Boundary Traversal of Binary Tree in DSA Java - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the Boundary Traversal of a binary tree?

Boundary Traversal is a way to visit all the nodes on the boundary of a binary tree. It includes the left boundary (top to bottom), all leaf nodes (left to right), and the right boundary (bottom to top).

beginner

Which nodes are included in the left boundary during boundary traversal?

The left boundary includes all nodes on the path from the root to the left-most leaf, excluding leaf nodes themselves if they are counted separately.

beginner

How do you identify leaf nodes in a binary tree?

Leaf nodes are nodes that do not have any children (no left or right child). They are the bottom-most nodes in the tree.

intermediate

Why is the right boundary added in reverse order during boundary traversal?

The right boundary is added from bottom to top to maintain the correct order of boundary nodes when traversing clockwise around the tree.

intermediate

What is the time complexity of boundary traversal in a binary tree?

The time complexity is O(n), where n is the number of nodes, because each node is visited at most once during the traversal.

Which of the following is NOT part of the boundary traversal of a binary tree?

A All leaf nodes

B All internal nodes

C Right boundary nodes

D Left boundary nodes

Boundary traversal includes left boundary, leaf nodes, and right boundary nodes, but not all internal nodes.

In boundary traversal, how are leaf nodes collected?

A From left to right across the entire tree

B Only from the right subtree

C From right to left across the entire tree

D Only from the left subtree

Leaf nodes are collected from left to right across the entire tree to maintain the boundary order.

What is the first node printed in boundary traversal?

A Right-most leaf node

B Left-most leaf node

C Root node

D Right boundary node

The root node is always the first node in the boundary traversal.

How is the right boundary added to the result in boundary traversal?

A Bottom to top

B Left to right

C Top to bottom

D Random order

The right boundary is added from bottom to top to maintain the correct clockwise order.

If a node is both a leaf and part of the left boundary, how is it handled in boundary traversal?

A Included twice

B Included only once as a left boundary node

C Excluded completely

D Included only once as a leaf node

Leaf nodes are included only once to avoid duplication, even if they appear in the left boundary.

Explain the steps to perform boundary traversal of a binary tree.

Think about visiting edges and leaves in a clockwise manner.

Describe how to avoid duplicate nodes when collecting boundary nodes in a binary tree.

Focus on how leaves can appear in multiple parts of the boundary.

Practice

1. What is the correct order of nodes visited in a boundary traversal of a binary tree?

easy

A. Root, leaves (left to right), left boundary (top-down), right boundary (bottom-up)

B. Leaves (left to right), root, left boundary (top-down), right boundary (bottom-up)

C. Root, left boundary (top-down), leaves (left to right), right boundary (bottom-up)

D. Left boundary (top-down), root, right boundary (bottom-up), leaves (left to right)

Solution

1. Step 1: Understand boundary traversal parts

   Boundary traversal visits root, then left boundary top-down, then leaves left to right, then right boundary bottom-up.

2. Step 2: Arrange traversal order

   Root is first, left boundary next, leaves after that, and right boundary last in reverse order.

3. Final Answer:

   Root, left boundary (top-down), leaves (left to right), right boundary (bottom-up) -> Option C

4. Quick Check:

   Boundary traversal order = Root + Left + Leaves + Right [OK]

Hint: Remember: Root, Left boundary, Leaves, Right boundary [OK]

Common Mistakes:

• Mixing order of leaves and boundaries
• Visiting right boundary top-down instead of bottom-up
• Skipping root node

2. Which of the following Java method signatures is correct for a function performing boundary traversal on a binary tree node?

easy

A. public void boundaryTraversal() Node root

B. void boundaryTraversal(Node root) public

C. public boundaryTraversal(Node root) void

D. public void boundaryTraversal(Node root)

Solution

1. Step 1: Recall Java method syntax

   Java methods start with access modifier, then return type, then method name and parameters.

2. Step 2: Match correct syntax

   public void boundaryTraversal(Node root) matches: public void boundaryTraversal(Node root). Others have wrong order or missing parts.

3. Final Answer:

   public void boundaryTraversal(Node root) -> Option D

4. Quick Check:

   Access modifier + return type + method name + parameters [OK]

Hint: Java method = access modifier + return type + name + params [OK]

Common Mistakes:

• Placing return type after method name
• Missing access modifier
• Incorrect parameter placement

3. Given the binary tree below, what is the output of the boundary traversal?

        1
       / \
      2   3
     / \   \
    4   5   6
       / \  /
      7  8 9

medium

A. [1, 2, 4, 7, 8, 9, 6]

B. [1, 2, 4, 7, 8, 9, 6, 3]

C. [1, 2, 4, 5, 7, 8, 9, 6, 3]

D. [1, 2, 4, 7, 8, 9, 3, 6]

Solution

1. Step 1: Identify boundary nodes

   Root: 1; Left boundary top-down: 2 (excluding leaf 4); Leaves left to right: 4,7,8,9; Right boundary bottom-up: 6,3 (excluding leaves).

2. Step 2: Combine nodes without duplicates

   Boundary traversal: 1 (root), 2 (left boundary), 4,7,8,9 (leaves), 6,3 (right boundary).

3. Final Answer:

   [1, 2, 4, 7, 8, 9, 6, 3] -> Option B

4. Quick Check:

   Boundary traversal output = [1,2,4,7,8,9,6,3] [OK]

Hint: Leaves included once; right boundary reversed; avoid duplicates [OK]

Common Mistakes:

• Including leaf nodes twice
• Wrong order of right boundary nodes
• Missing leaf nodes

4. Consider this Java method snippet for boundary traversal:

void printLeftBoundary(Node node) {
  if (node == null) return;
  System.out.print(node.data + " ");
  if (node.left != null) {
    printLeftBoundary(node.left);
  } else if (node.right != null) {
    printLeftBoundary(node.right);
  }
}

What is the bug in this code?

medium

A. It prints leaf nodes which should be excluded in left boundary

B. It does not print the root node

C. It causes infinite recursion on leaf nodes

D. It prints right boundary nodes instead of left

Solution

1. Step 1: Analyze leaf node printing

   The code prints node data before checking for children, thus printing leaf nodes as well.

2. Step 2: Identify leaf node exclusion missing

   Leaf nodes should not be printed in left boundary function, but this code prints them unconditionally after null check.

3. Final Answer:

   It prints leaf nodes which should be excluded in left boundary -> Option A

4. Quick Check:

   Left boundary excludes leaves, code prints them [OK]

Hint: Exclude leaf nodes in boundary functions to avoid duplicates [OK]

Common Mistakes:

• Not checking if node is leaf before printing
• Confusing left and right boundary logic
• Missing base case for null nodes

5. You have a binary tree where some nodes have only right children, and leaves are only on the rightmost path. How should you modify the boundary traversal algorithm to correctly print the boundary without duplicates?

hard

A. Skip printing left boundary if no left child; print leaves only once; print right boundary bottom-up excluding leaves

B. Print all nodes in preorder to cover all boundaries and leaves

C. Print left boundary top-down including leaves; skip right boundary

D. Print leaves first, then left and right boundaries in any order

Solution

1. Step 1: Understand tree structure

   Since leaves are only on rightmost path and some nodes have only right children, left boundary may be missing or partial.

2. Step 2: Modify traversal rules

   Skip left boundary if no left child; print leaves once; print right boundary bottom-up excluding leaves to avoid duplicates.

3. Step 3: Combine for correct boundary

   This ensures no duplicates and correct order for such skewed trees.

4. Final Answer:

   Skip printing left boundary if no left child; print leaves only once; print right boundary bottom-up excluding leaves -> Option A

5. Quick Check:

   Handle missing left boundary and leaf duplicates carefully [OK]

Hint: Skip missing boundaries; print leaves once; reverse right boundary [OK]

Common Mistakes:

• Printing leaves multiple times
• Ignoring missing left boundary
• Printing right boundary top-down causing wrong order