BST balancing problem in Data Structures Theory - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the BST balancing problem?

The BST balancing problem is about keeping a binary search tree (BST) balanced so that its height stays small. This helps keep operations like search, insert, and delete fast.

beginner

Why does an unbalanced BST cause problems?

An unbalanced BST can become like a linked list, making operations take longer, up to the number of nodes. This slows down searching and updating data.

intermediate

Name one common method to balance a BST.

One common method is using self-balancing trees like AVL trees or Red-Black trees, which automatically keep the tree balanced after insertions and deletions.

beginner

What does 'height' mean in the context of a BST?

Height is the number of edges on the longest path from the root node down to a leaf node. Lower height means faster operations.

intermediate

How does balancing a BST improve search time?

Balancing keeps the tree's height close to log₂(n), where n is the number of nodes. This means search time stays fast, around log₂(n) steps instead of n.

What happens if a BST becomes unbalanced?

A It behaves like a linked list, slowing down operations

B It becomes a perfect binary tree

C It automatically balances itself

D It deletes all nodes

An unbalanced BST can become like a linked list, making operations slower.

Which of these is a self-balancing BST?

A Linked list

B AVL tree

C Binary heap

D Stack

AVL trees are self-balancing BSTs that keep the tree height small.

What does balancing a BST mainly aim to reduce?

A Memory usage

B Number of nodes

C Number of leaves

D Tree height

Balancing aims to reduce the tree height to improve operation speed.

What is the worst-case height of an unbalanced BST with n nodes?

A n

B log₂(n)

C 1

D n²

In the worst case, an unbalanced BST can have height equal to n, like a linked list.

Which operation is NOT directly improved by balancing a BST?

A Search

B Insert

C Sorting an array

D Delete

Balancing a BST improves search, insert, and delete, but not sorting an unrelated array.

Explain why balancing a BST is important and how it affects performance.

Think about how the shape of the tree changes operation times.

Describe one method used to keep a BST balanced automatically.

Consider trees that adjust themselves after changes.