Q. In a Red-Black tree, what property must be maintained after every insertion?
-
A.
The tree must be complete.
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B.
The tree must be balanced.
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C.
The root must always be black.
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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 terms of balancing, how do AVL trees differ from Red-Black trees?
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A.
AVL trees are less strict
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B.
Red-Black trees are more strict
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C.
AVL trees are more strict
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D.
They are identical
Solution
AVL trees are more strictly balanced than Red-Black trees, which allows for faster lookups.
Correct Answer:
C
— AVL trees are more strict
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Q. What is the average time complexity for searching in an AVL tree?
-
A.
O(n)
-
B.
O(log n)
-
C.
O(n log n)
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D.
O(1)
Solution
The average time complexity for searching in an AVL tree is O(log n) due to its balanced structure.
Correct Answer:
B
— O(log n)
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Q. What is the maximum number of nodes in a Red-Black tree of height h?
-
A.
2^h
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B.
2^(h+1)-1
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C.
h^2
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D.
h!
Solution
The maximum number of nodes in a Red-Black tree of height h is 2^(h+1)-1.
Correct Answer:
B
— 2^(h+1)-1
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Q. What is the time complexity for deleting an element from an AVL tree?
-
A.
O(n)
-
B.
O(log n)
-
C.
O(n log n)
-
D.
O(1)
Solution
Deleting an element from an AVL tree also takes O(log n) time, as it may require rebalancing.
Correct Answer:
B
— O(log n)
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Q. What is the time complexity of inserting an element into an AVL tree?
-
A.
O(n)
-
B.
O(log n)
-
C.
O(n log n)
-
D.
O(1)
Solution
Inserting an element into an AVL tree takes O(log n) time due to the need to maintain balance after insertion.
Correct Answer:
B
— O(log n)
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Q. What is the worst-case time complexity for searching an element in a Red-Black Tree?
-
A.
O(n)
-
B.
O(log n)
-
C.
O(n log n)
-
D.
O(1)
Solution
The worst-case time complexity for searching an element in a Red-Black Tree is O(log n) due to its balanced nature.
Correct Answer:
B
— O(log n)
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Q. Which operation is more expensive in terms of time complexity in AVL trees compared to Red-Black trees?
-
A.
Insertion
-
B.
Deletion
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C.
Searching
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D.
All of the above
Solution
Deletion in AVL trees can be more expensive due to the need for multiple rotations to maintain balance.
Correct Answer:
B
— Deletion
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Q. Which tree structure allows for faster insertion and deletion operations?
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A.
AVL Tree
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B.
Red-Black Tree
-
C.
Both are equal
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D.
Neither
Solution
Red-Black Trees generally allow for faster insertion and deletion operations compared to AVL Trees due to fewer rotations.
Correct Answer:
B
— Red-Black Tree
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