Boundary Traversal of Binary Tree in DSA Javascript - Execution Trace

Concept Flow - Boundary Traversal of Binary Tree

Start at root

↓

Add root to boundary

↓

Traverse left boundary (top-down)

↓

Traverse leaf nodes (left to right)

↓

Traverse right boundary (bottom-up)

↓

Combine all parts for boundary traversal

The traversal collects nodes from the left boundary top-down, then all leaf nodes left to right, and finally the right boundary bottom-up, starting from the root.

Execution Sample

DSA Javascript

function boundaryTraversal(root) {
  if (!root) return [];
  let result = [root.val];
  // left boundary
  // leaf nodes
  // right boundary
  return result;
}

This code outlines the steps to collect the boundary nodes of a binary tree in order.

Execution Table

Step	Operation	Nodes in Boundary List	Pointer Changes	Visual State
1	Start at root	[1]	root -> 1	1 / \ 2 3 / \ \ 4 5 6
2	Add left boundary (excluding leaves)	[1, 2]	current -> 2	1 / \ 2 3 / \ \ 4 5 6
3	Add leaf nodes (left to right)	[1, 2, 4, 5, 6]	leaf nodes visited: 4,5,6	1 / \ 2 3 / \ \ 4 5 6
4	Add right boundary (excluding leaves) bottom-up	[1, 2, 4, 5, 6, 3]	current -> 3	1 / \ 2 3 / \ \ 4 5 6
5	Traversal complete	[1, 2, 4, 5, 6, 3]	None	Final boundary: 1 -> 2 -> 4 -> 5 -> 6 -> 3

💡 All boundary nodes collected: left boundary, leaves, right boundary

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	Final
result	[]	[1, 2]	[1, 2, 4, 5, 6]	[1, 2, 4, 5, 6, 3]	[1, 2, 4, 5, 6, 3]
current (left boundary)	1	2	2	2	2
current (right boundary)	null	null	null	3	3

Key Moments - 3 Insights

Why do we exclude leaf nodes when adding left and right boundaries?

Because leaf nodes are added separately in the leaf traversal step to avoid duplicates, as shown in execution_table rows 2 and 3.

Why is the right boundary added in bottom-up order?

To maintain the correct boundary order, the right boundary nodes are collected top-down but added to the result in reverse (bottom-up), as seen in execution_table row 4.

What happens if the tree has only root node?

The traversal adds only the root node to the boundary list and stops, as shown in execution_table row 1.

Visual Quiz - 3 Questions

Look at the execution_table, what nodes are in the boundary list after step 3?

A [1, 2]

B [1, 2, 3]

C [1, 2, 4, 5, 6]

D [1, 3, 6]

💡 Hint

Check the 'Nodes in Boundary List' column at step 3 in execution_table.

At which step is the right boundary added to the boundary list?

A Step 4

B Step 3

C Step 2

D Step 5

💡 Hint

Look at the 'Operation' column in execution_table for when right boundary is added.

If the tree had no right subtree, how would the boundary list change after step 4?

A Right boundary nodes would be added as usual

B Right boundary nodes would be empty, so no change after step 4

C Left boundary nodes would be added again

D Leaf nodes would be skipped

💡 Hint

Refer to variable_tracker and execution_table steps for right boundary additions.

Concept Snapshot

Boundary Traversal of Binary Tree:
- Start at root, add root to result
- Traverse left boundary top-down (exclude leaves)
- Traverse all leaf nodes left to right
- Traverse right boundary bottom-up (exclude leaves)
- Combine all for final boundary list

Full Transcript

Boundary traversal collects nodes on the outer edge of a binary tree. It starts by adding the root node. Then it adds the left boundary nodes from top to bottom, excluding leaf nodes to avoid duplicates. Next, it adds all leaf nodes from left to right. Finally, it adds the right boundary nodes from bottom to top, again excluding leaves. This order ensures the boundary is traversed correctly without repeating nodes. The execution table shows each step with the nodes added and the tree state. The variable tracker follows the result list and pointers used. Key moments clarify why leaves are excluded in boundary traversals and why the right boundary is added in reverse order. The visual quiz tests understanding of these steps and their effects on the boundary list.