Boundary Traversal of Binary Tree in DSA Typescript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to check if a node is a leaf node.

DSA Typescript

function isLeaf(node: TreeNode | null): boolean {
  return node !== null && node.left === null && node.[1] === null;
}

Drag options to blanks, or click blank then click option'

Aright

Bparent

Cvalue

Ddata

Attempts:

3 left

💡 Hint

Common Mistakes

Checking only left child for null.

Using incorrect property names like 'value' or 'data'.

A leaf node has no left or right children, so both must be null.

2fill in blank

medium

Complete the code to traverse the left boundary excluding leaf nodes.

DSA Typescript

function addLeftBoundary(root: TreeNode | null, res: number[]): void {
  let curr = root?.left;
  while (curr !== null) {
    if (!isLeaf(curr)) res.push(curr.val);
    curr = curr.left !== null ? curr.left : curr.[1];
  }
}

Drag options to blanks, or click blank then click option'

Anext

Bparent

Cright

Dcurr.val

Attempts:

3 left

💡 Hint

Common Mistakes

Moving to parent or next node which is not part of boundary.

Using node value instead of node reference.

If left child is null, move to right child to continue left boundary traversal.

3fill in blank

hard

Fix the error in the code to add leaf nodes in left-to-right order.

DSA Typescript

function addLeaves(root: TreeNode | null, res: number[]): void {
  if (root === null) return;
  if (isLeaf(root)) {
    res.push(root.val);
    return;
  }
  addLeaves(root.[1], res);
  addLeaves(root.right, res);
}

Drag options to blanks, or click blank then click option'

Aright

Bleft

Cparent

Dnext

Attempts:

3 left

💡 Hint

Common Mistakes

Traversing right subtree before left subtree.

Using incorrect property names.

To add leaves in left-to-right order, traverse left subtree first, then right subtree.

4fill in blank

hard

Fill both blanks to add the right boundary nodes in bottom-up order excluding leaf nodes.

DSA Typescript

function addRightBoundary(root: TreeNode | null, res: number[]): void {
  let curr = root?.right;
  const stack: number[] = [];
  while (curr !== null) {
    if (!isLeaf(curr)) stack.push(curr.val);
    curr = curr.[1] !== null ? curr.[1] : curr.[2];
  }
  while (stack.length > 0) {
    res.push(stack.pop()!);
  }
}

Drag options to blanks, or click blank then click option'

Aright

Bleft

Cparent

Dnext

Attempts:

3 left

💡 Hint

Common Mistakes

Going left first instead of right.

Not using a stack to reverse order.

Traverse right boundary by going right if possible, else left child.

5fill in blank

hard

Fill all three blanks to complete the boundary traversal function.

DSA Typescript

function boundaryTraversal(root: TreeNode | null): number[] {
  const res: number[] = [];
  if (root === null) return res;
  if (!isLeaf(root)) res.push(root.val);
  addLeftBoundary(root, res);
  addLeaves(root, res);
  addRightBoundary(root, res);
  return res;
}

// Helper function to check leaf
function isLeaf(node: TreeNode | null): boolean {
  return node !== null && node.left === null && node.[1] === null;
}

// Add left boundary
function addLeftBoundary(root: TreeNode | null, res: number[]): void {
  let curr = root?.left;
  while (curr !== null) {
    if (!isLeaf(curr)) res.push(curr.val);
    curr = curr.left !== null ? curr.left : curr.[2];
  }
}

// Add leaves
function addLeaves(root: TreeNode | null, res: number[]): void {
  if (root === null) return;
  if (isLeaf(root)) {
    res.push(root.val);
    return;
  }
  addLeaves(root.left, res);
  addLeaves(root.right, res);
}

// Add right boundary
function addRightBoundary(root: TreeNode | null, res: number[]): void {
  let curr = root?.right;
  const stack: number[] = [];
  while (curr !== null) {
    if (!isLeaf(curr)) stack.push(curr.val);
    curr = curr.right !== null ? curr.right : curr.[3];
  }
  while (stack.length > 0) {
    res.push(stack.pop()!);
  }
}

Drag options to blanks, or click blank then click option'

Aright

Bleft

Cparent

Dnext

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing left and right child in traversal.

Incorrect leaf node check.

Leaf check uses right child; left boundary goes left then right; right boundary goes right then left.

Practice

1. What is the main purpose of Boundary Traversal in a binary tree?

easy

A. To print all leaf nodes only

B. To print all nodes on the boundary in anti-clockwise direction

C. To print nodes level by level

D. To print nodes in in-order traversal

Solution

1. Step 1: Understand boundary traversal definition

   Boundary traversal prints nodes on the edges of the tree, including left boundary, leaves, and right boundary.

2. Step 2: Identify traversal direction

   The traversal is done in anti-clockwise direction starting from root, left boundary, leaves, then right boundary.

3. Final Answer:

   To print all nodes on the boundary in anti-clockwise direction -> Option B

4. Quick Check:

   Boundary traversal = anti-clockwise boundary nodes [OK]

Hint: Boundary traversal prints edges anti-clockwise [OK]

Common Mistakes:

• Confusing boundary traversal with leaf node traversal
• Thinking it prints nodes level-wise
• Assuming it prints in-order nodes

2. Which of the following TypeScript function signatures correctly represents a function to perform boundary traversal of a binary tree?

easy

A. function boundaryTraversal(): number[]

B. function boundaryTraversal(root: TreeNode): void

C. function boundaryTraversal(root: TreeNode, result: number[]): void

D. function boundaryTraversal(root: TreeNode): number[]

Solution

1. Step 1: Analyze function purpose

   The function should take the root node and return an array of numbers representing boundary nodes.

2. Step 2: Check signatures

   function boundaryTraversal(root: TreeNode): number[] takes root and returns number array, matching expected usage. function boundaryTraversal(root: TreeNode): void returns void, so no output. function boundaryTraversal(root: TreeNode, result: number[]): void requires external array input, less common. function boundaryTraversal(): number[] has no input, so invalid.

3. Final Answer:

   function boundaryTraversal(root: TreeNode): number[] -> Option D

4. Quick Check:

   Function returns boundary nodes array [OK]

Hint: Function should return array of boundary nodes [OK]

Common Mistakes:

• Using void return type without output
• Missing root parameter
• Expecting external array input unnecessarily

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

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

medium

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

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

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

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

Solution

1. Step 1: Identify left boundary nodes

   Left boundary excluding leaves: 1, 2

2. Step 2: Identify leaf nodes left to right

   Leaves: 4, 7, 8, 9, 6

3. Step 3: Identify right boundary nodes bottom to top excluding leaves

   Right boundary: 3

4. Step 4: Combine in anti-clockwise order

   Boundary = left boundary + leaves (excluding duplicates) + right boundary = [1, 2, 4, 7, 8, 9, 6, 3]

5. Final Answer:

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

6. Quick Check:

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

Hint: Combine left boundary, leaves, right boundary anti-clockwise [OK]

Common Mistakes:

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

4. Consider the following TypeScript code snippet for boundary traversal. What is the bug?

function printBoundary(root: TreeNode | null) {
  if (!root) return;
  console.log(root.val);
  printLeftBoundary(root.left);
  printLeaves(root.left);
  printLeaves(root.right);
  printRightBoundary(root.right);
}

function printLeftBoundary(node: TreeNode | null) {
  if (!node || (!node.left && !node.right)) return;
  console.log(node.val);
  if (node.left) printLeftBoundary(node.left);
  else printLeftBoundary(node.right);
}

function printRightBoundary(node: TreeNode | null) {
  if (!node || (!node.left && !node.right)) return;
  if (node.right) printRightBoundary(node.right);
  else printRightBoundary(node.left);
  console.log(node.val);
}

medium

A. Left boundary includes leaf nodes which should be excluded

B. Root node is printed twice

C. Right boundary nodes are printed before recursive calls, causing wrong order

D. Leaves are printed twice because printLeaves is called on both left and right subtrees

Solution

1. Step 1: Analyze left boundary function

   printLeftBoundary prints node.val even if node is leaf, but leaves should be excluded from left boundary.

2. Step 2: Check leaf exclusion condition

   Condition (!node.left && !node.right) returns early, so leaves are excluded from printing in left boundary, so no bug here.

3. Step 3: Re-examine leaf printing calls

   printLeaves is called separately on left and right subtrees, so leaves are printed once only.

4. Step 4: Check right boundary printing order

   Right boundary prints after recursive calls, which is correct for bottom-up order.

5. Step 5: Identify actual bug

   Left boundary function prints node.val before recursive call, so leaf nodes on left boundary get printed twice: once in left boundary and once in leaves.

6. Final Answer:

   Left boundary includes leaf nodes which should be excluded -> Option A

7. Quick Check:

   Leaf nodes must not print in left boundary [OK]

Hint: Exclude leaves from left/right boundary printing [OK]

Common Mistakes:

• Printing leaves twice
• Printing right boundary in wrong order
• Printing root twice

5. You want to modify boundary traversal to print nodes in clockwise order starting from root. Which change is correct?

hard

A. Print root, then right boundary top-down, then leaves right to left, then left boundary bottom-up

B. Print root, then left boundary top-down, then leaves left to right, then right boundary bottom-up

C. Print root, then leaves left to right, then left boundary top-down, then right boundary bottom-up

D. Print root, then right boundary bottom-up, then leaves right to left, then left boundary top-down

Solution

1. Step 1: Understand clockwise boundary traversal order

   Clockwise traversal starts at root, then right boundary top-down, leaves right to left, then left boundary bottom-up.

2. Step 2: Match options with traversal order

   Print root, then right boundary top-down, then leaves right to left, then left boundary bottom-up matches this order exactly. Print root, then left boundary top-down, then leaves left to right, then right boundary bottom-up is anti-clockwise order. Options C and D mix orders incorrectly.

3. Final Answer:

   Print root, then right boundary top-down, then leaves right to left, then left boundary bottom-up -> Option A

4. Quick Check:

   Clockwise = root + right boundary + leaves + left boundary [OK]

Hint: Clockwise = root, right boundary, leaves, left boundary [OK]

Common Mistakes:

• Confusing clockwise with anti-clockwise order
• Printing boundaries in wrong direction
• Mixing leaf traversal order