1. Implement a binary search algorithm for a sorted array.
2. Write a function that finds the square root of a number using binary search.
3. Create a program to search for a target value in a rotated sorted array.
4. Implement an algorithm to find the peak element in an array using binary search.
5. Write a function to search for a range of indices for a given target in a sorted array.
6. Create a program that finds the first and last occurrence of a number in a sorted array.
7. Implement an algorithm to find the smallest missing positive integer in an array.
8. Write a function that checks if a number is a Fibonacci number using binary search.
9. Create a program that finds the closest element to a target in a sorted array.
10. Implement an algorithm to count the number of occurrences of a number in a sorted array.
11. Write a function to find the k-th largest element in an unsorted array.
12. Create a program that searches for a value in a 2D matrix.
13. Implement a function that finds the longest increasing subsequence in an array.
14. Write a program to find the first duplicate number in an unsorted array.
15. Create an algorithm to find the intersection of two arrays.
16. Implement a function to check if a string can be rearranged to form a palindrome.
17. Write a program that finds all anagrams of a string from a list of words.
18. Create a function that finds the longest substring without repeating characters.
19. Implement an algorithm to perform ternary search on a sorted array.
20. Write a function that checks if two strings are permutations of each other.
21. Create a program that finds the longest common prefix string among an array of strings.
22. Implement a function to determine if a word exists in a crossword puzzle.
23. Write a program to search for a pattern in a text using the Rabin-Karp algorithm.
24. Create a function that finds the maximum element in a bitonic array.
25. Implement an algorithm to find the first occurrence of a string in another string.
26. Write a function that checks if a number is prime using a searching method.
27. Create a program to search for the longest palindrome in a string.
28. Implement a function that finds the longest substring with at most k distinct characters.
29. Write a program to find the median of two sorted arrays.
30. Create an algorithm to search for an element in a nearly sorted array.
31. Implement a function that finds the majority element in an array.
32. Write a program to find the count of distinct elements in a sliding window.
33. Create a function that finds all unique triplets in an array that sum up to zero.
34. Implement an algorithm to find the two numbers that sum to a specific target.
35. Write a program that searches for a path in a maze using backtracking.
36. Create a function that finds the longest substring with exactly k distinct characters.
37. Implement an algorithm to check if a number exists in a sorted rotated array.
38. Write a program that finds the missing number from an array of n-1 integers.
39. Create a function that checks if a sequence of numbers can form an arithmetic progression.
40. Implement a program to search for a value in a linked list.