Priority Queues and Heaps for Competitive Exam Success

My Learning Cart

Priority Queues and Heaps

Download Q&A

Priority Queues and Heaps MCQ & Objective Questions

Understanding "Priority Queues and Heaps" is crucial for students preparing for various exams in India. These data structures are not only fundamental in computer science but also frequently appear in objective questions and MCQs. Practicing these concepts through targeted practice questions can significantly enhance your exam preparation and boost your scores in competitive assessments.

What You Will Practise Here

Definition and characteristics of Priority Queues
Types of Heaps: Min-Heap and Max-Heap
Heap operations: Insertion, Deletion, and Heapify
Applications of Priority Queues in algorithms
Complexity analysis of Heap operations
Common algorithms using Heaps, such as Heap Sort
Real-world applications of Priority Queues in scheduling

Exam Relevance

The topic of Priority Queues and Heaps is relevant across various examination boards in India, including CBSE and State Boards. It is also significant for competitive exams like NEET and JEE. Students can expect questions that test their understanding of the properties of heaps, operations, and applications in algorithm design. Common question patterns include theoretical questions, problem-solving scenarios, and application-based queries.

Common Mistakes Students Make

Confusing Min-Heaps with Max-Heaps and their properties
Overlooking the time complexity of different heap operations
Misunderstanding the practical applications of Priority Queues
Failing to visualize the heap structure during problem-solving

FAQs

Question: What is a Priority Queue?
Answer: A Priority Queue is an abstract data type where each element has a priority, and elements are served based on their priority rather than their order in the queue.

Question: How do you perform insertion in a Max-Heap?
Answer: Insertion in a Max-Heap involves adding the new element at the end of the heap and then performing the "heapify" operation to maintain the heap property.

Now that you have a clear understanding of Priority Queues and Heaps, it's time to put your knowledge to the test! Solve practice MCQs and important questions to reinforce your understanding and excel in your exams.

Q. How do you remove the maximum element from a max-heap?

A. Remove the root and re-heapify
B. Remove the last element
C. Swap the root with the last element
D. Both A and C

Solution

To remove the maximum element from a max-heap, you swap the root with the last element, remove the last element, and then re-heapify.

Correct Answer: D — Both A and C

Q. In a min-heap, which of the following is true?

A. The root is the smallest element
B. The root is the largest element
C. All parent nodes are smaller than their children
D. Both A and C

Solution

In a min-heap, the root is the smallest element, and all parent nodes are smaller than their children.

Correct Answer: D — Both A and C

Q. In a min-heap, which of the following statements is true?

A. The parent node is always greater than its children
B. The parent node is always less than its children
C. All nodes are in sorted order
D. The smallest element is at the bottom

Solution

In a min-heap, the parent node is always less than or equal to its children, ensuring that the smallest element is at the root.

Correct Answer: B — The parent node is always less than its children

Q. What is the maximum height of a binary heap with n elements?

A. n
B. log n
C. n log n
D. 2n

Solution

The maximum height of a binary heap is log n, as it is a complete binary tree.

Correct Answer: B — log n

Q. What is the primary difference between a binary heap and a binary search tree?

A. Binary heaps are complete binary trees, while binary search trees are not
B. Binary heaps allow duplicate elements, while binary search trees do not
C. Binary heaps are used for priority queues, while binary search trees are used for searching
D. All of the above

Solution

The primary differences include that binary heaps are complete binary trees used for priority queues, while binary search trees are not necessarily complete and are used for searching.

Correct Answer: D — All of the above

Q. What is the primary use of a priority queue?

A. Sorting elements
B. Finding the shortest path
C. Managing tasks based on priority
D. Storing elements in a specific order

Solution

A priority queue is used to manage tasks based on their priority, allowing for efficient retrieval of the highest (or lowest) priority task.

Correct Answer: C — Managing tasks based on priority

Q. What is the result of performing a 'decrease key' operation in a min-heap?

A. The key is increased
B. The key is decreased and the heap property is maintained
C. The key is removed
D. The heap is destroyed

Solution

The 'decrease key' operation reduces the value of a key and may require re-heapifying to maintain the heap property.

Correct Answer: B — The key is decreased and the heap property is maintained

Q. What is the result of performing a heap sort on an array?

A. An unsorted array
B. A partially sorted array
C. A sorted array
D. A reverse sorted array

Solution

Heap sort transforms the array into a max-heap and then repeatedly extracts the maximum element, resulting in a sorted array.

Correct Answer: C — A sorted array

Q. What is the space complexity of a binary heap storing n elements?

A. O(1)
B. O(n)
C. O(log n)
D. O(n log n)

Solution

The space complexity of a binary heap storing n elements is O(n) because it needs to store all n elements.

Correct Answer: B — O(n)

Q. What is the space complexity of a binary heap?

A. O(1)
B. O(n)
C. O(log n)
D. O(n log n)

Solution

The space complexity of a binary heap is O(n) because it stores n elements in an array.

Correct Answer: B — O(n)

Q. What is the time complexity of deleting the maximum element from a max-heap?

A. O(1)
B. O(log n)
C. O(n)
D. O(n log n)

Solution

Deleting the maximum element from a max-heap involves removing the root and then re-heapifying, which takes O(log n) time.

Correct Answer: B — O(log n)

Q. What is the worst-case time complexity for building a heap from an array of n elements?

A. O(n)
B. O(n log n)
C. O(log n)
D. O(1)

Solution

The worst-case time complexity for building a heap from an array of n elements is O(n) using the heapify process.

Correct Answer: A — O(n)

Q. Which algorithm is commonly used to convert an array into a heap?

A. Heapify
B. Merge Sort
C. Quick Sort
D. Insertion Sort

Solution

The 'Heapify' algorithm is used to convert an array into a heap structure, ensuring the heap property is maintained.

Correct Answer: A — Heapify

Q. Which algorithm uses a priority queue to find the shortest path in a graph?

A. Dijkstra's Algorithm
B. Kruskal's Algorithm
C. Prim's Algorithm
D. Bellman-Ford Algorithm

Solution

Dijkstra's Algorithm uses a priority queue to efficiently find the shortest path from a source vertex to all other vertices in a graph.

Correct Answer: A — Dijkstra's Algorithm

Q. Which of the following is a characteristic of a binary heap?

A. Complete binary tree
B. Balanced binary tree
C. Binary search tree
D. Unbalanced tree

Solution

A binary heap is a complete binary tree, meaning all levels are fully filled except possibly for the last level.

Correct Answer: A — Complete binary tree

Q. Which of the following is NOT a valid implementation of a priority queue?

A. Array
B. Linked List
C. Binary Search Tree
D. Max-Heap

Solution

While a binary search tree can be used to implement a priority queue, it is not a typical or efficient implementation compared to heaps.

Correct Answer: C — Binary Search Tree

Q. Which of the following is true about a max-heap?

A. The parent node is always smaller than its children
B. The parent node is always larger than its children
C. It is a complete binary tree
D. Both B and C

Solution

In a max-heap, the parent node is always larger than its children, and it is also a complete binary tree.

Correct Answer: D — Both B and C

Q. Which of the following operations can be performed in O(1) time on a priority queue implemented with a max-heap?

A. Insert
B. Delete Max
C. Get Max
D. Decrease Key

Solution

Getting the maximum element in a max-heap can be done in O(1) time since the maximum element is always at the root.

Correct Answer: C — Get Max

Q. Which of the following operations can be performed in O(log n) time in a binary heap?

A. Insertion
B. Deletion of the maximum element
C. Heapify
D. All of the above

Solution

All of the listed operations (insertion, deletion of the maximum element, and heapify) can be performed in O(log n) time in a binary heap.

Correct Answer: D — All of the above

Showing 1 to 19 of 19 (1 Pages)

School

College

Degree

Competitve

Skills

Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely