Binary Search Tree Quiz
Questions and Solutions​
1. What is a binary search tree (BST)?​
- Options:
- A) A tree where each node has at most two children.
- B) A tree where the left child is greater than the parent.
- C) A tree where the left child is less than the parent and the right child is greater.
- D) A tree where all nodes are on one side.
- Answer: C) A tree where the left child is less than the parent and the right child is greater.
- Explanation: In a BST, each node's left child is less than the node, and the right child is greater, maintaining the sorted order.
2. What is the time complexity for searching an element in a balanced binary search tree?​
- Options:
- A) O(n)
- B) O(log n)
- C) O(n log n)
- D) O(1)
- Answer: B) O(log n)
- Explanation: In a balanced BST, the height of the tree is log(n), making search operations efficient at O(log n).
3. Which of the following is true about the in-order traversal of a binary search tree?​
- Options:
- A) It visits the nodes in descending order.
- B) It visits the nodes in ascending order.
- C) It visits nodes in random order.
- D) It does not visit all nodes.
- Answer: B) It visits the nodes in ascending order.
- Explanation: In-order traversal of a BST visits nodes in ascending order due to the property of BST.
4. Which operation in a binary search tree can have a worst-case time complexity of O(n)?​
- Options:
- A) Insertion
- B) Deletion
- C) Searching
- D) All of the above
- Answer: D) All of the above
- Explanation: In the worst case, all operations can degrade to O(n) if the tree becomes unbalanced.
5. What is the maximum number of nodes in a binary search tree with a height of 'h'?​
- Options:
- A) h
- B) 2^h - 1
- C) 2^h
- D) h^2
- Answer: B) 2^h - 1
- Explanation: A binary tree with height h can have at most 2^h - 1 nodes, which is full at height h.
6. Which of the following traversals can be used to get a sorted order of elements in a binary search tree?​
- Options:
- A) Pre-order
- B) In-order
- C) Post-order
- D) Level-order
- Answer: B) In-order
- Explanation: In-order traversal yields a sorted order of elements in a BST.
7. In a binary search tree, what would happen if you tried to insert a duplicate value?​
- Options:
- A) It will replace the existing value.
- B) It will be ignored.
- C) It will cause an error.
- D) It will create a duplicate node.
- Answer: B) It will be ignored.
- Explanation: BSTs typically do not allow duplicate values, so the insertion of a duplicate is ignored.
8. What is the time complexity for finding the lowest common ancestor (LCA) of two nodes in a binary search tree?​
- Options:
- A) O(n)
- B) O(log n)
- C) O(h)
- D) O(1)
- Answer: C) O(h)
- Explanation: Finding the LCA can take O(h) time, where h is the height of the tree, depending on the position of the nodes.
9. Which of the following operations requires tree rotation in a binary search tree?​
- Options:
- A) Insertion
- B) Deletion
- C) Balancing
- D) Both A and B
- Answer: C) Balancing
- Explanation: Rotations are needed during insertion and deletion to maintain balance in self-balancing BSTs.
10. How can you check if a binary tree is a binary search tree?​
- Options:
- A) By checking if in-order traversal is sorted.
- B) By checking if all nodes have two children.
- C) By checking if all nodes have unique values.
- D) By performing a pre-order traversal.
- Answer: A) By checking if in-order traversal is sorted.
- Explanation: If the in-order traversal of the tree is sorted, it confirms that the tree is a valid BST.