JNTUK B.Tech 2-1(R23) Advanced Data Structures and Algorithms Important Questions are now available, by preparing these questions you cab get good marks in your external exams. Here you can find all JNTUK R23 syllabus, important questions, materials, previous year papers. In the questions given below, the Blooms Taxonomy levels are show after the questions.
UNIT-I
2-Mark Questions:
1. Define the terms "space complexity" and "time complexity." [Knowledge]
2. Explain the difference between big O, big Omega, and big Theta notations. [Comprehension]
3. Insert the value 25 into an AVL tree with nodes containing 10, 20, and 30. [Application]
4. Analyze the worst-case time complexity of the AVL tree insertion algorithm. [Analysis]
5. Design an algorithm to find the height of a B-tree. [Synthesis]
6. Discuss the advantages and disadvantages of using AVL trees for database indexing. [Evaluation]
10-Mark Questions:
1. Explain the concept of asymptotic notation and its importance in algorithm analysis. [Comprehension]
2. Implement the AVL tree insertion algorithm using a programming language of your choice. [Application]
3. Prove the correctness of the B-tree insertion algorithm using mathematical induction. [Analysis]
4. Design an algorithm to find the median element in an AVL tree. [Synthesis]
5. Compare and contrast the performance of AVL trees and B-trees for different types of data and operations. [Evaluation]
6. Design a hybrid data structure that combines the advantages of AVL trees and B-trees. [Synthesis]
7. Analyze the space complexity of the B-tree search algorithm. [Analysis]
8. Implement the B-tree deletion algorithm using a programming language of your choice. [Application]
9. Design a data structure that supports efficient range queries on a set of integers. [Synthesis]
10. Discuss the trade-offs between space and time complexity when choosing between AVL trees and B-trees for a particular application. [Evaluation]
UNIT-II
2-Mark Questions:
1. Define a heap and its properties. [Knowledge]
2. Explain the difference between a min heap and a max heap.[Comprehension]
3. Build a max heap from the following elements: 10, 20, 30, 40, 50. [Application]
4. Analyze the time complexity of the heap sort algorithm.[Analysis]
5. Design an algorithm to find the k-th smallest element in a max heap.[Synthesis]
6. Discuss the advantages and disadvantages of using heaps for implementing priority queues. [Evaluation]
7. Define the terms "vertex," "edge," and "degree" in graph theory.[Knowledge]
8. Explain the difference between adjacency list and adjacency matrix representations of graphs.[Comprehension]
9. Perform a depth-first search on the following graph, starting from vertex A. [Application]
10. Analyze the time complexity of Dijkstra's algorithm for finding the shortest path in a graph. [Analysis]
10-Mark Questions:
1. Explain the concept of heap and its applications in various algorithms. [Comprehension]
2. Implement the heap sort algorithm using a programming language of your choice. [Application]
3. Prove the correctness of the heap sort algorithm using mathematical induction. [Analysis]
4. Design a data structure that supports efficient insertion, deletion, and finding the minimum element in a dynamic set of elements.[Synthesis]
5. Compare and contrast the performance of heaps and AVL trees for implementing priority queues.[Evaluation]
6. Explain the concept of graph traversal and its applications.[Comprehension]
7. Implement Dijkstra's algorithm for finding the shortest path in a graph.[Application]
8. Analyze the space complexity of the breadth-first search algorithm.[Analysis]
9. Design an algorithm to detect cycles in a directed graph.[Synthesis]
10. Discuss the trade-offs between different graph representations (adjacency list vs. adjacency matrix) for various graph algorithms.[Evaluation]
11. Define the divide-and-conquer paradigm.[Knowledge]
12. Explain the steps involved in the divide-and-conquer approach.[Comprehension]
13. Implement the quick sort algorithm using a programming language of your choice.[Application]
14. Analyze the worst-case and average-case time complexity of the quick sort algorithm.[Analysis]
15. Design a divide-and-conquer algorithm to find the closest pair of points in a plane.[Synthesis]
16. Compare and contrast the performance of quick sort and merge sort for different types of input data.[Evaluation]
17. Define the term "convex hull." [Knowledge]
18. Explain the Graham scan algorithm for finding the convex hull of a set of points.[Comprehension]
UNIT-III
2-Mark Questions:
1. Define the greedy method and its principle.[Knowledge]
2. Explain the difference between the 0/1 knapsack problem and the fractional knapsack problem. Comprehension]
3. Solve the job sequencing with deadlines problem for the following jobs: (Job, Profit, Deadline) = {(1, 20, 2), (2, 15, 1), (3, 10, 3)}.[Application]
4. Analyze the time complexity of Kruskal's algorithm for finding the minimum spanning tree.[Analysis]
5. Design a greedy algorithm to find the minimum number of coins required to make a given amount of change.[Synthesis]
6. Discuss the advantages and disadvantages of the greedy method compared to other algorithms.[Evaluation]
7. Define dynamic programming and its principle. [Knowledge]
8. Explain the concept of memoization in dynamic programming.[Comprehension]
9. Solve the 0/1 knapsack problem using dynamic programming for the following items: (Item, Weight, Value) = {(1, 2, 20), (2, 3, 30), (3, 4, 40)}.[Application]
10. Analyze the time complexity of the Bellman-Ford algorithm for finding the shortest paths in a graph.[Analysis]
10-Mark Questions:
1. Explain the greedy method and its applications in various optimization problems.[Comprehension]
2. Implement the Dijkstra's algorithm for finding the shortest paths in a graph using a programming language of your choice.[Application]
3. Prove the correctness of Prim's algorithm for finding the minimum spanning tree using mathematical induction.[Analysis]
4. Design a greedy algorithm to solve the fractional knapsack problem. [Synthesis]
5. Compare and contrast the greedy method and dynamic programming for solving optimization problems. [Evaluation]
6. Explain the concept of dynamic programming and its applications in various algorithms. [Comprehension]
7. Implement the Floyd-Warshall algorithm for finding all pairs shortest paths in a graph using a programming language of your choice.[Application]
8. Analyze the space complexity of the dynamic programming solution for the 0/1 knapsack problem. [Analysis]
9. Design a dynamic programming algorithm to solve the string editing problem. [Synthesis]
10. Discuss the trade-offs between the greedy method and dynamic programming for solving the traveling salesman problem.[Evaluation]
UNIT-IV
2-Mark Questions:
1. Define backtracking and its principle.[Knowledge]
2. Explain the concept of pruning in backtracking. [Comprehension]
3. Solve the 8-queens problem using backtracking. [Application]
4. Analyze the time complexity of the backtracking solution for the sum of subsets problem. [Analysis]
5. Design a backtracking algorithm to solve the graph coloring problem. [Synthesis]
6. Discuss the advantages and disadvantages of backtracking compared to other algorithms. [Evaluation]
7. Define branch and bound and its principle. [Knowledge]
8. Explain the concept of bounding in branch and bound. [Comprehension]
9. Solve the 0/1 knapsack problem using branch and bound. [Application]
10. Analyze the time complexity of the branch and bound solution for the traveling salesman problem. [Analysis]
10-Mark Questions:
1. Explain the backtracking algorithm and its applications in various problems. [Comprehension]
2. Implement the backtracking solution for the graph coloring problem using a programming language of your choice. [Application]
3. Prove the correctness of the backtracking solution for the 8-queens problem. [Analysis]
4. Design a backtracking algorithm to solve the Hamiltonian cycle problem. [Synthesis]
5. Compare and contrast the backtracking algorithm and dynamic programming for solving the 0/1 knapsack problem. [Evaluation]
6. Explain the branch and bound algorithm and its applications in various optimization problems. [Comprehension]
7. Implement the branch and bound solution for the traveling salesman problem using a programming language of your choice. [Application]
8. Analyze the space complexity of the branch and bound solution for the 0/1 knapsack problem. [Analysis]
9. Design a branch and bound algorithm to solve the job shop scheduling problem. [Synthesis]
10. Discuss the trade-offs between backtracking and branch and bound for solving optimization problems. [Evaluation]
UNIT-V
2-Mark Questions:
1. Define the terms "NP-hard" and "NP-complete." [Knowledge]
2. Explain the significance of Cook's theorem. [Comprehension]
3. Determine whether the following problem is in NP: Given a graph G and an integer k, does G have a clique of size k? [Application]
4. Analyze the complexity of the clique decision problem. [Analysis]
5. Prove that the chromatic number decision problem is NP-hard. [Synthesis]
6. Discuss the implications of the NP-completeness of the traveling salesman problem. [Evaluation]
7. Define the scheduling identical processors problem.[Knowledge]
8. Explain the difference between the job shop scheduling problem and the flow shop scheduling problem. [Comprehension]
9. Solve the scheduling identical processors problem for the following jobs with processing times: 2, 3, 4, 5.[Application]
10. Analyze the complexity of the job shop scheduling problem. [Analysis]
10-Mark Questions:
1. Explain the concept of NP-completeness and its implications for algorithm design.[Comprehension]
2. Prove that the 3-SAT problem is NP-complete. [Application]
3. Analyze the complexity of the chromatic number decision problem.[Analysis]
4. Prove that the traveling salesman problem is NP-hard.[Synthesis]
5. Discuss the practical implications of the NP-hardness of the scheduling identical processors problem. [Evaluation]
6. Explain the concept of approximation algorithms for NP-hard problems. [Comprehension]
7. Design an approximation algorithm for the traveling salesman problem. [Application]
8. Analyze the performance guarantee of the approximation algorithm for the traveling salesman problem. [Analysis]
9. Prove that the job shop scheduling problem is NP-hard. [Synthesis]
10. Discuss the trade-offs between exact algorithms and approximation algorithms for NP-hard problems.[Evaluation]