B. There are many ways to find the maximum element in an array and you have no doubt seen an iterative algorithm for it. The divide-and-conquer approach is to divide an array into two halves (as in merge sort), get the maximum of each half, then compare those two maxima to return the larger.

• Write pseudocode using the book's notation expressing the approach just given
• Implement that algorithm in Java >= 8 or Python >= 3.7. Call the program either DCMaximum.java or dcmaximum.py and write it so that it takes as input a file called numbers.txt. It should print the maximum of the values in that file.
• Write down the recurrence relation that computes the number of comparisons between array elements performed by this algorithm.
• Solve the recurrence relation using the recursion tree method.