Watch 10 video solutions for Maximize Total Cost of Alternating Subarrays, a medium level problem involving Array, Dynamic Programming. This walkthrough by NeetCode has 605,143 views views. Want to try solving it yourself? Practice on FleetCode or read the detailed text solution.
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:
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, ensuring each element belongs to exactly one subarray.
Formally, if nums is split into k subarrays, where k > 1, at indices i1, i2, ..., ik − 1, where 0 <= i1 < i2 < ... < ik - 1 < n - 1, then the total cost will be:
cost(0, i1) + cost(i1 + 1, i2) + ... + cost(ik − 1 + 1, n − 1)
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:
1 <= nums.length <= 105-109 <= nums[i] <= 109