• Expected Output: [[1], [2, 3, 4], [5, 6]]
• Justification: The root node 1 is at level 0. Nodes 2, 3, and 4 are the children of 1 and are at level 1. Nodes 5 and 6 are the children of 2, and at level 3.

Example 2

• Input: root = [7, null, 3, 8, 5, null, 2, 9, null, 6, null, 1, 4, 10]

• Expected Output: [[7], [3, 8, 5], [2, 9, 6, 1, 4, 10]]
• Justification: The root node 7 is at level 0. Nodes 3, 8, and 5 are its children at level 1. Nodes 2, 9, 6, 1, 4, and 10 are at level 2.

Example 3

• Input: root = [10, null, 15, 12, null, 20, null, 25, null, 30, 40]

• Expected Output: [[10], [15, 12], [20, 25], [30, 40]]
• Justification: The root node 10 is at level 0. Nodes 15 and 12 are its children at level 1. Node 20 and 25 are at level 2. Nodes 30, and 40 are at level 3.

Constraints:

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

Solution

To solve this problem, we use a queue-based approach to perform a level order traversal of the n-ary tree. The main idea is to process all nodes level by level, starting from the root. We use a queue to keep track of nodes at each level. At each step, we remove nodes from the queue, record their values, and add their children to the queue. This ensures that we traverse all nodes at the current level before moving to the next.

This approach is effective because it processes each node exactly once, which makes it efficient with a time complexity of O(N), where N is the total number of nodes in the tree. The use of a queue helps manage nodes level by level, ensuring that the output is correctly grouped. By storing nodes of each level in a separate list, we maintain the order of traversal and construct the desired output format.

Step-by-Step Algorithm

1. Initialize Result and Queue:

   • Create an empty list result to store the final output.
   • If root is null, return the empty result.
   • Initialize a queue and add the root node to it.

2. Level Order Traversal:

   • While the queue is not empty:
     • Determine the number of nodes at the current level (size).
     • Create an empty list level for the current level values.
     • For each node at the current level:
       • Remove the node from the queue and add its value to level.
       • Add all children of the node to the queue.
     • Add level to the result.

3. Return Result:

   • Return the result containing all level values.

Algorithm Walkthrough

For the input root = [1, null, 2, 3, 4, null, 5, 6]:

1. Initialize:
   Start by creating an empty list result = [] to store the output and a queue initialized with the root node: queue = [1].

2. First Level:

   • The size of the current level is size = 1 (only the root node).
   • Create an empty list for this level: level = [].
   • Dequeue the first node, 1, from the queue, and add its value to level: level = [1].
   • Enqueue its children, 2, 3, 4, into the queue: queue = [2, 3, 4].
   • Add the level list to the result: result = [[1]].

3. Second Level:

   • The size of the current level is size = 3 (nodes 2, 3, 4).
   • Create an empty list for this level: level = [].
   • Dequeue node 2 from the queue, add its value to level: level = [2], and enqueue its children 5, 6: queue = [3, 4, 5, 6].
   • Dequeue node 3, add its value to level: level = [2, 3] (node 3 has no children).
   • Dequeue node 4, add its value to level: level = [2, 3, 4] (node 4 has no children).
   • Add the level list to the result: result = [[1], [2, 3, 4]].

4. Third Level:

   • The size of the current level is size = 2 (nodes 5, 6).
   • Create an empty list for this level: level = [].
   • Dequeue node 5 from the queue, add its value to level: level = [5] (node 5 has no children).
   • Dequeue node 6, add its value to level: level = [5, 6] (node 6 has no children).
   • Add the level list to the result: result = [[1], [2, 3, 4], [5, 6]].

5. Completion:

   • The queue is now empty, which means all levels have been processed.
   • Return the result: [[1], [2, 3, 4], [5, 6]].

Code