Tree Traversal Postorder Left Right Root in DSA Typescript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of postorder traversal on this tree?

Given the binary tree below, what is the postorder traversal output?

Tree structure:

    1
   / \
  2   3
 / \
4   5

DSA Typescript

class TreeNode {
  val: number;
  left: TreeNode | null;
  right: TreeNode | null;
  constructor(val: number, left: TreeNode | null = null, right: TreeNode | null = null) {
    this.val = val;
    this.left = left;
    this.right = right;
  }
}

function postorderTraversal(root: TreeNode | null): number[] {
  if (!root) return [];
  return [...postorderTraversal(root.left), ...postorderTraversal(root.right), root.val];
}

const root = new TreeNode(1,
  new TreeNode(2, new TreeNode(4), new TreeNode(5)),
  new TreeNode(3)
);

console.log(postorderTraversal(root));

A [4, 5, 2, 3, 1]

B [1, 2, 3, 4, 5]

C [2, 4, 5, 3, 1]

D [4, 2, 5, 3, 1]

💡 Hint

Remember postorder visits left subtree, then right subtree, then root.

Postorder traversal visits nodes in Left, Right, Root order. For the given tree, it visits 4, then 5, then 2, then 3, then 1.

❓ Predict Output

intermediate

What is the postorder traversal output of this tree?

Consider this binary tree:

      10
     /  \
    5    15
        /  \
       12   20

What is the postorder traversal output?

DSA Typescript

class TreeNode {
  val: number;
  left: TreeNode | null;
  right: TreeNode | null;
  constructor(val: number, left: TreeNode | null = null, right: TreeNode | null = null) {
    this.val = val;
    this.left = left;
    this.right = right;
  }
}

function postorderTraversal(root: TreeNode | null): number[] {
  if (!root) return [];
  return [...postorderTraversal(root.left), ...postorderTraversal(root.right), root.val];
}

const root = new TreeNode(10,
  new TreeNode(5),
  new TreeNode(15, new TreeNode(12), new TreeNode(20))
);

console.log(postorderTraversal(root));

A [5, 15, 12, 20, 10]

B [12, 20, 15, 5, 10]

C [10, 5, 15, 12, 20]

D [5, 12, 20, 15, 10]

💡 Hint

Postorder visits left subtree, then right subtree, then root.

Postorder traversal visits nodes in Left, Right, Root order. Here, it visits 5, then 12, then 20, then 15, then 10.

🔧 Debug

advanced

Why does this postorder traversal code cause a runtime error?

Look at this TypeScript code for postorder traversal. It throws an error when run. What is the cause?

DSA Typescript

class TreeNode {
  val: number;
  left: TreeNode | null;
  right: TreeNode | null;
  constructor(val: number, left: TreeNode | null = null, right: TreeNode | null = null) {
    this.val = val;
    this.left = left;
    this.right = right;
  }
}

function postorderTraversal(root: TreeNode | null): number[] {
  if (root === null) return [];
  const left = postorderTraversal(root.left!);
  const right = postorderTraversal(root.right!);
  return [...left, ...right, root.val];
}

const root = new TreeNode(1, new TreeNode(2), new TreeNode(3));
console.log(postorderTraversal(root));

A Using '!' operator on possibly null left or right causes runtime error when child is null.

B The TreeNode constructor is missing initialization of left and right properties.

C The function returns in wrong order: root, left, right instead of left, right, root.

D Missing base case for null root causes infinite recursion.

💡 Hint

Check how the code handles null children with the '!' operator.

The '!' operator tells TypeScript to treat the value as non-null, but if the child is actually null, accessing it causes a runtime error. The code should check for null before recursion.

🧠 Conceptual

advanced

Which traversal order matches postorder traversal?

Which of these sequences correctly describes the order of visiting nodes in postorder traversal?

A Visit root node, then right subtree, then left subtree.

B Visit left subtree, then right subtree, then root node.

C Visit root node, then left subtree, then right subtree.

D Visit right subtree, then left subtree, then root node.

💡 Hint

Postorder means the root is visited last.

Postorder traversal visits nodes in the order: left subtree, right subtree, then root node.

❓ Predict Output

expert

What is the postorder traversal output of this complex tree?

Given the following binary tree, what is the postorder traversal output?

          7
         / \
        3   9
       /   / \
      1   8  10
       \      /
        2    5

DSA Typescript

class TreeNode {
  val: number;
  left: TreeNode | null;
  right: TreeNode | null;
  constructor(val: number, left: TreeNode | null = null, right: TreeNode | null = null) {
    this.val = val;
    this.left = left;
    this.right = right;
  }
}

function postorderTraversal(root: TreeNode | null): number[] {
  if (!root) return [];
  return [...postorderTraversal(root.left), ...postorderTraversal(root.right), root.val];
}

const root = new TreeNode(7,
  new TreeNode(3, new TreeNode(1, null, new TreeNode(2)), null),
  new TreeNode(9, new TreeNode(8), new TreeNode(10, new TreeNode(5), null))
);

console.log(postorderTraversal(root));

A [2, 1, 3, 8, 10, 5, 9, 7]

B [1, 2, 3, 8, 5, 10, 9, 7]

C [2, 1, 3, 8, 5, 10, 9, 7]

D [2, 1, 3, 8, 10, 9, 5, 7]

💡 Hint

Carefully follow left, right, root order recursively.

Postorder visits left subtree (2,1,3), then right subtree (8,5,10,9), then root (7). The correct sequence is [2, 1, 3, 8, 5, 10, 9, 7].

Practice

1. What is the order of nodes visited in a postorder tree traversal?

easy

A. Left subtree, Right subtree, Root node

B. Root node, Left subtree, Right subtree

C. Root node, Right subtree, Left subtree

D. Right subtree, Left subtree, Root node

Solution

1. Step 1: Understand postorder traversal definition

   Postorder traversal visits the left subtree first, then the right subtree, and finally the root node.

2. Step 2: Match the traversal order to options

   Left subtree, Right subtree, Root node correctly lists Left subtree, Right subtree, Root node order.

3. Final Answer:

   Left subtree, Right subtree, Root node -> Option A

4. Quick Check:

   Postorder = Left, Right, Root [OK]

Hint: Remember: postorder ends with root after children [OK]

Common Mistakes:

• Confusing postorder with preorder or inorder
• Visiting root before children
• Swapping left and right subtree order

2. Which of the following TypeScript function signatures correctly represents a postorder traversal of a binary tree node?

easy

A. function postorder(node: TreeNode | null): TreeNode[]

B. function postorder(node: TreeNode): number

C. function postorder(): TreeNode

D. function postorder(node: TreeNode | null): void

Solution

1. Step 1: Identify correct parameter and return type for traversal

   Traversal functions usually take a node or null and return void if printing or processing inline.

2. Step 2: Check options for correct signature

   function postorder(node: TreeNode | null): void takes a node or null and returns void, suitable for traversal printing or processing.

3. Final Answer:

   function postorder(node: TreeNode | null): void -> Option D

4. Quick Check:

   Traversal function signature = function postorder(node: TreeNode | null): void [OK]

Hint: Traversal usually takes node|null and returns void [OK]

Common Mistakes:

• Omitting null in parameter type
• Returning incorrect types like TreeNode or number
• Missing parameter in function signature

3. Given the following binary tree:

    1
   / \
  2   3
 / \
4   5

What is the output of a postorder traversal?

medium

A. [4, 5, 2, 3, 1]

B. [1, 2, 3, 4, 5]

C. [2, 4, 5, 3, 1]

D. [4, 2, 5, 3, 1]

Solution

1. Step 1: Traverse left subtree of root (1)

   Left subtree rooted at 2: postorder visits 4, then 5, then 2.

2. Step 2: Traverse right subtree and root

   Right subtree is 3, visited next. Finally, root 1 is visited.

3. Final Answer:

   [4, 5, 2, 3, 1] -> Option A

4. Quick Check:

   Postorder output = [4, 5, 2, 3, 1] [OK]

Hint: Postorder prints children before parent [OK]

Common Mistakes:

• Visiting root before children
• Mixing left and right subtree order
• Confusing with preorder or inorder output

4. Consider this TypeScript postorder traversal function:

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

What is the error in this code?

medium

A. It prints node value before children

B. It does not check for null nodes

C. It visits right subtree before left, reversing postorder

D. It returns a value but should be void

Solution

1. Step 1: Analyze traversal order in code

   The function calls postorder on right child first, then left child, then prints root.

2. Step 2: Compare with correct postorder order

   Correct postorder is left, right, root. This code reverses left and right order.

3. Final Answer:

   It visits right subtree before left, reversing postorder -> Option C

4. Quick Check:

   Left before right in postorder [OK]

Hint: Postorder = left first, then right, then root [OK]

Common Mistakes:

• Swapping left and right subtree calls
• Printing before visiting children
• Ignoring null checks

5. You want to collect all node values of a binary tree in postorder traversal into an array using TypeScript. Which code snippet correctly implements this?

hard

A. function postorder(node: TreeNode | null, result: number[]): void {
if (!node) return;
result.push(node.val);
postorder(node.left, result);
postorder(node.right, result);
}

B. function postorder(node: TreeNode | null, result: number[]): void {
if (!node) return;
postorder(node.left, result);
postorder(node.right, result);
result.push(node.val);
}

C. function postorder(node: TreeNode | null, result: number[]): number[] {
if (!node) return result;
result.push(node.val);
postorder(node.left, result);
postorder(node.right, result);
return result;
}

D. function postorder(node: TreeNode | null): number[] {
if (!node) return [];
return [node.val, ...postorder(node.left), ...postorder(node.right)];
}

Solution

1. Step 1: Understand postorder traversal collection

   Postorder visits left, then right, then root. Values should be pushed after children.

2. Step 2: Check each option for correct order and pushing

   function postorder(node: TreeNode | null, result: number[]): void { if (!node) return; postorder(node.left, result); postorder(node.right, result); result.push(node.val); } visits left, right, then pushes node value, correctly collecting postorder.

3. Final Answer:

   function postorder(node: TreeNode | null, result: number[]): void { if (!node) return; postorder(node.left, result); postorder(node.right, result); result.push(node.val); } -> Option B

4. Quick Check:

   Push after children = postorder [OK]

Hint: Push node value after left and right calls [OK]

Common Mistakes:

• Pushing node value before children
• Returning new arrays instead of using passed array
• Swapping left and right subtree calls