Problem Description
You are given an integer array nums with length n. The cost of a subarray nums[l..r] is defined as: cost(l, r) = nums[l] - nums[l + 1] + ... + nums[r] * (-1)^(r - l). Your task is to split nums into subarrays such that the total cost of the subarrays is maximized. Each element must belong to exactly one subarray. Return an integer denoting the maximum total cost of the subarrays after splitting the array optimally.
Key Insights
- The cost of a subarray alternates between adding and subtracting elements based on their position.
- To maximize total cost, one must consider both the individual costs of subarrays and the impact of splitting the array.
- A greedy approach or dynamic programming may be beneficial to effectively compute the maximum total cost while evaluating potential splits.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1)
Solution
The solution can be approached using a single pass through the array to calculate the cost of each subarray while considering potential splits. We will maintain a running total of costs, and whenever a new subarray is started, we will reset the current cost calculation. The alternating nature of the cost calculation requires careful handling of indices to ensure the correct sign is applied. The use of a variable to track the maximum total cost will help in determining the best configuration of subarrays as we iterate through the input array.