Adjacent Increasing Subarrays Detection I

Problem Description

Given an array nums of n integers and an integer k, determine whether there exist two adjacent subarrays of length k such that both subarrays are strictly increasing. Specifically, check if there are two subarrays 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 true if it is possible to find two such subarrays, and false otherwise.

Key Insights

• A subarray of length k is strictly increasing if each element is less than the next one.
• We need to check two subarrays that are adjacent, which means that the first subarray ends right before the second one starts.
• The overall problem can be solved efficiently by iterating through the array and checking the properties of the subarrays.

Space and Time Complexity

Time Complexity: O(n) - We are iterating through the array once. Space Complexity: O(1) - We are using a constant amount of space.

Solution

To solve the problem, we will:

1. Iterate through the array while checking if each subarray of length k is strictly increasing.
2. Maintain a boolean flag to track if we have found one strictly increasing subarray.
3. When we find a second strictly increasing subarray that is adjacent to the first one, we return true.
4. If we finish checking all potential subarrays without finding two adjacent ones, we return false.

The algorithm primarily uses a single loop and checks the conditions for strictly increasing subarrays.

Code Solutions