What is a heap in data structures?
A) A complete binary tree that satisfies the heap property
B) A linear data structure
C) A type of binary search tree
D) A non-linear data structure
Answer: A) A complete binary tree that satisfies the heap property
What are the two types of heaps?
A) Max heap and min heap
B) Binary heap and ternary heap
C) Complete heap and incomplete heap
D) Full heap and empty heap
Answer: A) Max heap and min heap
In a max heap, which property is maintained?
A) The key of a parent node is less than or equal to its children
B) The key of a parent node is greater than or equal to its children
C) All nodes must have two children
D) The tree must be balanced
Answer: B) The key of a parent node is greater than or equal to its children
What is the time complexity for inserting an element into a heap?
A) O(1)
B) O(log n)
C) O(n)
D) O(n log n)
Answer: B) O(log n)
What is the time complexity for removing the maximum element from a max heap?
A) O(1)
B) O(log n)
C) O(n)
D) O(n log n)
Answer: B) O(log n)
What is the main use of a heap?
A) Storing sorted data
B) Implementing priority queues
C) Storing data in a linear format
D) Representing graphs
Answer: B) Implementing priority queues
In a min heap, which property is maintained?
A) The key of a parent node is less than or equal to its children
B) The key of a parent node is greater than or equal to its children
C) The heap is always complete
D) The heap has at least one child
Answer: A) The key of a parent node is less than or equal to its children
What is the height of a complete binary heap with n nodes?
A) O(1)
B) log(n)
C) O(n)
D) O(n log n)
Answer: B) log(n)
Which of the following is true about heaps?
A) Heaps are always balanced
B) Heaps can be implemented using arrays
C) Heaps cannot be used to sort data
D) Heaps have a fixed size
Answer: B) Heaps can be implemented using arrays
What is the process of restoring the heap property after an insertion called?
A) Sifting down
B) Sifting up
C) Balancing
D) Rotating
Answer: B) Sifting up
What is the process of restoring the heap property after a deletion called?
A) Sifting down
B) Sifting up
C) Balancing
D) Rotating
Answer: A) Sifting down
Which data structure can efficiently implement a priority queue?
A) Stack
B) Queue
C) Binary tree
D) Heap
Answer: D) Heap
What is the time complexity of heap sort?
A) O(n)
B) O(n log n)
C) O(n^2)
D) O(log n)
Answer: B) O(n log n)
What is the primary disadvantage of a binary heap?
A) It is inefficient for searching
B) It requires too much memory
C) It is always unbalanced
D) It cannot be implemented with arrays
Answer: A) It is inefficient for searching
What is the primary characteristic of a binary heap?
A) It is a complete binary tree
B) It is a balanced binary tree
C) It is a binary search tree
D) It can have nodes with only one child
Answer: A) It is a complete binary tree
What happens to the structure of a heap after extracting the maximum element?
A) It remains the same
B) The last element is moved to the root
C) The heap is destroyed
D) It becomes a binary search tree
Answer: B) The last element is moved to the root
Which operation is not typically supported by heaps?
A) Insert
B) Delete
C) Find maximum
D) Find arbitrary element
Answer: D) Find arbitrary element
How are heaps typically represented in memory?
A) Using linked lists
B) Using arrays
C) Using hash tables
D) Using trees
Answer: B) Using arrays
What is the value of the root node in a min heap?
A) The maximum value
B) The minimum value
C) The average value
D) The median value
Answer: B) The minimum value
What is a d-ary heap?
A) A heap with d children per node
B) A type of binary heap
C) A complete binary tree
D) A linear heap
Answer: A) A heap with d children per node
Which of the following is a property of a max heap?
A) The left subtree is larger than the right subtree
B) The parent node is always less than the child nodes
C) The largest element is at the root
D) All leaf nodes are at the same level
Answer: C) The largest element is at the root
In a binary heap, what is the index of the left child of a node at index i?
A) 2i
B) 2i + 1
C) 2i + 2
D) i/2
Answer: A) 2i + 1
In a binary heap, what is the index of the right child of a node at index i?
A) 2i
B) 2i + 1
C) 2i + 2
D) i/2
Answer: C) 2i + 2
What is the index of the parent of a node at index i in a binary heap?
A) i/2
B) (i-1)/2
C) i + 1
D) i – 1
Answer: B) (i-1)/2
What is the purpose of a Fibonacci heap?
A) To improve the performance of the binary heap
B) To store elements in sorted order
C) To provide faster decrease-key operations
D) To maintain a balanced tree
Answer: C) To provide faster decrease-key operations
What is a priority queue?
A) A queue that maintains the order of insertion
B) A data structure that retrieves the highest priority element first
C) A stack that allows priority access
D) A regular queue
Answer: B) A data structure that retrieves the highest priority element first
What happens if you try to insert an element into a full binary heap?
A) It throws an error
B) It overwrites the root element
C) It becomes a min heap
D) It automatically expands
Answer: A) It throws an error
How does a binary heap differ from a binary search tree?
A) Heaps are sorted, while binary search trees are not
B) Heaps allow efficient access to the largest or smallest element
C) Binary search trees have a complete structure, while heaps do not
D) Both structures allow random access
Answer: B) Heaps allow efficient access to the largest or smallest element
What is the main advantage of using heaps over arrays for priority queues?
A) Heaps require less memory
B) Heaps allow for faster insertions and deletions
C) Heaps are always balanced
D) Heaps are easier to implement
Answer: B) Heaps allow for faster insertions and deletions
What is the use of a binary heap in the Dijkstra’s algorithm?
A) To store the graph
B) To efficiently retrieve the next node with the smallest distance
C) To keep track of visited nodes
D) To maintain the order of nodes
Answer: B) To efficiently retrieve the next node with the smallest distance
What is a skew heap?
A) A binary heap that is always complete
B) A binary heap that allows arbitrary structure
C) A self-adjusting heap
D) A balanced binary tree
Answer: C) A self-adjusting heap
What operation does the heapify function perform?
A) Constructs a heap from an array
B) Deletes the minimum element
C) Inserts a new element
D) Balances the heap
Answer: A) Constructs a heap from an array
What is the relationship between heaps and sorting algorithms?
A) Heaps cannot be used for sorting
B) Heaps are used in heap sort
C) Heaps always produce sorted data
D) Heaps require more time than other sorting algorithms
Answer: B) Heaps are used in heap sort
Which type of heap is best suited for implementing a priority queue?
A) Binary heap
B) Ternary heap
C) Fibonacci heap
D) All of the above
Answer: D) All of the above
What is the impact of deleting the root in a heap?
A) The heap is destroyed
B) The last element is moved to the root and heapify is performed
C) The heap remains unchanged
D) The entire heap must be rebuilt
Answer: B) The last element is moved to the root and heapify is performed
How does a pair of heaps differ from other heaps?
A) They maintain a balanced structure
B) They allow for fast merging of heaps
C) They are implemented using linked lists
D) They do not support priority queues
Answer: B) They allow for fast merging of heaps
What type of data structure can a binary heap be implemented as?
A) Array
B) Linked list
C) Tree
D) All of the above
Answer: A) Array
What is the main disadvantage of a Fibonacci heap?
A) It is difficult to implement
B) It uses too much memory
C) It is less efficient than binary heaps for all operations
D) It cannot be used for priority queues
Answer: A) It is difficult to implement
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