$1$ Part$1$: The maximum$-$subarray problem.

Design a solution$($Java code$)$ to get the maximum subarray $($subarray with the largest sum$)$ when a random integer subarray is given. Values of this subarray could be both positive and negative.

Apply both brute force and divide$-$and$-$conquer approaches to solve this problem on your own computer; what is the complexity of both approaches?

What problem size $n_0$ gives the crossover point at which the recursive algorithm beats the brute$-$force algorithm? Then, change the base case of the recursive algorithm to use the brute$-$force algorithm whenever the problem size is less than $n_0.$ Does that change the crossover point?