Data Structures & Algorithms for Competitive Exam Prep

Data Structures & Algorithms

Q. How does the balancing factor of an AVL tree node get calculated?

A. Height of left subtree - height of right subtree
B. Height of right subtree - height of left subtree
C. Number of nodes in left subtree - number of nodes in right subtree
D. Number of nodes in right subtree - number of nodes in left subtree

Solution

The balancing factor of an AVL tree node is calculated as the height of the left subtree minus the height of the right subtree.

Correct Answer: A — Height of left subtree - height of right subtree

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Q. How does the balancing of an AVL tree differ from that of a Red-Black tree?

A. AVL trees are more rigidly balanced than Red-Black trees
B. Red-Black trees are always perfectly balanced
C. AVL trees allow more flexibility in balancing
D. There is no difference

Solution

AVL trees are more rigidly balanced than Red-Black trees, which allows AVL trees to provide faster lookups at the cost of more complex insertions and deletions.

Correct Answer: A — AVL trees are more rigidly balanced than Red-Black trees

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Q. How does the height of an AVL tree compare to that of a Red-Black tree?

A. AVL trees are always shorter.
B. Red-Black trees are always shorter.
C. They have the same height.
D. AVL trees are shorter in the worst case.

Solution

AVL trees are more strictly balanced, which can lead to a shorter height compared to Red-Black trees in the worst case.

Correct Answer: D — AVL trees are shorter in the worst case.

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Q. How does the insertion operation in a Red-Black Tree differ from that in an AVL Tree?

A. Red-Black Trees require fewer rotations
B. AVL Trees allow duplicate values
C. Red-Black Trees are always balanced
D. AVL Trees are faster for insertion

Solution

Insertion in Red-Black Trees typically requires fewer rotations compared to AVL Trees.

Correct Answer: A — Red-Black Trees require fewer rotations

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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

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. How does the presence of duplicate elements affect the binary search algorithm?

A. It has no effect
B. It slows down the search
C. It can return any index of the duplicates
D. It makes the search impossible

Solution

Binary search can return any index of the duplicates, as it does not guarantee which duplicate will be found first.

Correct Answer: C — It can return any index of the duplicates

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Q. How does the time complexity of searching in a Red-Black Tree compare to that in an AVL Tree?

A. Red-Black Tree is faster
B. AVL Tree is faster
C. Both have the same time complexity
D. It depends on the implementation

Solution

Both Red-Black Trees and AVL Trees have a search time complexity of O(log n).

Correct Answer: C — Both have the same time complexity

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Q. How does the time complexity of searching in a Red-Black Tree compare to that of an AVL Tree?

A. Red-Black is faster
B. AVL is faster
C. Both have the same complexity
D. Red-Black is slower

Solution

Both Red-Black Trees and AVL Trees have a search time complexity of O(log n).

Correct Answer: C — Both have the same complexity

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Q. How many colors are used in a Red-Black tree?

A. One
B. Two
C. Three
D. Four

Solution

A Red-Black tree uses two colors: red and black, to maintain balance and ensure properties.

Correct Answer: B — Two

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Q. How many comparisons does binary search make in the worst case for an array of size 16?

A. 4
B. 5
C. 6
D. 7

Solution

The worst-case number of comparisons is log2(16) = 4, but since we start counting from 0, it takes 5 comparisons.

Correct Answer: D — 7

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Q. How many comparisons does binary search make in the worst case for an array of size n?

A. n
B. log n
C. n log n
D. 1

Solution

In the worst case, binary search makes log n comparisons to find the target or determine its absence.

Correct Answer: B — log n

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Q. How many leaf nodes can a binary tree with n internal nodes have?

A. n + 1
B. n
C. 2n
D. n - 1

Solution

A binary tree with n internal nodes can have n + 1 leaf nodes.

Correct Answer: A — n + 1

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Q. How many leaf nodes can a full binary tree with n internal nodes have?

A. n + 1
B. n
C. 2n
D. n/2

Solution

A full binary tree with n internal nodes has n + 1 leaf nodes.

Correct Answer: A — n + 1

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Q. How many leaf nodes does a full binary tree with 'n' internal nodes have?

A. n
B. n + 1
C. 2n
D. n/2

Solution

A full binary tree with 'n' internal nodes has 'n + 1' leaf nodes.

Correct Answer: B — n + 1

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Q. How many nodes are there in a full binary tree of height h?

A. h
B. 2^h
C. 2^(h+1) - 1
D. 2^h - 1

Solution

A full binary tree of height h has 2^(h+1) - 1 nodes.

Correct Answer: C — 2^(h+1) - 1

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Q. How many rotations are needed in the worst case for a single insertion in an AVL tree?

A. 1
B. 2
C. 3
D. 4

Solution

In the worst case, a single insertion in an AVL tree may require up to 2 rotations to maintain balance.

Correct Answer: B — 2

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Q. How many rotations are needed in the worst case for balancing an AVL tree after an insertion?

A. 1
B. 2
C. 3
D. 0

Solution

In the worst case, 2 rotations may be needed to balance an AVL tree after an insertion.

Correct Answer: B — 2

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Q. How many rotations are needed in the worst case to balance an AVL tree after an insertion?

A. 1
B. 2
C. 3
D. None

Solution

In the worst case, 2 rotations may be needed to balance an AVL tree after an insertion.

Correct Answer: B — 2

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Q. How many rotations are needed in the worst case when inserting a node in an AVL tree?

A. 1
B. 2
C. 3
D. 4

Solution

In the worst case, at most 2 rotations are needed to maintain the balance of an AVL tree after insertion.

Correct Answer: B — 2

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Q. How many rotations are needed in the worst case when inserting a node into an AVL tree?

A. 1
B. 2
C. 3
D. 4

Solution

In the worst case, inserting a node into an AVL tree may require up to 2 rotations to restore balance.

Correct Answer: C — 3

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Q. How many rotations are needed to balance an AVL tree after a single insertion?

A. 0
B. 1
C. 2
D. 3

Solution

Typically, only one rotation is needed to balance an AVL tree after a single insertion, unless it is a double rotation case.

Correct Answer: B — 1

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Q. How many rotations are needed to balance an AVL tree after an insertion?

A. At most one.
B. At most two.
C. At most three.
D. No rotations are needed.

Solution

At most two rotations are needed to balance an AVL tree after an insertion, depending on the case of imbalance.

Correct Answer: B — At most two.

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Q. How many rotations are required in the worst case for balancing an AVL tree after an insertion?

A. 1
B. 2
C. 3
D. 0

Solution

In the worst case, 2 rotations may be required to balance an AVL tree after an insertion.

Correct Answer: B — 2

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Q. How many rotations are required in the worst case to balance an AVL tree after an insertion?

A. 1
B. 2
C. 3
D. 4

Solution

In the worst case, 2 rotations are required to balance an AVL tree after an insertion.

Correct Answer: B — 2

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Q. How many rotations are required in the worst case when inserting a node in a Red-Black Tree?

A. 0
B. 1
C. 2
D. 3

Solution

In the worst case, up to 2 rotations may be required to maintain the properties of a Red-Black Tree after insertion.

Correct Answer: C — 2

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Q. How many rotations are required in the worst case when inserting a node in an AVL tree?

A. 1
B. 2
C. 3
D. 4

Solution

In the worst case, only 1 or 2 rotations are required to maintain the balance of an AVL tree after insertion.

Correct Answer: B — 2

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Q. How many rotations are required in the worst case when inserting a node into an AVL tree?

A. 1
B. 2
C. 3
D. 4

Solution

In the worst case, inserting a node into an AVL tree may require up to 2 rotations to maintain balance.

Correct Answer: B — 2

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Q. If a binary search algorithm is implemented recursively, what is its space complexity due to recursion?

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

Solution

The space complexity of a recursive binary search is O(log n) due to the call stack.

Correct Answer: B — O(log n)

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Q. If a binary search algorithm is implemented recursively, what is the space complexity?

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

Solution

The space complexity is O(log n) due to the recursive call stack.

Correct Answer: B — O(log n)

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Q. If a binary search algorithm is implemented recursively, what is the space complexity due to recursion?

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

Solution

The space complexity of a recursive binary search is O(log n) due to the call stack used for recursion.

Correct Answer: B — O(log n)

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Data Structures & Algorithms

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