In a 'Maximum Subarray Problem', given an array A of integers, the task is to find a contiguous subarray of A such that the sum of the values in the subarray is the maximum. Here, there is no restriction on the size of the subarray that has maximum sum or the nature of integers in the array or the subarray. Design and analyze an efficient algorithm for each of the following variants of the problem:

a) Result is a contiguous subarray whose sum is the maximum and the length is minimal.

b) Result is a contiguous subarray of non-negative integers whose sum is the maximum and the length is minimal.

c) Input is an array of non-negative integers (zero inclusive). Result is contiguous subarray whose sum is the maximum and the length is minimal.

d) Result is a non-contiguous subarray whose sum is the maximum.

Only pseudocode is required in written format...(no actual code in any language)

pls provide with logic, illustration, pseudocode, proof of correctness and time complexity calculations......all needed.