Q. In which scenario would a Red-Black tree be preferred over an AVL tree?
A.
When frequent insertions and deletions are expected.
B.
When memory usage is a critical factor.
C.
When the dataset is static and does not change.
D.
When the tree needs to be perfectly balanced.
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Solution
Red-Black trees are generally preferred when there are frequent insertions and deletions because they are less rigidly balanced than AVL trees, allowing for faster insertions and deletions.
Correct Answer:
A
— When frequent insertions and deletions are expected.
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Q. What is the main application of AVL trees in computer science?
A.
Database indexing
B.
Memory management
C.
Network routing
D.
File compression
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Solution
AVL trees are commonly used in database indexing due to their efficient search, insert, and delete operations.
Correct Answer:
A
— Database indexing
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Q. What is the main disadvantage of AVL trees compared to Red-Black trees?
A.
AVL trees require more rotations during insertions and deletions.
B.
AVL trees are less memory efficient.
C.
AVL trees cannot store duplicate values.
D.
AVL trees are harder to implement.
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Solution
AVL trees require more rotations during insertions and deletions to maintain balance, making them less efficient in scenarios with frequent updates.
Correct Answer:
A
— AVL trees require more rotations during insertions and deletions.
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Q. What is the primary advantage of using an AVL tree over a regular binary search tree?
A.
AVL trees are easier to implement.
B.
AVL trees maintain a balanced height, ensuring O(log n) time complexity for search operations.
C.
AVL trees allow duplicate values.
D.
AVL trees require less memory.
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Solution
AVL trees maintain a balanced height, which ensures that search operations can be performed in O(log n) time, unlike regular binary search trees which can degrade to O(n) in the worst case.
Correct Answer:
B
— AVL trees maintain a balanced height, ensuring O(log n) time complexity for search operations.
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Q. What is the time complexity for searching an element in a balanced AVL tree?
A.
O(n)
B.
O(log n)
C.
O(n log n)
D.
O(1)
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Solution
The time complexity for searching an element in a balanced AVL tree is O(log n) due to its balanced nature.
Correct Answer:
B
— O(log n)
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Q. Which of the following is a common application of AVL trees?
A.
Implementing a priority queue.
B.
Maintaining a sorted list of items.
C.
Storing data in a hash table.
D.
Implementing a stack.
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Solution
AVL trees are commonly used to maintain a sorted list of items due to their efficient search, insertion, and deletion operations.
Correct Answer:
B
— Maintaining a sorted list of items.
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Q. Which of the following is NOT a property of AVL trees?
A.
The heights of two child subtrees of any node differ by at most one
B.
Every node is colored either red or black
C.
In-order traversal yields sorted order
D.
The tree is a binary search tree
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Solution
AVL trees do not have a coloring property; that is a characteristic of Red-Black trees.
Correct Answer:
B
— Every node is colored either red or black
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Q. Which of the following properties is NOT true for Red-Black trees?
A.
Every node is either red or black.
B.
The root is always black.
C.
All leaves (NIL nodes) are red.
D.
Red nodes cannot have red children.
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Solution
In Red-Black trees, all leaves (NIL nodes) are black, not red. This is one of the properties that helps maintain balance.
Correct Answer:
C
— All leaves (NIL nodes) are red.
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Q. Which of the following properties is true for Red-Black trees?
A.
Every node is either red or black
B.
The root must be red
C.
All leaves are black
D.
Both A and C
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Solution
In Red-Black trees, every node is either red or black, and all leaves (NIL nodes) are black, ensuring balanced properties.
Correct Answer:
D
— Both A and C
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Q. Which of the following statements about Red-Black trees is true?
A.
They are always perfectly balanced.
B.
They can have a maximum of two consecutive red nodes.
C.
They are faster for search operations than AVL trees.
D.
They require more memory than AVL trees.
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Solution
In Red-Black trees, a red node cannot have a red child, which means they can have a maximum of one consecutive red node.
Correct Answer:
B
— They can have a maximum of two consecutive red nodes.
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Q. Which operation is more efficient in a Red-Black tree compared to an AVL tree?
A.
Searching
B.
Insertion
C.
Deletion
D.
All of the above
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Solution
Insertion operations in Red-Black trees are generally more efficient than in AVL trees due to fewer rotations required.
Correct Answer:
B
— Insertion
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Q. Which operation is more efficient in an AVL tree compared to a Red-Black tree?
A.
Insertion
B.
Deletion
C.
Searching
D.
All of the above
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Solution
Searching is more efficient in AVL trees because they are more strictly balanced than Red-Black trees, leading to a shorter height.
Correct Answer:
C
— Searching
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