1. Write a program to implement the A* algorithm for pathfinding on a grid.
2. Write a program to find the maximum sum rectangle in a 2D matrix.
3. Write a program to implement the K-means clustering algorithm.
4. Write a program to find the longest palindromic substring using Manacher's algorithm.
5. Write a program to calculate the number of unique paths in a grid with obstacles using dynamic programming.
6. Write a program to implement the LRU cache using a doubly linked list and a hash map.
7. Write a program to serialize and deserialize a binary tree using a queue.
8. Write a program to find all strongly connected components in a directed graph using Tarjan's algorithm.
9. Write a program to implement a self-balancing binary search tree (AVL tree).
10. Write a program to implement the Fast Fourier Transform (FFT) algorithm.
11. Write a program to calculate the nth Fibonacci number using matrix exponentiation.
12. Write a program to find the minimum spanning tree of a graph using Prim's algorithm.
13. Write a program to implement the KMP string matching algorithm.
14. Write a program to find the maximum flow in a flow network using the Edmonds-Karp algorithm.
15. Write a program to implement a trie data structure and perform insert and search operations.
16. Write a program to solve the N-Queens problem using backtracking.
17. Write a program to find the longest increasing subsequence using binary search.
18. Write a program to implement the Bellman-Ford algorithm for finding shortest paths in a graph.
19. Write a program to find the shortest path in an unweighted graph using BFS.
20. Write a program to implement a bloom filter.
21. Write a program to perform a topological sort on a directed acyclic graph (DAG).
22. Write a program to calculate the edit distance between two strings using dynamic programming.
23. Write a program to implement the Ford-Fulkerson method for computing maximum flow.
24. Write a program to solve the knapsack problem using dynamic programming.
25. Write a program to implement a binary search tree with insert, delete, and search functions.
26. Write a program to find the longest common subsequence between two strings using dynamic programming.
27. Write a program to perform integer factorization using Pollard's rho algorithm.
28. Write a program to implement the sieve of Eratosthenes to generate prime numbers.
29. Write a program to find the next permutation of a sequence of numbers.
30. Write a program to calculate the least common multiple (LCM) of two numbers.
31. Write a program to implement the Rabin-Karp algorithm for substring search.
32. Write a program to find the maximum subarray sum using the divide and conquer approach.
33. Write a program to implement the Z-algorithm for substring search.
34. Write a program to calculate the probability of winning a game using dynamic programming.
35. Write a program to find the longest path in a directed acyclic graph.
36. Write a program to implement the dynamic programming approach to solve the coin change problem.
37. Write a program to find the maximum product subarray in an array.
38. Write a program to implement the Knuth-Morris-Pratt (KMP) string matching algorithm.
39. Write a program to calculate the number of unique paths in a grid with obstacles using memoization.
40. Write a program to implement a segment tree for range queries.