Q. How does the insertion operation in an AVL tree differ from that in a Red-Black tree?
A.
AVL trees require more rotations
B.
Red-Black trees require more rotations
C.
Both require the same number of rotations
D.
Insertion is the same in both
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Solution
Insertion in an AVL tree may require more rotations to maintain balance compared to a Red-Black tree, which allows for a more relaxed balancing approach.
Correct Answer:
A
— AVL trees require more rotations
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Q. In an AVL tree, what is the maximum height difference between the left and right subtrees of any node?
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Solution
In an AVL tree, the height difference (balance factor) between the left and right subtrees of any node must be at most 1 to maintain balance.
Correct Answer:
B
— 1
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Q. What happens to the balance factor of an AVL tree node after a right rotation?
A.
It increases by 1.
B.
It decreases by 1.
C.
It remains the same.
D.
It becomes zero.
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Solution
After a right rotation, the balance factor of the node that was rotated down decreases by 1.
Correct Answer:
B
— It decreases by 1.
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Q. What is the primary reason for using a Red-Black tree over an AVL tree?
A.
Faster search times
B.
Faster insertion and deletion times
C.
Easier implementation
D.
More memory efficient
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Solution
Red-Black trees allow for faster insertion and deletion operations compared to AVL trees because they require fewer rotations to maintain balance.
Correct Answer:
B
— Faster insertion and deletion times
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Q. What is the worst-case time complexity for deletion in an AVL tree?
A.
O(n)
B.
O(log n)
C.
O(n log n)
D.
O(1)
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Solution
The worst-case time complexity for deletion in an AVL tree is O(log n) due to the tree's balanced structure.
Correct Answer:
B
— O(log n)
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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.
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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 scenarios would require a right rotation in an AVL tree?
A.
Left-Left case
B.
Right-Right case
C.
Left-Right case
D.
Right-Left case
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Solution
A right rotation is required in an AVL tree during a Left-Left case, where a node is inserted into the left subtree of the left child.
Correct Answer:
A
— Left-Left case
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Q. Which operation is NOT performed in a Red-Black tree during insertion?
A.
Coloring the new node red
B.
Rotating the tree
C.
Recoloring nodes
D.
Removing the root node
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Solution
Removing the root node is not an operation performed during the insertion process in a Red-Black tree.
Correct Answer:
D
— Removing the root node
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