Tree Traversal Postorder Left Right Root in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the order of visiting nodes in Postorder Tree Traversal?

In Postorder traversal, nodes are visited in this order: Left subtree, Right subtree, then Root node.

intermediate

Why is Postorder traversal useful in expression trees?

Postorder traversal visits children before the parent, which matches the order needed to evaluate expressions (operands before operators).

beginner

Show the Postorder traversal output for this tree:
Root: 1
Left child: 2
Right child: 3

The Postorder traversal visits Left (2), Right (3), then Root (1). So output is: 2 -> 3 -> 1 -> null

beginner

What is the base case in a recursive Postorder traversal function?

The base case is when the current node is null (no node), then return without doing anything.

beginner

How does Postorder traversal differ from Preorder traversal?

Postorder visits Left, Right, Root; Preorder visits Root, Left, Right. The root is visited last in Postorder, but first in Preorder.

In Postorder traversal, which node is visited last?

A Root node

B Left child

C Right child

D None

Postorder visits Left subtree, then Right subtree, and finally the Root node.

What is the first step in Postorder traversal of a node?

A Visit the root node

B Visit the right subtree

C Visit the left subtree

D Return null

Postorder traversal starts by visiting the left subtree first.

Which traversal order matches this sequence: Left, Right, Root?

A Level order

B Inorder

C Preorder

D Postorder

Postorder traversal visits nodes in Left, Right, Root order.

In Postorder traversal, what happens when a null node is reached?

A Return immediately

B Visit the node

C Visit left child

D Visit right child

When a null node is reached, the function returns immediately as there is nothing to visit.

Which of these is NOT a correct step in Postorder traversal?

A Visit left subtree

B Visit root node first

C Visit right subtree

D Visit root node last

In Postorder traversal, the root node is visited last, not first.

Explain how Postorder traversal works on a binary tree.

Think about the order of visiting children before the parent.

Describe a real-life scenario where Postorder traversal is useful.

Consider tasks that require finishing all subtasks before the main task.

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