Data Structures & Algorithms for Competitive Exam Prep

Data Structures & Algorithms

Q. In a queue implemented using an array, what is the time complexity of enqueue operation in the worst case?

A. O(1)
B. O(n)
C. O(log n)
D. O(n^2)

Solution

In the worst case, if the array is full and needs to be resized, the enqueue operation can take O(n) time.

Correct Answer: B — O(n)

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Q. In a queue implemented using two stacks, what is the time complexity of the dequeue operation in the worst case?

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

Solution

In the worst case, the dequeue operation may require transferring all elements from one stack to another, resulting in O(n) time complexity.

Correct Answer: B — O(n)

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Q. In a queue implemented using two stacks, what is the worst-case time complexity for the dequeue operation?

A. O(1)
B. O(n)
C. O(log n)
D. O(n^2)

Solution

In the worst case, the dequeue operation may require transferring all elements from one stack to another, resulting in a time complexity of O(n).

Correct Answer: B — O(n)

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Q. In a queue, what happens when an element is dequeued?

A. It is removed from the front
B. It is removed from the back
C. It is moved to the front
D. It is added to the back

Solution

In a queue, the dequeue operation removes the element from the front, following the FIFO principle.

Correct Answer: A — It is removed from the front

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Q. In a queue, what is the time complexity of dequeuing an element?

A. O(1)
B. O(n)
C. O(log n)
D. O(n^2)

Solution

Dequeuing an element from a queue is done in constant time, O(1), when implemented using a linked list.

Correct Answer: A — O(1)

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Q. In a queue, what is the time complexity of enqueue operation?

A. O(1)
B. O(n)
C. O(log n)
D. O(n^2)

Solution

The enqueue operation in a queue can be performed in constant time, O(1).

Correct Answer: A — O(1)

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Q. In a queue, what operation is used to remove an element?

A. Push
B. Pop
C. Enqueue
D. Dequeue

Solution

The operation used to remove an element from a queue is called 'Dequeue'.

Correct Answer: D — Dequeue

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Q. In a queue, which operation is performed in constant time?

A. Enqueue
B. Dequeue
C. Peek
D. All of the above

Solution

All operations (enqueue, dequeue, and peek) can be performed in constant time O(1) in a properly implemented queue.

Correct Answer: D — All of the above

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Q. In a queue, which operation is performed to remove an element?

A. Push
B. Pop
C. Enqueue
D. Dequeue

Solution

The operation to remove an element from a queue is called Dequeue, following the FIFO (First In, First Out) principle.

Correct Answer: D — Dequeue

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Q. In a queue, which operation is used to remove an element?

A. Push
B. Pop
C. Enqueue
D. Dequeue

Solution

The operation used to remove an element from a queue is called Dequeue.

Correct Answer: D — Dequeue

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Q. In a recursive implementation of binary search, what is the base case?

A. When the array is empty
B. When the target is found
C. When the left index exceeds the right index
D. When the mid index is zero

Solution

The base case for recursion in binary search is when the left index exceeds the right index, indicating the target is not found.

Correct Answer: C — When the left index exceeds the right index

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Q. In a Red-Black tree, what color can the root node be?

A. Red
B. Black
C. Either Red or Black
D. None of the above

Solution

The root node of a Red-Black tree must always be black to maintain the properties of the tree.

Correct Answer: B — Black

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Q. In a Red-Black tree, what color is the root node required to be?

A. Red
B. Black
C. Either red or black
D. None of the above

Solution

The root node of a Red-Black tree is required to be black, which is one of the properties that help maintain the balance of the tree.

Correct Answer: B — Black

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Q. In a Red-Black tree, what color is the root node?

A. Red
B. Black
C. Green
D. Blue

Solution

The root of a Red-Black tree is always black to maintain the properties of the tree.

Correct Answer: B — Black

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Q. In a Red-Black tree, what happens when a red node is inserted as a child of another red node?

A. The tree remains valid.
B. The tree is immediately balanced.
C. A recoloring and rotation may be needed.
D. The insertion is not allowed.

Solution

When a red node is inserted as a child of another red node, a recoloring and possibly a rotation are needed to maintain the properties of the Red-Black tree.

Correct Answer: C — A recoloring and rotation may be needed.

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Q. In a Red-Black tree, what happens when a red node is inserted?

A. It is always the root.
B. It may cause a violation of Red-Black properties.
C. It is always a leaf.
D. It cannot be inserted.

Solution

Inserting a red node may cause a violation of the Red-Black properties, requiring adjustments.

Correct Answer: B — It may cause a violation of Red-Black properties.

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Q. In a Red-Black tree, what is the maximum height of the tree in terms of the number of nodes n?

A. 2n
B. n
C. log(n)
D. 2 * log(n)

Solution

The maximum height of a Red-Black tree is 2 * log(n), ensuring that the tree remains balanced.

Correct Answer: D — 2 * log(n)

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Q. In a Red-Black tree, what is the maximum number of black nodes on any path from the root to a leaf?

A. 1
B. 2
C. 3
D. It can vary.

Solution

In a Red-Black tree, the number of black nodes can vary, but every path from the root to the leaves must have the same number of black nodes.

Correct Answer: D — It can vary.

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Q. In a Red-Black tree, what must be true about the children of a red node?

A. They must be red.
B. They must be black.
C. They can be either color.
D. They must be leaf nodes.

Solution

In a Red-Black tree, the children of a red node must be black to maintain the tree's properties.

Correct Answer: B — They must be black.

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Q. In a Red-Black Tree, what must be true about the path from any node to its descendant leaves?

A. All paths must have the same number of black nodes
B. All paths must have the same number of red nodes
C. All paths must alternate colors
D. All paths must have at least one red node

Solution

In a Red-Black Tree, every path from a node to its descendant leaves must have the same number of black nodes.

Correct Answer: A — All paths must have the same number of black nodes

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Q. In a Red-Black Tree, what must be true about the path from the root to any leaf?

A. All paths must have the same number of black nodes.
B. All paths must have the same number of red nodes.
C. All paths must have the same number of total nodes.
D. All paths must alternate colors.

Solution

In a Red-Black Tree, every path from the root to any leaf must have the same number of black nodes to maintain balance.

Correct Answer: A — All paths must have the same number of black nodes.

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Q. In a Red-Black tree, what property ensures that no two red nodes are adjacent?

A. Root property
B. Red property
C. Black property
D. Leaf property

Solution

The Red property of Red-Black trees states that no two red nodes can be adjacent, ensuring that the tree remains balanced.

Correct Answer: B — Red property

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Q. In a Red-Black tree, what property ensures that the tree remains approximately balanced?

A. Every node is either red or black
B. The root is always black
C. Every red node must have two black children
D. All leaves are black

Solution

In a Red-Black tree, every red node must have two black children, which helps maintain balance and ensures that no path from the root to a leaf is more than twice as long as any other such path.

Correct Answer: C — Every red node must have two black children

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Q. In a Red-Black tree, what property ensures that the tree remains balanced?

A. Every node has two children
B. The root is always black
C. No two red nodes can be adjacent
D. All leaves are at the same level

Solution

In a Red-Black tree, no two red nodes can be adjacent, which helps maintain balance and ensures that the longest path from the root to a leaf is no more than twice as long as the shortest path.

Correct Answer: C — No two red nodes can be adjacent

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Q. In a Red-Black Tree, what property must be maintained after an insertion?

A. The tree must be a complete binary tree
B. The root must always be red
C. Every path from a node to its descendant leaves must have the same number of black nodes
D. All leaves must be red

Solution

In a Red-Black Tree, every path from a node to its descendant leaves must have the same number of black nodes.

Correct Answer: C — Every path from a node to its descendant leaves must have the same number of black nodes

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Q. In a Red-Black tree, what property must be maintained after every insertion?

A. The tree must be complete.
B. The tree must be balanced.
C. The root must always be black.
D. All leaves must be red.

Solution

In a Red-Black tree, the root must always be black to maintain the properties of the tree.

Correct Answer: C — The root must always be black.

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Q. In a singly linked list, how can you find the middle element in one pass?

A. Use two pointers
B. Count nodes first
C. Use recursion
D. Use a stack

Solution

By using two pointers, where one moves twice as fast as the other, you can find the middle element in one pass.

Correct Answer: A — Use two pointers

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Q. In a singly linked list, how do you access the last element?

A. Direct access
B. Iterate from the head
C. Use a tail pointer
D. Access via index

Solution

In a singly linked list, you must iterate from the head to access the last element, as there is no direct access.

Correct Answer: B — Iterate from the head

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Q. In a singly linked list, how do you delete a node given only access to that node?

A. Set the node to null
B. Copy the next node's data
C. Change the previous node's pointer
D. You cannot delete it

Solution

To delete a node in a singly linked list when you only have access to that node, you can copy the data from the next node and then delete the next node.

Correct Answer: B — Copy the next node's data

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Q. In a singly linked list, how do you find the middle element?

A. Traverse the list twice
B. Use two pointers
C. Count elements first
D. Use a stack

Solution

Using two pointers, where one moves twice as fast as the other, allows you to find the middle element in O(n) time.

Correct Answer: B — Use two pointers

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Data Structures & Algorithms

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