Binary Tree Zigzag Level Order Traversal
Binary Tree Zigzag Level Order Traversal is a variation of standard level order traversal that tests whether you understand how traversal order can be controlled without changing the structure of the tree.
You are given the root of a binary tree. Your task is to return the node values level by level, but with a twist:
- The direction of traversal alternates at each level.
- The first level is read from left to right.
- The second level is read from right to left.
- The third level goes left to right again, and so on.
This alternating pattern creates a zigzag, or spiral, traversal of the tree.
The output is typically a list of lists, where each inner list contains the values of one level in the required order.
Why this problem is not just a small tweak
At first, this looks like a minor variation of breadth-first search. Many candidates try to modify BFS on the fly by reversing lists or inserting values at the front.
That can work, but without a clear plan, the solution becomes messy and inefficient.
Interviewers use this problem to see whether you can adapt a standard traversal cleanly while maintaining readable logic and correct ordering.
Want to explore more coding problem solutions? Check out the Shortest Path in Binary Matrix and Binary Search Tree Iterator.
The core traversal idea
The foundation of the solution is still level order traversal, also known as breadth-first search.
You process the tree one level at a time using a queue. The queue ensures nodes are visited in the correct structural order.
The only difference from normal level order traversal is how you record values for each level.
You keep a simple flag that tracks the current direction. When the flag indicates left to right, you record values in normal order. When it indicates right to left, you record values in reverse order.
The traversal of the tree itself does not change. Only the way values are collected changes.
How zigzag ordering is handled cleanly
For each level, you know how many nodes belong to that level by checking the queue size at the start of the loop.
You then process exactly that many nodes, removing them from the queue and adding their children to the queue for the next level.
As you collect values, you place them into a temporary list for the current level.
If the current direction is left to right, you append values normally.
If the direction is right to left, you insert values at the beginning of the list or fill the list from the end toward the front.
After finishing the level, you flip the direction flag and add the completed list to the final result.
This keeps the logic structured and avoids reversing entire lists unnecessarily.
Why this approach works well
The tree is traversed exactly once, and every node is processed in constant time.
The zigzag behavior is controlled entirely by a small piece of state, not by complex pointer manipulation or multiple data structures.
This separation of concerns, traversal versus ordering, is what makes the solution easy to reason about and easy to explain.
Performance in simple terms
The traversal visits each node once, so the time complexity is linear in the number of nodes.
Extra space is used for the queue and the output structure, both of which scale with the size of the tree.
This is optimal for a level order traversal problem.
Common pitfalls to avoid
A frequent mistake is to reverse the list for each level after building it, which adds unnecessary overhead.
Another is forgetting to toggle the direction flag at the right time, which breaks the zigzag pattern.
Some candidates also try to change the order in which children are enqueued. That often leads to confusing logic and subtle bugs.
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