Problem Description
You are given an integer array nums. The value of this array is defined as the sum of |nums[i] - nums[i + 1]| for all 0 <= i < nums.length - 1. You are allowed to select any subarray of the given array and reverse it. You can perform this operation only once. Find the maximum possible value of the final array.
Key Insights
- The value of the array depends on the differences between adjacent elements.
- Reversing a subarray can change the differences between elements both inside and outside the reversed section.
- It is essential to evaluate the impact of reversing every possible subarray on the overall array value.
- The goal is to maximize the total sum of absolute differences after one reversal.
Space and Time Complexity
Time Complexity: O(n^2) in the worst case, where n is the length of the array.
Space Complexity: O(1), as we are using a constant amount of extra space.
Solution
To solve this problem, we need to evaluate the effect of reversing each possible subarray. We can do this by calculating the initial value of the array and then iterating through all possible subarrays to compute how the value changes upon reversing each one. Specifically, for each subarray defined by indices i and j, we can update the total value by removing the contributions from the original subarray and adding the contributions from the reversed subarray. This requires careful consideration of the adjacent elements to ensure all changes are accounted for.