Data Structures & Algorithms for Competitive Exam Prep

Data Structures & Algorithms

Q. Which of the following is true about a complete binary tree?

A. All levels are fully filled except possibly the last level.
B. All nodes have two children.
C. It is always balanced.
D. It has a maximum height of log n.

Solution

In a complete binary tree, all levels are fully filled except possibly the last level, which is filled from left to right.

Correct Answer: A — All levels are fully filled except possibly the last level.

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Q. Which of the following is true about a doubly linked list?

A. Each node has one pointer
B. Nodes can be traversed in both directions
C. It uses less memory than a singly linked list
D. It is always sorted

Solution

A doubly linked list allows traversal in both directions because each node has two pointers.

Correct Answer: B — Nodes can be traversed in both directions

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Q. Which of the following is true about a queue?

A. LIFO structure
B. FIFO structure
C. Random access
D. None of the above

Solution

A queue is a FIFO (First In, First Out) data structure.

Correct Answer: B — FIFO structure

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Q. Which of the following is true about a stack?

A. Elements can be accessed in any order
B. Elements are removed in FIFO order
C. Elements are removed in LIFO order
D. None of the above

Solution

In a stack, elements are removed in LIFO (Last In, First Out) order.

Correct Answer: C — Elements are removed in LIFO order

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Q. Which of the following is true about arrays?

A. They can grow dynamically
B. They allow random access
C. They are always faster than linked lists
D. They require more memory than linked lists

Solution

Arrays allow random access to elements using indices, which is a key feature that differentiates them from linked lists.

Correct Answer: B — They allow random access

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Q. Which of the following is true about AVL trees compared to Red-Black trees?

A. AVL trees are faster for lookup operations.
B. Red-Black trees are faster for lookup operations.
C. Both have the same performance.
D. AVL trees are easier to implement.

Solution

AVL trees are generally faster for lookup operations due to their stricter balancing.

Correct Answer: A — AVL trees are faster for lookup operations.

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Q. Which of the following is true about BFS?

A. It uses a stack
B. It finds the shortest path in unweighted graphs
C. It is faster than DFS
D. It cannot be implemented recursively

Solution

BFS finds the shortest path in unweighted graphs by exploring all neighbors at the present depth prior to moving on to nodes at the next depth level.

Correct Answer: B — It finds the shortest path in unweighted graphs

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Q. Which of the following is true about DFS?

A. It can be implemented using recursion
B. It always finds the shortest path
C. It uses a queue
D. It is not suitable for cyclic graphs

Solution

DFS can be implemented using recursion, as it explores each branch of the graph until it reaches a leaf node.

Correct Answer: A — It can be implemented using recursion

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Q. Which of the following is true about linked lists compared to arrays?

A. Linked lists have a fixed size
B. Arrays allow dynamic resizing
C. Linked lists allow efficient insertions/deletions
D. Arrays are more memory efficient

Solution

Linked lists allow efficient insertions and deletions as they do not require shifting elements like arrays do.

Correct Answer: C — Linked lists allow efficient insertions/deletions

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Q. Which of the following is true about Quick Sort?

A. It is always faster than Merge Sort
B. It is not in-place
C. It can be implemented using recursion
D. It is stable

Solution

Quick Sort can be implemented using recursion, although it is not a stable sorting algorithm.

Correct Answer: C — It can be implemented using recursion

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Q. Which of the following is true about Red-Black Trees?

A. They are always perfectly balanced
B. They can have a maximum height of 2 log n
C. They guarantee O(log n) time for all operations
D. They require more memory than AVL trees

Solution

Red-Black Trees guarantee O(log n) time complexity for search, insertion, and deletion operations due to their balancing properties.

Correct Answer: C — They guarantee O(log n) time for all operations

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Q. Which of the following is true about the balancing of AVL trees?

A. They require rotations to maintain balance after insertions and deletions.
B. They do not require any balancing.
C. They can only be balanced by deleting nodes.
D. They are always balanced after every insertion.

Solution

AVL trees require rotations to maintain balance after insertions and deletions to ensure that the balance factor remains within the allowed range.

Correct Answer: A — They require rotations to maintain balance after insertions and deletions.

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Q. Which of the following is true about the height of a binary tree with n nodes?

A. Height = n
B. Height = log n
C. Height <= n
D. Height = n/2

Solution

The height of a binary tree with n nodes can be at most n in the case of a skewed tree, hence Height <= n.

Correct Answer: C — Height <= n

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Q. Which of the following is true about the height of a binary tree?

A. Height is the number of nodes in the longest path from root to leaf
B. Height is the number of edges in the longest path from root to leaf
C. Height is always equal to the number of levels in the tree
D. Height can be negative

Solution

The height of a binary tree is defined as the number of edges in the longest path from the root to a leaf node.

Correct Answer: B — Height is the number of edges in the longest path from root to leaf

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Q. Which of the following is true about the height of a Red-Black tree?

A. It can be at most twice the height of an AVL tree.
B. It is always equal to the height of a binary search tree.
C. It is always less than or equal to log(n).
D. It can be greater than the height of an AVL tree.

Solution

The height of a Red-Black tree can be at most twice the height of an AVL tree, making it less balanced.

Correct Answer: A — It can be at most twice the height of an AVL tree.

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Q. Which of the following is true about the inorder traversal of a binary search tree?

A. It visits nodes in random order.
B. It visits nodes in descending order.
C. It visits nodes in ascending order.
D. It visits only the leaf nodes.

Solution

Inorder traversal of a binary search tree visits nodes in ascending order.

Correct Answer: C — It visits nodes in ascending order.

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Q. Which of the following is true about the level-order traversal of a binary tree?

A. It is depth-first
B. It uses a stack
C. It visits nodes level by level
D. It is faster than in-order traversal

Solution

Level-order traversal visits nodes level by level, typically implemented using a queue.

Correct Answer: C — It visits nodes level by level

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Q. Which of the following is true about the performance of AVL trees?

A. Faster than Red-Black Trees for all operations
B. Slower than Red-Black Trees for all operations
C. Faster for search operations but slower for insertions
D. Slower for search operations but faster for insertions

Solution

AVL trees provide faster search operations due to their stricter balancing, but they can be slower for insertions and deletions because they may require more rotations.

Correct Answer: C — Faster for search operations but slower for insertions

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Q. Which of the following modifications can be made to binary search to find the first occurrence of a target value?

A. Change the comparison operator
B. Use a different data structure
C. Modify the mid-point calculation
D. Continue searching left after finding the target

Solution

To find the first occurrence, continue searching to the left even after finding the target value.

Correct Answer: D — Continue searching left after finding the target

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Q. Which of the following operations can be performed in constant time on an array?

A. Insertion at end
B. Deletion from beginning
C. Accessing an element
D. Insertion at beginning

Solution

Accessing an element in an array by its index is done in constant time, O(1).

Correct Answer: C — Accessing an element

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Q. Which of the following operations can be performed in O(1) time on a linked list?

A. Insertion at the end
B. Deletion from the beginning
C. Searching for an element
D. Traversal

Solution

Deletion from the beginning of a linked list can be done in O(1) time as it only requires updating the head pointer.

Correct Answer: B — Deletion from the beginning

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Q. Which of the following operations can be performed in O(1) time on a stack?

A. Push
B. Pop
C. Peek
D. All of the above

Solution

All operations (push, pop, and peek) can be performed in O(1) time on a stack.

Correct Answer: D — All of the above

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Q. Which of the following operations can cause a violation of the AVL tree property?

A. Insertion of a node.
B. Deletion of a node.
C. Both insertion and deletion.
D. Traversal of the tree.

Solution

Both insertion and deletion can cause the AVL tree to become unbalanced, requiring rebalancing operations.

Correct Answer: C — Both insertion and deletion.

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Q. Which of the following operations can cause an imbalance in an AVL tree?

A. Insertion
B. Deletion
C. Both Insertion and Deletion
D. Traversal

Solution

Both insertion and deletion operations can cause an imbalance in an AVL tree, requiring rebalancing.

Correct Answer: C — Both Insertion and Deletion

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Q. Which of the following operations has a time complexity of O(1) in a stack?

A. Push
B. Pop
C. Peek
D. All of the above

Solution

All operations (Push, Pop, and Peek) in a stack are performed in constant time, O(1).

Correct Answer: D — All of the above

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Q. Which of the following operations has a time complexity of O(n) in a linked list?

A. Accessing an element
B. Inserting at the end
C. Deleting a node
D. Searching for a value

Solution

Searching for a value in a linked list requires traversing the list, which takes O(n) time in the worst case.

Correct Answer: D — Searching for a value

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Q. Which of the following operations has a time complexity of O(n) in a singly linked list?

A. Insertion at head
B. Insertion at tail
C. Deletion at head
D. Accessing an element by index

Solution

Accessing an element by index in a singly linked list requires traversing the list, which takes O(n) time.

Correct Answer: D — Accessing an element by index

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Q. Which of the following operations has a time complexity of O(n) in a stack?

A. Push
B. Pop
C. Peek
D. None of the above

Solution

All basic operations (Push, Pop, Peek) in a stack have a time complexity of O(1). Therefore, the correct answer is 'None of the above'.

Correct Answer: D — None of the above

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Q. Which of the following operations has the worst time complexity in a singly linked list?

A. Accessing an element
B. Inserting an element
C. Deleting an element
D. Traversing the list

Solution

Accessing an element in a singly linked list requires traversal from the head to the desired node, which takes O(n) time in the worst case.

Correct Answer: A — Accessing an element

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Q. Which of the following operations is guaranteed to be O(log n) in an AVL tree?

A. Insertion
B. Deletion
C. Searching
D. All of the above

Solution

All operations (insertion, deletion, and searching) in an AVL tree are guaranteed to be O(log n) due to the tree's balanced nature.

Correct Answer: D — All of the above

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Data Structures & Algorithms

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