Zigzag Level Order Traversal in DSA Typescript - Execution Trace

Concept Flow - Zigzag Level Order Traversal

Start at root node

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Initialize queue with root

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While queue not empty

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Process all nodes at current level

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Collect node values in order

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If level is even: left to right

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If level is odd: right to left

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Add children of current level nodes to queue

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Increase level count

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Repeat until queue empty

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Return zigzag order list

Start from the root, process nodes level by level using a queue, alternate the order of values collected at each level to create a zigzag pattern.

Execution Sample

DSA Typescript

function zigzagLevelOrder(root: TreeNode | null): number[][] {
  if (!root) return [];
  const result: number[][] = [];
  const queue: TreeNode[] = [root];
  let level = 0;
  while (queue.length) {
    const size = queue.length;
    const currentLevel: number[] = [];
    for (let i = 0; i < size; i++) {
      const node = queue.shift()!;
      if (level % 2 === 0) currentLevel.push(node.val);
      else currentLevel.unshift(node.val);
      if (node.left) queue.push(node.left);
      if (node.right) queue.push(node.right);
    }
    result.push(currentLevel);
    level++;
  }
  return result;
}

This code traverses a binary tree level by level, collecting node values in zigzag order by alternating insertion direction each level.

Execution Table

Step	Operation	Nodes in Queue	Level	Current Level Nodes Processed	Current Level Values	Queue After Processing	Visual State
1	Initialize queue with root (1)	[1]	0	0/1	[]	[1]	Level 0: []
2	Process node 1	[]	0	1/1	[1]	[2,3]	Level 0: [1]
3	Add current level values to result	[2,3]	0	1/1	[1]	[2,3]	Result: [[1]]
4	Increase level to 1	[2,3]	1	0/2	[]	[2,3]	Level 1: []
5	Process node 2	[3]	1	1/2	[2]	[3,4,5]	Level 1: [2] (insert at front)
6	Process node 3	[4,5]	1	2/2	[3,2]	[4,5,6,7]	Level 1: [3,2] (insert at front)
7	Add current level values to result	[4,5,6,7]	1	2/2	[3,2]	[4,5,6,7]	Result: [[1],[3,2]]
8	Increase level to 2	[4,5,6,7]	2	0/4	[]	[4,5,6,7]	Level 2: []
9	Process node 4	[5,6,7]	2	1/4	[4]	[5,6,7]	Level 2: [4]
10	Process node 5	[6,7]	2	2/4	[4,5]	[6,7]	Level 2: [4,5]
11	Process node 6	[7]	2	3/4	[4,5,6]	[7]	Level 2: [4,5,6]
12	Process node 7	[]	2	4/4	[4,5,6,7]	[]	Level 2: [4,5,6,7]
13	Add current level values to result	[]	2	4/4	[4,5,6,7]	[]	Result: [[1],[3,2],[4,5,6,7]]
14	Queue empty, end traversal	[]	3	0/0	[]	[]	Traversal complete

💡 Queue is empty, all levels processed

Variable Tracker

Variable	Start	After Step 2	After Step 6	After Step 12	Final
queue	[1]	[2,3]	[4,5,6,7]	[]	[]
level	0	0	1	2	3
currentLevel	[]	[1]	[3,2]	[4,5,6,7]	[]
result	[]	[]	[[1]]	[[1],[3,2]]	[[1],[3,2],[4,5,6,7]]

Key Moments - 3 Insights

Why do we use unshift (insert at front) on odd levels instead of push?

Because on odd levels we want to reverse the order of node values to create the zigzag pattern. This is shown in execution_table rows 5 and 6 where values are inserted at the front, reversing their order.

Why do we process all nodes currently in the queue before increasing the level?

Because each level consists of all nodes currently in the queue at the start of the loop iteration. This ensures we collect values level by level, as seen in execution_table rows 2-3 and 5-7.

What happens if the tree is empty (root is null)?

The function returns an empty array immediately, as shown in the code sample line 2: if (!root) return []. No traversal happens.

Visual Quiz - 3 Questions

Look at the execution_table at step 6, what is the order of current level values?

A [2, 3]

B [1]

C [3, 2]

D [4, 5, 6, 7]

💡 Hint

Check the 'Current Level Values' column at step 6 in execution_table

At which step does the queue become empty, ending the traversal?

A Step 12

B Step 14

C Step 13

D Step 10

💡 Hint

Look for the step where 'Queue' column is empty and 'Traversal complete' in Visual State

If we changed the code to always push node values (no unshift), how would the result change?

A All levels would be left to right order

B All levels would be right to left order

C The traversal would stop early

D The queue would never empty

💡 Hint

Refer to key_moments about why unshift is used on odd levels

Concept Snapshot

Zigzag Level Order Traversal:
- Use a queue to traverse tree level by level
- For even levels, append node values left to right
- For odd levels, insert node values right to left (using unshift)
- Add children to queue for next level
- Repeat until queue empty
- Return list of levels with zigzag order

Full Transcript

Zigzag Level Order Traversal visits nodes of a binary tree level by level, but alternates the order of values collected at each level to create a zigzag pattern. We start with the root node in a queue. While the queue is not empty, we process all nodes currently in the queue as one level. For even levels, we add node values to the current level list from left to right. For odd levels, we insert node values at the front to reverse the order. After processing a level, we add all children of nodes to the queue for the next level. We repeat this until the queue is empty. The final result is a list of lists, each representing a level's node values in zigzag order.