed.

Notes

• A level-order traversal (e.g., using a queue) is a common approach to solve this problem.
• Keep track of the last node visited at each level. The next node visited at that level should have its next_right pointer set to the last node.
• When moving to the next level, reset the last pointer to null.
• The child pointers should not be modified. The focus is solely on populating the next_right pointers.
• Consider how to handle the last node at each level to ensure its next_right pointer is set to null.