Adjacent Increasing Subarrays Detection II

Adjacent Increasing Subarrays Detection II

What is this problem about?

The Adjacent Increasing Subarrays Detection II coding problem is a more advanced version of the previous task. Instead of checking if a specific length $k$ works, you are asked to find the maximum possible value of k such that there exist two adjacent strictly increasing subarrays of length $k$.

Why is this asked in interviews?

Google frequently asks this to see if candidates can move from "detection" to "optimization." It tests your ability to recognize that if a length $k$ is valid, any length smaller than $k$ is also valid. This monotonic property is a huge hint that a more efficient search strategy can be applied.

Algorithmic pattern used

This problem often involves the Binary Search on Answer interview pattern. Since the possible values for $k$ range from $1$ to $n/2$, you can binary search for the largest $k$ that satisfies the condition. Within each binary search step, you use a linear scan (the "Detection I" logic) as the validator. Alternatively, a more optimized $O(N)$ approach can be achieved using a Two Pointers or dynamic programming-style array to store the maximum increasing length at each position.

Example explanation

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

1. The longest increasing sequence is [1, 2, 3, 4] (length 4) and the next is [4, 5, 6, 7] (length 4).
2. Wait—the condition is "strictly increasing." The second 4 breaks the strict increase if we tried to combine them.
3. However, we can have two adjacent subarrays: [1, 2, 3] and [4, 5, 6], both of length $k=3$.
4. The algorithm would identify $k=3$ as the maximum.

Common mistakes candidates make

• Linear Search for k: Incrementing $k$ from 1 upwards, which results in $O(N^2)$ complexity, potentially failing on large inputs.
• Ignoring the Overlap: Not realizing that one long increasing sequence of length $L$ can provide two adjacent subarrays of length $L/2$.
• Strict vs. Non-Strict: Forgetting that a single "equal" value (like 5, 5) resets the increasing count.

Interview preparation tip

Whenever an interview question asks for the "maximum value of X" and the property is "if X works, X-1 also works," always consider Binary Search on the result.