1. What are the key differences between polynomial-time and exponential-time algorithms?
2. Explain the concept of NP-completeness and provide examples of NP-complete problems.
3. How does the Cook-Levin theorem establish the concept of NP-completeness?
4. Describe the significance of the P vs NP problem in computer science.
5. What is a randomized algorithm, and how does it differ from a deterministic algorithm?
6. Explain the Monte Carlo method and its applications in algorithm design.
7. What is the concept of approximation algorithms, and when are they used?
8. Discuss the trade-offs between time complexity and space complexity in algorithms.
9. What is a greedy algorithm, and under what conditions does it guarantee an optimal solution?
10. Describe the Bellman-Ford algorithm and its applications to graphs with negative weights.
11. Explain the concept of the dynamic programming paradigm and its key principles.
12. How do you solve the traveling salesman problem using dynamic programming?
13. What are FPT (Fixed Parameter Tractable) algorithms, and how do they differ from traditional algorithms?
14. Discuss the significance of polynomial-time reductions in complexity theory.
15. Explain the concept of linear programming and its use in optimization problems.
16. What is the simplex method, and how does it solve linear programming problems?
17. Describe the interior-point method for solving linear programming problems.
18. What are the applications of the Hungarian algorithm in combinatorial optimization?
19. How does the Floyd-Warshall algorithm find all pairs shortest paths, and what is its time complexity?
20. Discuss the role of flow networks in solving the maximum flow problem.
21. Explain the concept of a min-cut and its relationship to max-flow in networks.
22. What is the significance of the Ford-Fulkerson method in network flow problems?
23. Describe the Karp-Sipser algorithm for finding maximum matchings in bipartite graphs.
24. What is the significance of amortized analysis in algorithm design?
25. Explain the concept of a hash function and its properties.
26. How does a bloom filter work, and what are its advantages and limitations?
27. Describe the significance of the randomized quicksort algorithm and its average-case performance.
28. What is a suffix tree, and how is it constructed and utilized in string processing?
29. Explain the Rabin-Karp algorithm for substring search and its hashing mechanism.
30. Discuss the applications of the Knuth-Morris-Pratt algorithm in string matching.
31. How does the Boyer-Moore algorithm improve substring search efficiency?
32. What is a segment tree, and how does it enable efficient range queries?
33. Explain the concept of a Fenwick tree (binary indexed tree) and its applications.
34. What are the characteristics of a red-black tree, and how does it maintain balance?
35. Describe the AVL tree balancing mechanism and its rotations.
36. What is the significance of the B-tree in database indexing?
37. Explain the concept of a skip list and its probabilistic balancing.
38. Discuss the role of backtracking algorithms in solving combinatorial problems.
39. How does the branch-and-bound technique work in optimization problems?
40. What is a decision tree, and how is it used in machine learning?