N-ary Tree Level Order Traversal

Problem Statement

In the problem at hand, we need to perform a level order traversal on an n-ary tree, where each node can have more than two children. Level order traversal, also known as breadth-first traversal, involves visiting all the nodes at the present depth prior to moving on to nodes at the next level of depth. The given n-ary trees are described using a serialization method where children of a node are denoted by subsequent values followed by a 'null' value indicating the end of a particular level or branch. The challenge thus revolves around correctly parsing this structure and retrieving values in the specified order.

Examples

Example 1

Input:

root = [1,null,3,2,4,null,5,6]

Output:

[[1],[3,2,4],[5,6]]

Example 2

Input:

root = [1,null,2,3,4,5,null,null,6,7,null,8,null,9,10,null,null,11,null,12,null,13,null,null,14]

Output:

[[1],[2,3,4,5],[6,7,8,9,10],[11,12,13],[14]]

Constraints

• The height of the n-ary tree is less than or equal to 1000
• The total number of nodes is between [0, 104]

Approach and Intuition

1. Interpret the serialized n-ary tree structure:

   • The serialization format splits nodes and their respective children by a 'null' value. This formatting helps indicate transitions between levels of the n-ary tree.

2. Implement BFS (Breadth-First Search) using a queue:

   • A queue can be utilized effectively here for visiting nodes layer by layer. Starting from the root node, enqueue it.
   • Process each node by dequeuing it, recording its value, and enqueueing all its children. This processing is continued until the queue is empty.
   • The main loop runs while the queue has elements, ensuring that each level is completely processed before moving to the next.

3. Handle edge cases:

   • The tree could be empty, represented by an empty serialization, in which case the output should be an empty list as well.

Based on the problem description and the constraints provided (an n-ary tree with the height of up to 1000 and up to 10^4 nodes), the proposed breadth-first search approach should handle the typical cases efficiently, considering modern compute capacities.

Solutions

class Solution {
    
    private List<List<Integer>> levels = new ArrayList<>();
    
    public List<List<Integer>> levelOrder(Node root) {
        if (root != null) {
            processNode(root, 0);
        }
        return levels;
    }
    
    private void processNode(Node node, int depth) {
        if (levels.size() <= depth) {
            levels.add(new ArrayList<>());
        }
        levels.get(depth).add(node.val);
        for (Node child : node.children) {
            processNode(child, depth + 1);
        }
    }
}