In java,

1. Implement a method that will search a given array using the linear search algorithm.

2. Implement a method that will search a given array using a recursive binary search algorithm.

Test the program for array sizes N = 16, 32, 64, 128, 256, 512, 1024, 2048, ......, 2²⁵. Initialize the array with random numbers between the ranges 1 through N and use the same array for testing linear search and binary search. Remember to sort the array before using binary search. Use a text file with 1,000 random numbers in the range 1 through 2²⁵ as the search keys.

Note that you have sort the input array before using the binary search algorithm, you can use any sort method available (e.g., sort method in the Java Collection Framework).

Update: the randomly generated numbers from 1 through N, cannot be repetitive.

the range is 1 through 2²⁵