adjacent-increasing-subarrays-detection-ii

Given an array nums of n integers, your task is to find the maximum value of k for which there exist two adjacent subarrays of length k each, such that both subarrays are strictly increasing. Specifically, check if there are two subarrays of length k starting at indices a and b (a < b), where:

• Both subarrays nums[a..a + k - 1] and nums[b..b + k - 1] are strictly increasing.


• The subarrays must be adjacent, meaning b = a + k.

Return the maximum possible value of k.

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

Example 1:

Input: nums = [2,5,7,8,9,2,3,4,3,1]

Output: 3

Explanation:

• The subarray starting at index 2 is [7, 8, 9], which is strictly increasing.


• The subarray starting at index 5 is [2, 3, 4], which is also strictly increasing.


• These two subarrays are adjacent, and 3 is the maximum possible value of k for which two such adjacent strictly increasing subarrays exist.

Example 2:

Input: nums = [1,2,3,4,4,4,4,5,6,7]

Output: 2

Explanation:

• The subarray starting at index 0 is [1, 2], which is strictly increasing.


• The subarray starting at index 2 is [3, 4], which is also strictly increasing.


• These two subarrays are adjacent, and 2 is the maximum possible value of k for which two such adjacent strictly increasing subarrays exist.

Constraints:

• 2 <= nums.length <= 2 * 105


• -109 <= nums[i] <= 109