You are given an array of integers. Your task is to find the maximum sum that can be obtained by selecting a contiguous subarray of elements within the array.

Provide two different algorithms to solve the problem using the following approaches:

Naive Approach: Write a naive algorithm that iterates through all possible subarrays and calculates their sums. Return the maximum sum found among all subarrays.

Divide and Conquer Approach: Write a divide and conquer algorithm that efficiently solves the problem by recursively dividing the array into smaller subproblems, finding the maximum sum subarray in each subproblem, and combining the results to find the maximum sum subarray for the entire array.

Provide the asymptotic time complexity analysis for both approaches.