Binary Tree Level Order Traversal

Given the root of a binary tree, return a list of lists of integers, where each inner list represents the nodes at a specific level of the tree, traversed from left to right. This problem is a fundamental tree traversal algorithm with applications in various areas like graph analysis, data visualization, and understanding hierarchical data structures.

Problem Description

You are tasked with implementing a function that performs a level order traversal of a binary tree. Level order traversal means visiting all nodes level by level, starting from the root (level 0), then all nodes at level 1, then level 2, and so on. The nodes at each level should be collected into a separate list, and the final result should be a list of these lists.

What needs to be achieved:

• Traverse the binary tree in level order.
• Collect the values of all nodes at each level into a separate list.
• Return a list containing these lists, representing the level order traversal.

Key Requirements:

• The traversal should be from left to right within each level.
• The root node is considered to be at level 0.
• Handle empty trees gracefully.

Expected Behavior:

The function should return an empty list if the input tree is empty (root is null/None). Otherwise, it should return a list of lists, where each inner list contains the values of the nodes at a particular level.

Edge Cases to Consider:

• Empty tree (root is null/None).
• Tree with only one node.
• Unbalanced trees (trees where the left and right subtrees have significantly different depths).
• Trees with varying node values.

Examples

Example 1:

Input: root = [3,9,20,null,null,15,7]
       (A binary tree represented as a list where null indicates a missing node)
Output: [[3],[9,20],[15,7]]
Explanation: The tree has three levels. Level 0 contains only the root node (3). Level 1 contains nodes 9 and 20. Level 2 contains nodes 15 and 7.

Example 2:

Input: root = [1,2,3,4,5,6,7]
Output: [[1],[2,3],[4,5,6,7]]
Explanation: The tree has three levels. Level 0 contains the root node (1). Level 1 contains nodes 2 and 3. Level 2 contains nodes 4, 5, 6, and 7.

Example 3:

Input: root = null
Output: []
Explanation: The tree is empty, so the output is an empty list.

Constraints

• The number of nodes in the tree can range from 0 to 1000.
• The values of the nodes are integers.
• The tree is a binary tree (each node has at most two children).
• 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(W), where W is the maximum width of the tree (maximum number of nodes at any level).

Notes

Consider using a queue to efficiently manage the nodes to be visited at each level. The queue will help you process nodes level by level. Think about how to determine the next level to process and how to add the children of the current level's nodes to the queue. Remember to handle null nodes appropriately to avoid errors.