3196 - Maximize Total Cost of Alternating Subarrays\.

Medium

You are given an integer array nums with length n.

The cost of a subarray nums[l..r], where 0 <= l <= r < n, is defined as:

<code>cost(l, r) = numsl - numsl + 1 + ... + numsr * (−1)^{r − l}</code>

Your task is to split nums into subarrays such that the total cost of the subarrays is maximized , ensuring each element belongs to exactly one subarray.

Formally, if nums is split into k subarrays, where k > 1, at indices <code>i₁, i₂, ..., i_{k − 1}</code>, where <code>0 <= i₁< i₂< ... < i_{k - 1}< n - 1</code>, then the total cost will be:

<code>cost(0, i₁) + cost(i₁ + 1, i₂) + ... + cost(i_{k − 1} + 1, n − 1)</code>

Return an integer denoting the maximum total cost of the subarrays after splitting the array optimally.

Note: If nums is not split into subarrays, i.e. k = 1, the total cost is simply cost(0, n - 1).

Example 1:

Input: nums = 1,-2,3,4

Output: 10

Explanation:

One way to maximize the total cost is by splitting [1, -2, 3, 4] into subarrays [1, -2, 3] and [4]. The total cost will be (1 + 2 + 3) + 4 = 10.

Example 2:

Input: nums = 1,-1,1,-1

Output: 4

Explanation:

One way to maximize the total cost is by splitting [1, -1, 1, -1] into subarrays [1, -1] and [1, -1]. The total cost will be (1 + 1) + (1 + 1) = 4.

Example 3:

Input: nums = 0

Output: 0

Explanation:

We cannot split the array further, so the answer is 0.

Example 4:

Input: nums = 1,-1

Output: 2

Explanation:

Selecting the whole array gives a total cost of 1 + 1 = 2, which is the maximum.

Constraints:

• <code>1 <= nums.length <= 10⁵</code>

• <code>-10⁹<= numsi<= 10⁹</code>