You are given an array of integers nums(0-indexed) and an integer k.
The score of a subarray (i, j) is defined as min(nums[i], nums[i+1], ..., nums[j]) * (j - i + 1). A good subarray is a subarray where i <= k <= j.
Return the maximum possible score of a good subarray.
Example 1:
Input: nums = [1,4,3,7,4,5], k = 3
Output: 15
Explanation: The optimal subarray is (1, 5) with a score of min(4,3,7,4,5) * (5-1+1) = 3 * 5 = 15.
Example 2:
Input: nums = [5,5,4,5,4,1,1,1], k = 0
Output: 20
Explanation: The optimal subarray is (0, 4) with a score of min(5,5,4,5,4) * (4-0+1) = 4 * 5 = 20.
Constraints:
1 <= nums.length <= 105
1 <= nums[i] <= 2 * 104
0 <= k < nums.length
Solutions
Solution 1: Monotonic Stack
We can enumerate each element $nums[i]$ in $nums$ as the minimum value of the subarray, and use a monotonic stack to find the first position $left[i]$ on the left that is less than $nums[i]$ and the first position $right[i]$ on the right that is less than or equal to $nums[i]$. Then, the score of the subarray with $nums[i]$ as the minimum value is $nums[i] \times (right[i] - left[i] - 1)$.
It should be noted that the answer can only be updated when the left and right boundaries $left[i]$ and $right[i]$ satisfy $left[i]+1 \leq k \leq right[i]-1$.
The time complexity is $O(n)$, and the space complexity is $O(n)$. Here, $n$ is the length of the array $nums$.