1. Write a program to calculate the nth Fibonacci number using dynamic programming.
2. Implement a function to find the longest increasing subsequence in an array.
3. Write a program to determine the minimum number of coins required to make a certain amount given an array of coin denominations.
4. Create a function that finds the maximum sum of non-adjacent elements in an array.
5. Write a program to solve the "0/1 Knapsack Problem" using dynamic programming.
6. Implement a function to compute the number of ways to climb a staircase with n steps when you can take 1 or 2 steps at a time.
7. Write a program to find the edit distance between two strings using dynamic programming.
8. Create a function to calculate the maximum profit from stock prices given in an array where you can buy and sell once.
9. Implement a program to find the number of unique paths in a grid from the top left to the bottom right corner.
10. Write a program to solve the "Longest Common Subsequence" problem.
11. Create a function to count the number of ways to partition a set into two subsets such that the sum of elements in both subsets is equal.
12. Implement a program to calculate the maximum product of a contiguous subarray in an array.
13. Write a function to find the number of ways to make change for a given amount using a given set of coins.
14. Create a program to determine if a string can be segmented into words from a given dictionary.
15. Implement a function to calculate the nth Catalan number using dynamic programming.
16. Write a program to find the minimum path sum in a grid from the top left to the bottom right corner.
17. Create a function to find the longest palindromic subsequence in a string.
18. Implement a program to solve the "Rod Cutting Problem" using dynamic programming.
19. Write a program to determine the number of ways to reach the top of a hill with a given number of steps.
20. Create a function to find the maximum sum of a contiguous subarray.
21. Implement a program to calculate the minimum edit distance to convert one string into another.
22. Write a function to find the longest common prefix among an array of strings.
23. Create a program to find the maximum sum of non-contiguous subarrays.
24. Implement a function to compute the minimum number of cuts needed to partition a string into palindromic substrings.
25. Write a program to solve the "Subset Sum Problem."
26. Create a function to count the number of subsets with a given sum in an array.
27. Implement a program to find the longest substring without repeating characters.
28. Write a function to find the longest substring that is a palindrome.
29. Create a program to calculate the minimum cost path in a weighted grid.
30. Implement a function to find the longest consecutive sequence in an array.
31. Write a program to find the minimum cost to cut a rod into pieces of given lengths.
32. Create a function to determine the number of binary search trees that can be formed with n nodes.
33. Implement a program to find the maximum length of a subarray with at most k distinct elements.
34. Write a function to count the number of ways to fill a knapsack with given weights.
35. Create a program to find the longest path in a directed acyclic graph (DAG).
36. Implement a function to find the minimum number of squares that sum to a given number.
37. Write a program to find the maximum sum of a subarray that does not contain a certain element.
38. Create a function to find the number of ways to arrange parentheses in a valid manner.
39. Implement a program to find the maximum value of an expression that can be obtained using the numbers in an array.
40. Write a function to compute the longest common subsequence of three strings.