1. Write a program to solve a system of linear equations using matrix methods.
2. Write a program to implement the Fast Fourier Transform algorithm.
3. Write a program to calculate the least common multiple (LCM) of multiple numbers.
4. Write a program to find the determinant of a matrix using recursion.
5. Write a program to implement the Sieve of Eratosthenes to find all prime numbers up to n.
6. Write a program to calculate the eigenvalues and eigenvectors of a matrix.
7. Write a program to implement Dijkstra’s algorithm for shortest paths in a graph.
8. Write a program to find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm.
9. Write a program to solve a quadratic equation using the quadratic formula.
10. Write a program to compute the Fibonacci sequence using matrix exponentiation.
11. Write a program to find the inverse of a matrix using the Gauss-Jordan elimination method.
12. Write a program to implement the Newton-Raphson method for finding roots of equations.
13. Write a program to generate the first n terms of the Catalan numbers.
14. Write a program to compute the convex hull of a set of points using the Graham scan algorithm.
15. Write a program to find the number of unique paths in a grid using dynamic programming.
16. Write a program to implement the A* algorithm for pathfinding in a grid.
17. Write a program to calculate the area under a curve using numerical integration (e.g., Trapezoidal rule).
18. Write a program to solve the traveling salesman problem using dynamic programming.
19. Write a program to calculate the power set of a set of numbers.
20. Write a program to find the largest prime factor of a given number.
21. Write a program to compute the factorial of a number using memoization.
22. Write a program to determine if a number is a perfect number.
23. Write a program to find the intersection of two arrays.
24. Write a program to calculate the binomial coefficient (n choose k).
25. Write a program to implement Kruskal’s algorithm for minimum spanning tree.
26. Write a program to calculate the sum of all digits in a large number.
27. Write a program to determine if a number is a strong prime.
28. Write a program to find the longest increasing subsequence in an array.
29. Write a program to compute the n-th Fibonacci number using Binet's formula.
30. Write a program to find all prime numbers in a given range using segmented sieve.
31. Write a program to generate all possible subsets of a given set.
32. Write a program to calculate the convex hull of a set of points in 2D space.
33. Write a program to determine if a number is an Armstrong number.
34. Write a program to solve a magic square of size n.
35. Write a program to find the number of ways to make change for a given amount.
36. Write a program to implement the Monte Carlo method for estimating pi.
37. Write a program to calculate the sum of a series (e.g., Taylor series).
38. Write a program to find the largest product of three integers in an array.
39. Write a program to implement the Floyd-Warshall algorithm for all pairs shortest paths.
40. Write a program to find the nth prime number.