Zigzag Level Order Traversal in DSA C++ - Time & Space Complexity

Time Complexity: Zigzag Level Order Traversal

O(n)

Understanding Time Complexity

We want to understand how the time needed to traverse a tree in zigzag order changes as the tree grows.

Specifically, how does the number of nodes affect the work done?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

vector> zigzagLevelOrder(TreeNode* root) {
    vector> result;
    if (!root) return result;
    queue q; q.push(root);
    bool leftToRight = true;
    while (!q.empty()) {
        int size = q.size();
        vector level(size);
        for (int i = 0; i < size; ++i) {
            TreeNode* node = q.front(); q.pop();
            int index = leftToRight ? i : (size - 1 - i);
            level[index] = node->val;
            if (node->left) q.push(node->left);
            if (node->right) q.push(node->right);
        }
        leftToRight = !leftToRight;
        result.push_back(level);
    }
    return result;
}
    

This code visits each node level by level, alternating the order of values collected to create a zigzag pattern.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Visiting each node once in the tree.
• How many times: Exactly once per node, inside the while loop and for loop combined.

How Execution Grows With Input

As the number of nodes (n) increases, the code visits each node once, so the work grows directly with n.

Input Size (n)	Approx. Operations
10	About 10 visits
100	About 100 visits
1000	About 1000 visits

Pattern observation: The work grows linearly as the tree size grows.

Final Time Complexity

Time Complexity: O(n)

This means the time needed grows directly in proportion to the number of nodes in the tree.

Common Mistake

[X] Wrong: "Because of the zigzag pattern, the traversal takes more than linear time."

[OK] Correct: The zigzag only changes the order of values collected, but each node is still visited once, so the time stays linear.

Interview Connect

Understanding this traversal helps you show you can handle tree traversals with order changes, a common interview skill.

Self-Check

"What if we used a depth-first search instead of breadth-first search for zigzag traversal? How would the time complexity change?"