Check if Binary Tree is Balanced in DSA C++ - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does it mean for a binary tree to be balanced?

A binary tree is balanced if for every node, the height difference between its left and right subtrees is at most 1.

beginner

Why is checking balance important in binary trees?

Balanced trees ensure operations like search, insert, and delete run efficiently, typically in O(log n) time.

intermediate

What is the main idea behind the efficient algorithm to check if a binary tree is balanced?

Use a bottom-up approach that returns the height of subtrees and checks balance at the same time to avoid repeated height calculations.

intermediate

What does the function return if the subtree is not balanced in the efficient approach?

It returns -1 to indicate the subtree is not balanced, which helps stop further unnecessary checks.

beginner

In the context of checking if a binary tree is balanced, what is the height of a null node?

The height of a null node is defined as 0, meaning it contributes no height to the tree.

What is the maximum allowed height difference between left and right subtrees for a node to be balanced?

A 0

B 2

C 1

D 3

A balanced binary tree requires the height difference to be at most 1.

Which approach is more efficient to check if a binary tree is balanced?

A Level order traversal only

B Top-down approach calculating height repeatedly

C Inorder traversal only

D Bottom-up approach returning height and balance status

The bottom-up approach avoids repeated height calculations and stops early if imbalance is found.

What does a height function return when it detects an unbalanced subtree?

A 0

B -1

C 1

D Height of the subtree

Returning -1 signals that the subtree is unbalanced.

What is the height of an empty (null) subtree?

A 0

B -1

C 1

D Undefined

An empty subtree has height 0.

If a binary tree is balanced, what is the time complexity of checking it using the bottom-up approach?

A O(n)

B O(n^2)

C O(n log n)

D O(log n)

The bottom-up approach visits each node once, so it runs in O(n) time.

Explain how the bottom-up approach checks if a binary tree is balanced.

Think about how you can combine height calculation and balance checking in one function.

Describe why the top-down approach to check balance is less efficient than the bottom-up approach.

Consider how many times each node is processed in both approaches.