Binary Trees and Binary Search Trees: Interactive Learning Quizzes

Question 1

Which of the following statements about AVL trees is incorrect?

Accepted Answer

All nodes are at the same level.

Answer

The difference in height between the left and right subtrees of any node is at most 1.

Answer

AVL trees are always balanced.

Answer

The average depth of a node is O(log n).

Question 2

What is the purpose of a red-black tree?

Accepted Answer

To improve the average-case time complexity of search and insertion operations.

Answer

To maintain balance in a binary search tree.

Answer

To guarantee a constant-time search operation.

Answer

To represent hierarchical data structures efficiently.

Question 3

For a balanced binary search tree, what is the time complexity of searching for an element?

Accepted Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(1)

Question 4

What is the primary purpose of a binary search tree?

Accepted Answer

Efficiently searching and retrieving data

Answer

Organizing data hierarchically

Answer

Storing vast amounts of data

Answer

Performing complex mathematical calculations

Question 5

Which traversal algorithm is suitable for converting a binary tree into a linked list?

Accepted Answer

Inorder traversal

Answer

Preorder traversal

Answer

Postorder traversal

Answer

Breadth-first search

Question 6

What is the key difference between binary trees and binary search trees?

Accepted Answer

Binary search trees enforce a specific value ordering, unlike binary trees

Answer

Binary trees allow duplicates, while binary search trees do not

Answer

Binary trees are exclusively used for searching, while binary search trees can also sort

Answer

Binary search trees use nodes with keys and values, which is not the case in binary trees

Question 7

Which application can be implemented using a binary search tree?

Accepted Answer

A fast lookup dictionary

Answer

A priority queue

Answer

A graph data structure

Answer

A Bloom filter

Question 8

What is the worst-case time complexity of inserting a new element into an unbalanced binary search tree?

Accepted Answer

O(n)

Answer

O(log n)

Answer

O(n^2)

Answer

O(1)

Question 9

Nodes in a binary tree can have a maximum of how many children?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 10

In a binary search tree, what is the time complexity of searching for a key with n nodes?

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n log n)

Question 11

What is the distinction between pre-order and in-order traversals of a binary tree?

Accepted Answer

The order of visited nodes differs between the two.

Answer

The number of visited nodes differs between the two.

Answer

The time complexity differs between the two.

Answer

There is no difference between the two.

Question 12

What is the time complexity of inserting a key into a binary search tree?

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n log n)

Question 13

How do complete binary trees differ from full binary trees?

Accepted Answer

Complete binary trees have all levels filled except possibly the last, while full binary trees have all levels completely filled

Answer

Full binary trees have all levels filled except possibly the first, while complete binary trees have all levels completely filled

Answer

There is no distinction between complete and full binary trees

Answer

Complete binary trees have internal nodes with two children, unlike full binary trees

Question 14

What is the time complexity of determining the height of a binary tree?

Accepted Answer

O(n)

Answer

O(log n)

Answer

O(n^2)

Answer

O(1)

Question 15

What is the primary objective of employing threaded binary trees?

Accepted Answer

Optimizing traversal operations by eliminating the need for explicit pointers

Answer

Storing additional data associated with each node

Answer

Automatically balancing the tree during insertion and deletion

Answer

Representing non-binary trees using a binary tree structure

Question 16

Which algorithm is specifically designed to construct a binary search tree from an unsorted array?

Accepted Answer

Tree sort

Answer

Heap sort

Answer

Merge sort

Answer

Quick sort

Question 17

Which property does NOT apply to binary search trees?

Accepted Answer

The tree is always balanced.

Answer

Values in the left subtree are smaller than the node's value.

Answer

Values in the right subtree are larger than the node's value.

Question 18

Binary Search Trees (BSTs) adhere to the Binary Search Property. What does this property entail?

Accepted Answer

For any node, elements in the left subtree are always less than the node's value, while elements in the right subtree are always greater.

Answer

The left and right subtrees of each node have approximately the same number of elements.

Answer

The maximum path length from the root node to any leaf node is minimized.

Answer

The tree must be perfectly balanced, with all levels filled.

Question 19

In a perfectly balanced Binary Search Tree, what is the time complexity of searching for a specific element?

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Question 20

Identify the operation that can be performed on a binary tree but not on a binary search tree.

Accepted Answer

Storing non-comparable data

Answer

Insertion

Answer

Deletion

Answer

Inorder Traversal

Question 21

Which traversal method for a binary tree will output elements in ascending order if the tree is a Binary Search Tree?

Accepted Answer

Inorder Traversal

Answer

Preorder Traversal

Answer

Postorder Traversal

Answer

Breadth-First Search

Question 22

Binary Search Trees (BSTs) have various applications. Which of these is NOT a common use case for BSTs?

Accepted Answer

Storing large amounts of unstructured data

Answer

Maintaining sorted data for efficient searching

Answer

Implementing priority queues

Answer

Representing hierarchical data structures

Question 23

Identify a potential disadvantage of using Binary Search Trees (BSTs).

Accepted Answer

BSTs can become unbalanced, leading to poor performance

Answer

BSTs require more memory overhead compared to other data structures

Answer

BSTs cannot handle duplicate values efficiently

Answer

BSTs are always slower than other tree-based data structures

Question 24

In a balanced Binary Search Tree, what is the time complexity of inserting a new element?

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Question 25

What is the time complexity of searching for a node in a binary search tree with n nodes?

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Question 26

Consider the following binary tree:
      1
     / \
    2   3
   /   / \
  4   5   6
What is the mirror image of this tree?

Accepted Answer

1
              / \
             3   2
            / \   /
           6   5 4

Answer

Question 27

Binary search trees have a specific structure that can lead to a drawback. Which of the following is this drawback?

Accepted Answer

Suboptimal performance with unbalanced trees

Answer

Inherent limitation to store only numerical data types

Answer

Inability to handle duplicate data values

Question 28

Which of the following properties is a characteristic of every node in an AVL tree?

Accepted Answer

Height difference between subtrees of at most 1

Answer

A balance factor of 0

Answer

Equal height of left and right subtrees

Answer

Perfect balance of the tree

Question 29

Which real-world scenario is best suited for implementing a binary tree?

Accepted Answer

File system representation

Answer

Graph modeling

Answer

Hash table implementation

Answer

Sorted array storage

Question 30

Which traversal algorithm can transform a binary tree into a linked list, maintaining the left-to-right sequence of its nodes?

Accepted Answer

Inorder Traversal

Answer

Preorder Traversal

Answer

Postorder Traversal

Answer

Level-Order Traversal

Question 31

In a balanced Binary Search Tree (BST), what is the time complexity of inserting a new element?

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Question 32

Which characteristic uniquely defines a binary search tree (BST) and differentiates it from other binary trees?

Accepted Answer

A BST enforces the property that all values in its left subtree are less than the root, and all values in its right subtree are greater than the root.

Answer

A BST must adhere to strict height-balancing constraints.

Question 33

In a balanced binary search tree, what is the time complexity for searching for a specific element?

Accepted Answer

O(log n)

Answer

O(n^2)

Answer

O(n)

Answer

O(1)

Question 34

In a binary tree, what types of data can be stored within the nodes?

Accepted Answer

Virtually any data type, including complex objects, arrays, or even nested trees.

Answer

Data that can be represented as a single byte.

Answer

Only basic data types, like integers or strings.

Question 35

Which definition accurately describes a full binary tree?

Accepted Answer

Every node in the tree either has no children (is a leaf) or has exactly two children.

Answer

The number of leaves is always odd.

Answer

Every internal node has precisely one child.

Question 36

What is the primary purpose of a null link in the context of binary trees?

Accepted Answer

To indicate that a particular node has no child in that branch.

Answer

To establish a connection between two separate trees.

Answer

To store additional information related to the node.

Answer

To help balance the structure of the tree.

Question 37

Which operations are commonly supported by binary search trees?

Accepted Answer

Insertion, deletion, and searching

Answer

Only insertion and deletion

Answer

Only insertion and search

Answer

Only search and deletion

Question 38

What is the fundamental difference between preorder and postorder traversals in binary trees?

Accepted Answer

Preorder visits the root before its children, while postorder visits the root after its children.

Answer

Preorder traverses left child before right child, while postorder traverses right child before left child.

Answer

Preorder traverses the tree top-down, while postorder traverses bottom-up.

Question 39

What is the time complexity of searching for a specific key in a balanced binary search tree with n nodes?

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n^2)

Answer

O(n)

Question 40

Which of the following is a common application of binary search trees?

Accepted Answer

Implementing dictionaries or sets

Answer

Performing breadth-first search

Answer

Sorting a list of numbers

Answer

Finding the shortest path in a graph

Question 41

Which of the following statements about complete binary trees is true?

Accepted Answer

All levels except possibly the last are completely filled.

Answer

The number of nodes in a complete binary tree with height h is always 2^h-1.

Answer

The height of the tree is always equal to the number of nodes.

Question 42

Which of the following is a defining characteristic of a binary tree?

Accepted Answer

Each node can have a maximum of two child nodes.

Answer

Leaf nodes can have more than one child node.

Answer

Binary trees are inherently balanced.

Answer

Nodes can have an arbitrary number of child nodes.

Question 43

What is the primary purpose of a binary search tree (BST)?

Accepted Answer

To store and organize data in a sorted order for efficient searching and retrieval.

Answer

To minimize space consumption in memory.

Answer

To represent hierarchical relationships between data items.

Question 44

What is the time complexity for searching an element in a balanced binary search tree with n nodes?

Accepted Answer

O(log n)

Answer

O(log n^2)

Answer

O(n)

Answer

O(n^2)

Question 45

Which of the following is a key advantage of using a binary search tree over a linked list?

Accepted Answer

Faster searching and retrieval due to sorted data storage.

Answer

Less memory consumption.

Answer

More efficient space utilization.

Answer

Easier insertion and deletion of nodes.