I have been given an array of list of integers. I need to assume my first element is maximum contiguous sum. Then I have to find maximum contiguous sum of list excluding the first element. Then I have to see check if my assumed contiguous sum (the first element) is my real answer or I have to extend to the whole list. I need algorithm for this recursive method in JAVA.

For example:

A = {100, -50, 5, 3}

Assumed_sum (first element) = 100

Max_sum_from_subset_exculding_first_element = 8

But when I extend first element to the whole list, my sum is less than 100.

So, my contiguous sum is 100 which is my first element.

A = {100, -6, 5, 3}

Assumed_sum = 100

Max_sum_from_subset_excluding_first_element = 2

But when I extend first element to the whole list, my sum is 102.

So, my contiguous sum will be 102.