Adjacent Increasing Subarrays Detection II

Problem Description

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.

Key Insights

• A strictly increasing subarray means each element must be less than the subsequent element.
• We need to find two adjacent subarrays of the same length k, which implies checking pairs of indices in the original array.
• The problem can be solved efficiently by first identifying lengths of all strictly increasing subarrays and then checking for adjacent pairs.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve this problem, we can utilize a single pass through the array to identify the lengths of strictly increasing subarrays. We will maintain a list of lengths of these increasing segments. After that, we will iterate through this list to find the maximum k such that two adjacent segments of length k exist.

1. Traverse through the array and calculate lengths of all strictly increasing segments.
2. Store these lengths in a list.
3. Iterate through the list to find the maximum k for which two adjacent segments are equal.

Code Solutions