Data Structures & Algorithms for Competitive Exam Prep

Data Structures & Algorithms

Q. Which of the following statements about binary trees is true?

A. A binary tree can have at most two children per node.
B. A binary tree must be balanced.
C. A binary tree can only have integer values.
D. A binary tree cannot be empty.

Solution

A binary tree is defined as a tree data structure in which each node has at most two children, often referred to as the left and right child.

Correct Answer: A — A binary tree can have at most two children per node.

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Q. Which of the following statements about DFS is true?

A. It can be implemented using a queue
B. It is not suitable for large graphs
C. It can be implemented using recursion
D. It always finds the shortest path

Solution

DFS can be implemented using recursion, which is a common approach in many algorithms.

Correct Answer: C — It can be implemented using recursion

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Q. Which of the following statements about Dijkstra's algorithm is true?

A. It can handle negative weight edges.
B. It always finds the shortest path.
C. It is a depth-first search algorithm.
D. It can be used for unweighted graphs only.

Solution

Dijkstra's algorithm always finds the shortest path in graphs with non-negative weights.

Correct Answer: B — It always finds the shortest path.

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Q. Which of the following statements about Heap Sort is true?

A. It is a stable sort
B. It is an in-place sort
C. It is faster than Quick Sort
D. It requires O(n^2) time in the worst case

Solution

Heap Sort is an in-place sorting algorithm, meaning it requires only a constant amount of additional space.

Correct Answer: B — It is an in-place sort

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Q. Which of the following statements about Quick Sort is true?

A. It is stable
B. It can be implemented using a linked list
C. It always selects the median as pivot
D. It has a worst-case time complexity of O(n log n)

Solution

Quick Sort can be implemented using a linked list, but it is not stable and does not always select the median as pivot.

Correct Answer: B — It can be implemented using a linked list

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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.

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 of the following statements about stacks is true?

A. Stacks can be implemented using arrays or linked lists.
B. Stacks allow random access to elements.
C. Stacks are FIFO data structures.
D. Stacks can only store integers.

Solution

Stacks can indeed be implemented using both arrays and linked lists, while they follow LIFO (Last In, First Out) order.

Correct Answer: A — Stacks can be implemented using arrays or linked lists.

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Q. Which of the following statements is false regarding AVL trees?

A. They are a type of self-balancing binary search tree.
B. They can become unbalanced after insertion or deletion.
C. They require more rotations than Red-Black trees.
D. They can have duplicate values.

Solution

AVL trees do not allow duplicate values; they maintain a strict binary search tree property.

Correct Answer: D — They can have duplicate values.

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Q. Which of the following statements is true about AVL and Red-Black Trees?

A. AVL trees are faster for search operations than Red-Black trees
B. Red-Black trees are always more balanced than AVL trees
C. Both trees have the same height for n nodes
D. AVL trees require more memory than Red-Black trees

Solution

AVL trees are generally faster for search operations due to their stricter balancing, while Red-Black trees may require more memory due to their additional color attribute.

Correct Answer: A — AVL trees are faster for search operations than Red-Black trees

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Q. Which of the following statements is true about AVL trees?

A. They are always complete binary trees.
B. They can have duplicate values.
C. They are more rigidly balanced than Red-Black trees.
D. They require more memory than binary search trees.

Solution

AVL trees are more rigidly balanced than Red-Black trees, which helps in maintaining faster search times.

Correct Answer: C — They are more rigidly balanced than Red-Black trees.

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Q. Which of the following statements is true about binary search?

A. It can be used on unsorted arrays
B. It requires a sorted array
C. It is slower than linear search
D. It can only find unique elements

Solution

Binary search requires a sorted array to function correctly.

Correct Answer: B — It requires a sorted array

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Q. Which of the following statements is true about DFS?

A. It can be implemented using a queue.
B. It is not suitable for finding shortest paths.
C. It always uses less memory than BFS.
D. It visits nodes in level order.

Solution

DFS is not suitable for finding shortest paths in unweighted graphs as it does not explore all neighbors at the current depth before going deeper.

Correct Answer: B — It is not suitable for finding shortest paths.

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Q. Which of the following statements is true about Dijkstra's algorithm?

A. It can handle negative weight edges.
B. It always finds the shortest path.
C. It can be used for directed graphs only.
D. It requires a complete graph.

Solution

Dijkstra's algorithm always finds the shortest path in graphs with non-negative weights.

Correct Answer: B — It always finds the shortest path.

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Q. Which of the following statements is true about dynamic programming?

A. It is only applicable to optimization problems
B. It can be used for both optimization and counting problems
C. It is always faster than greedy algorithms
D. It requires a sorted input

Solution

Dynamic programming can be applied to both optimization and counting problems, making it versatile in problem-solving.

Correct Answer: B — It can be used for both optimization and counting problems

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Q. Which of the following statements is true about Red-Black trees?

A. They are always perfectly balanced
B. They can have a height of up to 2*log(n+1)
C. They require more memory than AVL trees
D. They are not suitable for dynamic datasets

Solution

In Red-Black trees, the height can be up to 2*log(n+1), which allows for efficient operations while not being perfectly balanced.

Correct Answer: B — They can have a height of up to 2*log(n+1)

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Q. Which of the following statements is true about the height of an AVL tree?

A. It can be greater than log(n)
B. It is always less than or equal to 1.44 log(n)
C. It is always equal to log(n)
D. It can be less than log(n)

Solution

The height of an AVL tree is guaranteed to be less than or equal to 1.44 log(n), ensuring efficient operations.

Correct Answer: B — It is always less than or equal to 1.44 log(n)

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Q. Which of the following statements is true regarding BFS?

A. It can be implemented using a stack
B. It can find the shortest path in weighted graphs
C. It uses a queue for traversal
D. It is faster than DFS in all cases

Solution

BFS uses a queue for traversal, allowing it to explore all neighbors at the present depth before moving on.

Correct Answer: C — It uses a queue for traversal

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Q. Which of the following statements is true regarding the balancing of AVL trees?

A. They require fewer rotations than Red-Black trees
B. They are always balanced after every insertion
C. They can become unbalanced after deletion
D. They do not require balancing at all

Solution

AVL trees can become unbalanced after deletion, requiring rebalancing through rotations.

Correct Answer: C — They can become unbalanced after deletion

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Q. Which of the following statements is true regarding the time complexity of DFS?

A. O(V + E)
B. O(V^2)
C. O(E log V)
D. O(V log V)

Solution

The time complexity of DFS is O(V + E) as it visits each vertex and edge once.

Correct Answer: A — O(V + E)

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Q. Which of the following techniques is commonly used in dynamic programming to build solutions?

A. Divide and conquer
B. Greedy algorithms
C. Bottom-up approach
D. Brute force

Solution

The bottom-up approach is commonly used in dynamic programming to build solutions iteratively from smaller subproblems.

Correct Answer: C — Bottom-up approach

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Q. Which of the following traversal methods can be implemented using a stack?

A. In-order
B. Pre-order
C. Post-order
D. All of the above

Solution

All three traversal methods can be implemented using a stack, either explicitly or through the call stack in recursion.

Correct Answer: D — All of the above

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Q. Which of the following traversal methods can be used to create a mirror image of a binary tree?

A. Pre-order
B. In-order
C. Post-order
D. All of the above

Solution

Any of the traversal methods (pre-order, in-order, post-order) can be used to create a mirror image of a binary tree.

Correct Answer: D — All of the above

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Q. Which of the following traversal methods can be used to obtain a sorted order of a binary search tree?

A. Pre-order
B. In-order
C. Post-order
D. Level-order

Solution

In-order traversal of a binary search tree visits nodes in sorted order, as it processes the left subtree, then the root, and finally the right subtree.

Correct Answer: B — In-order

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Q. Which of the following traversal methods can be used to obtain a sorted order of elements in a binary search tree?

A. Pre-order
B. Post-order
C. In-order
D. Level-order

Solution

In-order traversal of a binary search tree visits nodes in sorted order, making it the correct choice.

Correct Answer: C — In-order

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Q. Which of the following traversal methods can be used to print the nodes of a binary tree level by level?

A. In-order
B. Pre-order
C. Post-order
D. Level-order

Solution

Level-order traversal visits nodes level by level, making it suitable for printing nodes in that order.

Correct Answer: D — Level-order

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Q. Which of the following traversal methods uses a queue data structure?

A. In-order
B. Pre-order
C. Post-order
D. Level-order

Solution

Level-order traversal uses a queue to keep track of nodes at the current level before moving to the next level.

Correct Answer: D — Level-order

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Q. Which of the following traversal methods uses a queue?

A. Inorder
B. Preorder
C. Postorder
D. Level Order

Solution

Level Order traversal uses a queue to keep track of nodes at each level.

Correct Answer: D — Level Order

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Q. Which operation is guaranteed to be O(log n) in a Red-Black tree?

A. Insertion
B. Deletion
C. Searching
D. All of the above

Solution

All fundamental operations (insertion, deletion, and searching) in a Red-Black tree are guaranteed to be O(log n) due to the tree's balanced structure.

Correct Answer: D — All of the above

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Q. Which operation is guaranteed to be O(log n) in an AVL tree?

A. Insertion
B. Deletion
C. Searching
D. All of the above

Solution

All of the operations (insertion, deletion, and searching) in an AVL tree are guaranteed to be O(log n) due to its balanced structure.

Correct Answer: D — All of the above

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Q. Which operation is guaranteed to be O(log n) in both AVL and Red-Black trees?

A. Insertion
B. Deletion
C. Searching
D. All of the above

Solution

All of the operations (insertion, deletion, and searching) are guaranteed to be O(log n) in both AVL and Red-Black trees.

Correct Answer: D — All of the above

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Data Structures & Algorithms

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