Boundary Traversal of Binary Tree in DSA Go - Execution Trace

Concept Flow - Boundary Traversal of Binary Tree

Start at root

↓

Add root to boundary

↓

Traverse left boundary down

↓

Add leaf nodes from left to right

↓

Traverse right boundary up

↓

Combine all parts for final boundary

Start from root, add left boundary top-down, then leaves left to right, then right boundary bottom-up to get full boundary.

Execution Sample

DSA Go

func BoundaryTraversal(root *Node) []int {
  if root == nil { return []int{} }
  res := []int{root.Val}
  addLeftBoundary(root.Left, &res)
  addLeaves(root.Left, &res)
  addLeaves(root.Right, &res)
  addRightBoundary(root.Right, &res)
  return res
}

This code collects the boundary nodes of a binary tree in anti-clockwise order.

Execution Table

Step	Operation	Node Visited	Pointer Changes	Visual State
1	Start at root	1	root points to Node(1)	Boundary: [1]
2	Add left boundary top-down	2	current moves down left boundary	Boundary: [1, 2, 4]
3	Add leaf nodes left subtree	4, 7	traverse leaves	Boundary: [1, 2, 4, 7]
4	Add leaf nodes right subtree	8, 9	traverse leaves	Boundary: [1, 2, 4, 7, 8, 9]
5	Add right boundary bottom-up	3, 6	current moves up right boundary	Boundary: [1, 2, 4, 7, 8, 9, 6, 3]
6	Traversal complete	nil	none	Final Boundary: [1, 2, 4, 7, 8, 9, 6, 3]

💡 All boundary nodes visited in anti-clockwise order, traversal ends.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 5	Final
res (boundary list)	[]	[1, 2, 4]	[1, 2, 4, 7]	[1, 2, 4, 7, 8, 9]	[1, 2, 4, 7, 8, 9, 6, 3]	[1, 2, 4, 7, 8, 9, 6, 3]
current (left boundary)	Node(2)	Node(4)	nil	nil	nil	nil
current (right boundary)	Node(3)	Node(6)	nil	nil	nil	nil

Key Moments - 3 Insights

Why do we add leaf nodes separately after left boundary traversal?

Left boundary traversal adds only non-leaf nodes on the left edge (see Step 2). Leaf nodes are added separately (Steps 3 and 4) to avoid duplicates and to include leaves from both left and right subtrees.

Why is the right boundary added bottom-up?

Right boundary nodes are added bottom-up (Step 5) to maintain anti-clockwise order. Adding them top-down would reverse the boundary order.

What happens if the root has no left or right child?

If root has no left or right child, left and right boundary traversals add nothing, and only root and leaf nodes (which may be root itself) are added (Step 1 and leaf steps).

Visual Quiz - 3 Questions

Look at the execution table, what is the boundary list after Step 3?

A [1, 2, 4, 7]

B [1, 2, 4]

C [1, 2, 4, 7, 8]

D [1, 2]

💡 Hint

Check the 'Visual State' column at Step 3 in the execution_table.

At which step does the right boundary get added to the boundary list?

A Step 2

B Step 5

C Step 4

D Step 3

💡 Hint

Look for 'Add right boundary bottom-up' operation in the execution_table.

If the tree had no right subtree, how would the final boundary list change?

A It would exclude nodes 2 and 4

B It would include extra leaf nodes from right

C It would exclude nodes 3 and 6

D It would be empty

💡 Hint

Refer to variable_tracker and execution_table steps involving right boundary nodes.

Concept Snapshot

Boundary Traversal of Binary Tree:
- Start at root, add root value
- Traverse left boundary top-down (exclude leaves)
- Add all leaf nodes left to right
- Traverse right boundary bottom-up (exclude leaves)
- Combine all for anti-clockwise boundary
- Avoid duplicates by separating leaves

Full Transcript

Boundary traversal of a binary tree collects nodes on the outer edge in anti-clockwise order. We start at the root, add it to the boundary list. Then we traverse the left boundary from top to bottom, adding only non-leaf nodes. Next, we add all leaf nodes from left subtree and right subtree in left to right order. Finally, we traverse the right boundary from bottom to top, adding non-leaf nodes. This order ensures the boundary is collected without duplicates and in correct anti-clockwise order. The execution table shows each step with nodes visited and how the boundary list grows. Key moments clarify why leaves are added separately and why right boundary is added bottom-up. The visual quiz tests understanding of these steps and the final boundary list.