Tree Algorithms: Master the Fundamentals for Efficient Data Structures

Question 1

In a red-black tree, how are insertions performed while maintaining its balance properties? Provide a clear example illustrating the specific rules and transformations involved.

Accepted Answer

Insertions are done like in a binary search tree, followed by rebalancing the tree through rotations to maintain balance.

Answer

Insertions are done recursively, and the tree is rebalanced by changing the colors of nodes.

Answer

Insertions are done iteratively, and the tree is rebalanced by deleting and reinserting nodes.

Answer

Insertions are not possible in a red-black tree without violating its properties.

Question 2

In a binary search tree with n nodes, which algorithm efficiently locates a node with a given target value in O(log n) time?

Accepted Answer

Binary search

Answer

Breadth-first search

Answer

Depth-first search

Answer

Linear search

Question 3

Which of the following accurately compares the strengths and weaknesses of AVL trees and binary search trees?

Accepted Answer

AVL trees guarantee a balanced structure, making them more efficient for searching and insertion, while binary search trees do not.

Accepted Answer

Binary search trees are simpler to implement and use less memory compared to AVL trees.

Answer

AVL trees are always more efficient than binary search trees, regardless of the data distribution.

Answer

Binary search trees can handle duplicate values more efficiently than AVL trees.

Question 4

In a balanced AVL tree, what is the time complexity of deleting an element? Provide a brief explanation.

Accepted Answer

O(log n)

Answer

O(n)

Answer

O(log n^2)

Question 5

What is the primary objective of a rotation operation in a binary search tree?

Accepted Answer

To balance the tree after insertion or deletion

Answer

To facilitate insertion while preserving the search tree property

Answer

To enable deletion while maintaining the tree's structure

Answer

To locate the minimum or maximum value in the tree

Question 6

What is the worst-case time complexity for searching an element in an AVL tree?

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Question 7

Which tree traversal technique is most appropriate for printing the elements of a binary tree in ascending order?

Accepted Answer

In-order traversal

Answer

Pre-order traversal

Answer

Post-order traversal

Answer

Breadth-first search

Question 8

What is the average time complexity of searching for an element in an AVL tree?

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n log n)

Question 9

What is the time complexity of inserting an element into a red-black tree?

Accepted Answer

O(log n)

Answer

O(n)

Answer

O(n log n)

Answer

O(n^2)

Question 10

What is the time complexity for finding an element in an AVL tree of size 'n'?

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Question 11

To maintain balance in a red-black tree after inserting a node as the right child of a right child, which rotation is employed?

Accepted Answer

Right-left rotation

Answer

Left rotation

Answer

Right rotation

Answer

Left-right rotation

Question 12

Determine the minimum number of nodes in a full binary tree with height 'h'.

Accepted Answer

2^h - 1

Answer

h

Answer

2^h

Answer

h^2

Question 13

Which data structure does NOT belong to the tree family?

Accepted Answer

Hash table

Answer

Binary search tree

Answer

AVL tree

Answer

Red-black tree

Question 14

What is the time complexity of finding an element in a balanced AVL tree?

Accepted Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(1)

Question 15

In a red-black tree, what color must a node's parent be if the node is red?

Accepted Answer

Black

Answer

Red

Answer

Blue

Answer

Green

Question 16

Which of the following is not a feature of a balanced binary tree?

Accepted Answer

Worst-case height that grows linearly with the number of nodes

Answer

Similar heights for left and right subtrees

Answer

Efficient search and insertion operations

Answer

Suitability for implementing priority queues

Question 17

What is the maximum number of nodes in a binary tree of height h where each node has at most two children?

Accepted Answer

2^(h+1) - 1

Answer

2^h

Answer

h^2

Answer

2^h - 1

Question 18

Which of the following is NOT a fundamental tree algorithm used in data structures?

Accepted Answer

Heap sort

Answer

Binary search trees

Answer

AVL trees

Answer

Red-black trees

Question 19

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

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n log n)

Question 20

Which of the following is considered a self-balancing tree in data structures?

Accepted Answer

AVL tree

Answer

Binary search tree

Answer

Heap

Answer

Radix tree

Question 21

What is the primary difference between a binary search tree and a red-black tree?

Accepted Answer

Red-black trees are always balanced, while binary search trees are not

Answer

Red-black trees support more operations than binary search trees

Answer

Red-black trees are faster than binary search trees

Answer

Binary search trees are easier to implement than red-black trees

Question 22

What is the time complexity to search for an element in a red-black tree?

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n log n)

Question 23

What is the main disadvantage of AVL trees compared to binary search trees?

Accepted Answer

More complex insertion and deletion algorithms

Answer

Larger memory overhead

Answer

Slower search operations

Answer

Less efficient for large datasets

Question 24

What is the purpose of the 'left rotate' operation in tree algorithms?

Accepted Answer

To balance the tree after an insertion or deletion

Answer

To convert a binary search tree to an AVL tree

Answer

To find the minimum value in a binary search tree

Answer

To delete a node from a red-black tree

Question 25

What type of tree is used to implement a priority queue?

Accepted Answer

Binary heap

Answer

Red-black tree

Answer

AVL tree

Answer

Binary search tree

Question 26

True or False: A binary tree is considered complete if every level except the last is completely filled.

Accepted Answer

True

Answer

False

Question 27

Which traversal of a balanced binary search tree results in elements being listed in sorted order?

Accepted Answer

Inorder traversal

Answer

Preorder traversal

Answer

Postorder traversal

Answer

Level-order traversal

Question 28

In an AVL tree, what is the maximum time complexity for finding an element?

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Question 29

Which property of a binary search tree is incorrect?

Accepted Answer

The tree is inherently balanced.

Answer

Nodes on the left have smaller values than their parent.

Answer

Nodes on the right have larger values than their parent.

Answer

Inorder traversal produces a sorted sequence of elements.

Question 30

What is the primary objective of employing a splay tree?

Accepted Answer

Quicken search and insertion operations

Answer

Ensure tree balance

Answer

Maintain sorted data storage

Answer

Represent hierarchical data structures

Question 31

For finding a range of elements within a balanced binary search tree, which algorithm would be most suitable?

Accepted Answer

Binary search

Answer

Breadth-first search

Answer

Depth-first search

Answer

Dijkstra's algorithm

Question 32

An AVL tree is a type of self-balancing binary search tree that maintains a balance factor within a range of:

Accepted Answer

[-1, 1]

Answer

[-2, 2]

Answer

[-3, 3]

Answer

[-4, 4]

Question 33

The preorder traversal of a binary tree visits the nodes in the following order:

Accepted Answer

Root - Left - Right

Answer

Left - Right - Root

Answer

Root - Right - Left

Answer

Left - Root - Right

Question 34

The diameter of a tree is defined as:

Accepted Answer

The longest path between any two nodes

Answer

The shortest path between any two nodes

Answer

The maximum number of nodes in the tree

Answer

The minimum number of edges in the tree

Question 35

A binary tree that contains only one node is called a:

Accepted Answer

Singleton tree

Answer

Empty tree

Answer

Root tree

Answer

Leaf tree

Question 36

Which characteristic uniquely distinguishes an AVL tree from a binary search tree?

Accepted Answer

Balanced height

Answer

Ordered data

Answer

Self-organizing property

Answer

Left-right-left subtrees

Question 37

For a balanced binary search tree, what is the time complexity of searching for a key on average?

Accepted Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(1)

Question 38

What is the primary purpose of balancing a binary search tree?

Accepted Answer

Reducing search time complexity

Answer

Simplifying insertion and deletion operations

Answer

Achieving better memory utilization

Answer

Optimizing data compression

Question 39

What is the key advantage of employing a self-balancing tree?

Accepted Answer

Efficient search and insertion operations

Answer

Reduced memory requirements

Answer

Improved data organization for faster retrieval

Answer

Enhanced security measures

Question 40

What is the primary function of a sentinel node in a binary search tree?

Accepted Answer

Marking the end of a path for efficient traversal

Answer

Balancing the tree to maintain its structure

Answer

Storing additional data associated with the tree

Answer

Ensuring the tree is a complete binary tree

Question 41

What is the fundamental principle behind iterative traversal of a binary tree?

Accepted Answer

Employing a stack or queue to store and process nodes

Answer

Using recursion to visit nodes in a predefined order

Answer

Traversing the tree exclusively in a depth-first manner

Answer

Traversing the tree exclusively in a breadth-first manner

Question 42

Which algorithm is used for inserting a node into an AVL tree?

Accepted Answer

Double rotation

Answer

Breadth-first search

Answer

Depth-first search

Answer

Binary search

Question 43

What is the time complexity of finding a value in a balanced red-black tree?

Accepted Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(1)

Question 44

Which of the following is a benefit of using a threaded binary tree?

Accepted Answer

Faster traversal

Answer

Lower memory usage

Answer

Improved search performance

Answer

Supports duplicate values

Question 45

Which of the following algorithms can be used to convert a BST into a heap?

Accepted Answer

Heap sort

Answer

Bubble sort

Answer

Quick sort

Answer

Merge sort

Question 46

What is the purpose of a Huffman tree?

Accepted Answer

Data compression

Answer

Data encryption

Answer

Tree traversal visualization

Answer

Binary search optimization

Question 47

Which traversal method starts from the root and visitas nodes in a level-by-level manner?

Accepted Answer

Breadth-first

Answer

Preorder

Answer

Inorder

Answer

Postorder

Question 48

What is the difference between a balanced tree and an unbalanced tree?

Accepted Answer

Balanced trees have equal height subtrees, while unbalanced trees do not

Answer

Balanced trees have more leaves than unbalanced trees

Answer

Balanced trees use less memory than unbalanced trees

Answer

Balanced trees are always faster than unbalanced trees

Question 49

Which of the following statements about AVL trees is true?

Accepted Answer

AVL trees guarantee a maximum height of O(log n) for any number of nodes.

Answer

AVL trees are always perfectly balanced.

Answer

AVL trees require O(n^2) time to insert or delete a node.

Answer

AVL trees cannot handle duplicate values.

Question 50

Which traversal order would you use to visit the nodes of a binary tree in ascending order?

Accepted Answer

Inorder

Answer

Preorder

Answer

Postorder

Answer

Level-order

Question 51

What is the key distinction between red-black trees and AVL trees?

Accepted Answer

Red-black trees allow for some degree of imbalance, while AVL trees must be perfectly balanced.

Answer

AVL trees allow for some degree of imbalance, while red-black trees must be perfectly balanced.

Answer

Red-black trees use colors to maintain balance, while AVL trees use height information.

Answer

AVL trees use colors to maintain balance, while red-black trees use height information.

Question 52

Which of the following is NOT an advantage of using a balanced binary tree?

Accepted Answer

Reduced memory usage

Answer

Improved search performance

Answer

Increased insertion efficiency

Answer

More efficient range queries

Question 53

What is the purpose of a dummy node in a binary search tree?

Accepted Answer

To simplify the implementation of tree operations, particularly insertion and deletion

Answer

To improve the search performance of the tree

Answer

To balance the tree after insertions and deletions

Answer

To store additional information about the tree

Question 54

Which of the following is a potential drawback of using a binary search tree?

Accepted Answer

It can become unbalanced after repeated insertions and deletions, affecting search and insertion performance.

Answer

It requires O(n log n) time to insert or delete a node.

Answer

It is not suitable for storing duplicate values.

Answer

It cannot be used to efficiently perform range queries.

Question 55

What is the time complexity of inserting a node into a red-black tree?

Accepted Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(1)

Question 56

Which algorithm is used to search for a node in a binary search tree?

Accepted Answer

Binary search

Answer

Breadth-first search

Answer

Depth-first search

Answer

Linear search

Question 57

What is the time complexity of searching for a node with a given value in a balanced BST?

Accepted Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(log n^2)

Question 58

Which algorithm can be used to traverse a binary tree in pre-order?

Accepted Answer

Depth-first search

Answer

Breadth-first search

Answer

In-order traversal

Answer

Post-order traversal

Question 59

What is the definition of a subtree?

Accepted Answer

A node and all its descendants

Answer

A node and all its ancestors

Answer

A path from the root to a leaf

Answer

A cycle within a tree

Question 60

Which of the following is the definition of a complete binary tree?

Accepted Answer

A tree with all levels completely filled except possibly the last level

Answer

A tree with all nodes having either 0 or 2 children

Answer

A tree with all paths from the root to a leaf having the same length

Answer

A tree with all leaves at the same level

Question 61

What is the worst-case time complexity of searching for an element in a balanced binary search tree?

Accepted Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(1)

Question 62

What is the maximum number of nodes in a red-black tree of height h?

Accepted Answer

2^(h+1) - 1

Answer

2^(h) - 1

Answer

2^(2h) - 1

Answer

2^(2h+1) - 1

Question 63

Which of the following is not a fundamental operation on a binary search tree?

Accepted Answer

Sort

Answer

Insert

Answer

Delete

Answer

Search

Question 64

Which of the following is not an advantage of using a binary search tree over a linked list?

Accepted Answer

Can store duplicate elements

Answer

Faster search operations

Answer

More efficient memory usage

Answer

Easier to implement