FastPrep

Description

Solutions

Count the Number of Incremovable Subarrays II

📚RELATED PROBLEMS

You are given a 0-indexed array of positive integers nums.

A subarray of nums is called incremovable if nums becomes strictly increasing on removing the subarray. For example, the subarray [3, 4] is an incremovable subarray of [5, 3, 4, 6, 7] because removing this subarray changes the array [5, 3, 4, 6, 7] to [5, 6, 7], which is strictly increasing.

Return the total number of incremovable subarrays of nums.

Note that an empty array is considered strictly increasing.

A subarray is a contiguous non-empty sequence of elements within an array.

Example 1:

Input:  nums = [1,2,3,4]
Output: 10 
Explanation:
      
      The 10 incremovable subarrays are: [1], [2], [3], [4], [1,2], [2,3], [3,4], [1,2,3], [2,3,4], and [1,2,3,4], because on removing any one of these subarrays nums becomes strictly increasing. Note that you cannot select an empty subarray.

Example 2:

Input:  nums = [6,5,7,8]
Output: 7 
Explanation:
      
      The 7 incremovable subarrays are: [5], [6], [5,7], [6,5], [5,7,8], [6,5,7], and [6,5,7,8].
      It can be shown that there are only 7 incremovable subarrays in nums.

Example 3:

Input:  nums = [8,7,6,6]
Output: 3 
Explanation:
      
      The 3 incremovable subarrays are: [8,7,6], [7,6,6], and [8,7,6,6]. Note that [8,7] is not an incremovable subarray because after removing [8,7] nums becomes [6,6], which is sorted in ascending order but not strictly increasing.

Constraints:

1 <= nums.length <= 10^5
1 <= nums[i] <= 10^9