One example of a problem that can be solved using the divide and conquer algorithmic approach is the "Maximum Subarray Sum" problem.

  The problem statement is as follows: Given an array of integers, find a contiguous subarray with the largest sum.

  To solve this problem using the divide and conquer approach, we can divide the array into two halves and recursively find the maximum subarray sum in each half. Then, we check for the maximum subarray sum that crosses the middle point of the array. The maximum subarray sum would be either in the left half, right half, or crossing the middle.

  Here's a step-by-step approach to solving the problem using the divide and conquer algorithm:

  1. Divide the array into two halves, creating left and right subarrays.

  2. Recursively find the maximum subarray sum in the left and right subarrays.

  3. Find the maximum subarray sum that crosses the middle of the array. This can be done by starting from the middle element and expanding towards both ends, keeping track of the maximum sum encountered.

  4. Compare the maximum subarray sums obtained from steps 2 and 3, and return the maximum of the three values.

  For example, consider the array: [-2, 1, -3, 4, -1, 2, 1, -5, 4].

  1. Divide the array into two halves: [-2, 1, -3, 4] and [-1, 2, 1, -5, 4].

  2. Recursively find the maximum subarray sums in the left and right subarrays: 4 and 2.

  3. Find the maximum subarray sum that crosses the middle: From index 3 to 6, the sum is 6.

  4. Compare the maximum subarray sums from steps 2 and 3: The maximum is 6.

  Therefore, the maximum subarray sum is 6, achieved by the subarray [4, -1, 2, 1].

  This problem can be efficiently solved using the divide and conquer approach, as it reduces the problem size by half in each recursion, resulting in a time complexity of O(nlogn), where n is the size of the input array.