Binary Tree Zigzag Level Order Traversal

Given the root of a binary tree, return the level order traversal in a zigzag manner. This means traversing each level from left to right, then right to left, and repeating this pattern for each subsequent level. This problem is useful for understanding breadth-first search and manipulating tree structures in a specific order.

Problem Description

You are given the root of a binary tree. Your task is to perform a level order traversal of the tree, but with a "zigzag" pattern. This means that the first level should be traversed from left to right, the second level from right to left, the third level from left to right, and so on. The output should be a list (or array) containing the values of the nodes in the zigzag order.

Key Requirements:

• The traversal should be level-by-level.
• The direction of traversal should alternate between left-to-right and right-to-left for each level.
• The output should be a list of the node values in the order they are visited.

Expected Behavior:

The function should take the root of a binary tree as input and return a list of integers representing the zigzag level order traversal. If the input tree is empty (root is null), the function should return an empty list.

Edge Cases to Consider:

• Empty tree (root is null).
• Tree with only one node.
• Unbalanced tree.
• Tree with varying depths.

Examples

Example 1:

Input: [3,9,20,null,null,15,7]  (Represents the tree:
                                     3
                                    / \
                                   9   20
                                    \  / \
                                    15 7
                                   )
Output: [3,9,20,15,7]
Explanation: The first level (3) is traversed from left to right. The second level (9, 20) is traversed from right to left. The third level (15, 7) is traversed from left to right.

Example 2:

Input: [1]
Output: [1]
Explanation: A tree with only one node is traversed in a single level from left to right (which is just the node itself).

Example 3:

Input: [] (Empty tree)
Output: []
Explanation: An empty tree results in an empty output 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 (i.e., the maximum number of nodes at any level).

Notes

Consider using a queue to perform the level order traversal. Keep track of the level number and alternate the order of traversal based on whether the level is even or odd. You can use a boolean variable to toggle the direction of traversal. Remember to handle the edge case of an empty tree. Think about how to efficiently determine the width of each level.