1. Implement a function to perform fast Fourier transform (FFT) on a given sequence.
2. Write a function to solve the integer multiplication problem using Karatsuba's algorithm.
3. Given two arrays, find their median using the divide and conquer approach.
4. Implement a function to find the closest pair of points in a 3D space using divide and conquer.
5. Use divide and conquer to solve the maximum subarray problem and analyze the time complexity.
6. Given a set of points, implement the Chan's algorithm to find the convex hull in O(n log h) time.
7. Write a function to multiply two matrices using Strassen's algorithm.
8. Implement a function to find the longest increasing subsequence (LIS) with a time complexity of O(n log n).
9. Given a binary search tree, find the nearest common ancestor of two nodes using divide and conquer.
10. Write a function to find the longest palindromic subsequence in a string using divide and conquer.
11. Use divide and conquer to solve the "k-th largest element" problem in an unsorted array.
12. Given a string, implement an algorithm to find the longest substring with k unique characters.
13. Write a function to solve the fractional knapsack problem using a divide and conquer strategy.
14. Given a set of intervals, find the maximum number of non-overlapping intervals using divide and conquer.
15. Implement a function to solve the maximum sum rectangle in a 2D matrix using a divide and conquer approach.
16. Write a function to find the number of ways to partition a number into sums of positive integers using divide and conquer.
17. Given an array of integers, use a divide and conquer approach to count the number of inversions.
18. Implement a function to calculate the convex hull of a set of points using the divide and conquer technique.
19. Write a function to compute the median of two sorted arrays using the divide and conquer approach.
20. Use divide and conquer to solve the problem of finding the maximum product subarray.
21. Implement a function to find the longest common subsequence (LCS) among three strings using divide and conquer.
22. Given an array, find the longest contiguous subarray with a sum equal to zero using divide and conquer.
23. Write a function to find the minimum path sum in a grid from the top-left to the bottom-right corner using divide and conquer.
24. Implement a function to determine if a binary tree is height-balanced using divide and conquer.
25. Given a list of jobs with deadlines and profits, find the maximum profit that can be earned using a divide and conquer strategy.
26. Write a function to find the largest rectangle of 1s in a binary matrix using divide and conquer.
27. Implement a function to compute the optimal matrix chain multiplication order using divide and conquer.
28. Given a string, implement a function to check if it can be segmented into valid words from a dictionary using divide and conquer.
29. Use divide and conquer to find the maximum depth of a binary tree.
30. Implement a function to solve the word break problem using divide and conquer.
31. Given an array, find the longest increasing subsequence of length k using divide and conquer.
32. Write a function to check if a string is a rotation of another string using divide and conquer.
33. Implement a function to find the smallest and largest elements in an array using divide and conquer.
34. Use divide and conquer to solve the problem of finding the longest palindromic substring in a string.
35. Write a function to count the number of distinct characters in a string using divide and conquer.
36. Given an array of stock prices, find the maximum profit that can be made by buying and selling once using a divide and conquer strategy.
37. Implement a function to find the longest contiguous subarray with a product equal to a target using divide and conquer.
38. Write a function to count the number of unique paths from the top-left to the bottom-right corner of a grid with obstacles using divide and conquer.
39. Given a binary tree, find the diameter using a divide and conquer approach.
40. Implement a function to find the first non-repeating character in a string using divide and conquer.