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Topological Sort, Transform and Conquer, Balanced Search Trees MCQs

1. What is the time complexity of Topological Sort using DFS?

a) O(V) b) O(E) c) O(V + E) d) O(V log E)

2. Which of the following is true about Topological Sort?

a) It is only applicable to undirected graphs. b) It is used to sort vertices in a Directed Acyclic Graph (DAG). c) It has a time complexity of O(V²). d) It is used to find the shortest path in a graph.

3. What is the main idea behind Transform and Conquer: Presorting?

a) To solve problems by transforming them into a simpler form. b) To sort the input data before applying a problem-solving algorithm. c) To divide the problem into smaller subproblems. d) To use dynamic programming to solve the problem.

4. Which of the following is an example of Transform and Conquer: Presorting?

a) Merge Sort b) Binary Search c) Quick Sort d) Insertion Sort

5. What is the time complexity of finding the minimum and maximum in an unsorted array?

a) O(1) b) O(log n) c) O(n) d) O(n log n)

6. Which of the following is a balanced search tree?

a) Binary Search Tree b) AVL Tree c) Red-Black Tree d) Both b and c

7. What is the time complexity of searching in a balanced search tree?

a) O(1) b) O(log n) c) O(n) d) O(n log n)

8. Which of the following is true about AVL Trees?

a) They are unbalanced binary search trees. b) They maintain a balance factor of -1, 0, or 1 for each node. c) They have a worst-case time complexity of O(n) for search operations. d) They do not support insertion and deletion operations.

9. What is the time complexity of inserting an element into a Red-Black Tree?

a) O(1) b) O(log n) c) O(n) d) O(n log n)

10. Which of the following is true about Transform and Conquer?

a) It is used to solve problems by transforming them into a simpler form. b) It is used to divide the problem into smaller subproblems. c) It is used to solve problems using dynamic programming. d) It is used to solve problems using brute force.

11. What is the time complexity of finding the minimum and maximum in a sorted array?

a) O(1) b) O(log n) c) O(n) d) O(n log n)

12. Which of the following is true about Red-Black Trees?

a) They are unbalanced binary search trees. b) They maintain a balance factor of -1, 0, or 1 for each node. c) They have a worst-case time complexity of O(n) for search operations. d) They ensure that the tree remains balanced after insertions and deletions.

13. What is the time complexity of deleting an element from a balanced search tree?

a) O(1) b) O(log n) c) O(n) d) O(n log n)

14. Which of the following is true about Presorting?

a) It is used to solve problems by transforming them into a simpler form. b) It is used to sort the input data before applying a problem-solving algorithm. c) It is used to divide the problem into smaller subproblems. d) It is used to solve problems using dynamic programming.

15. What is the time complexity of finding the minimum and maximum in a balanced search tree?

a) O(1) b) O(log n) c) O(n) d) O(n log n)

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