Count the Number of Incremovable Subarrays I

Count the Number of Incremovable Subarrays I

What is this problem about?

The Count the Number of Incremovable Subarrays I coding problem asks you to find the number of subarrays such that after removing them, the remaining elements form a strictly increasing sequence.

For example, if the array is [1, 2, 3, 1, 2], removing the subarray [3, 1] leaves [1, 2, 2], which is NOT strictly increasing. Removing [3, 1, 2] leaves [1, 2], which IS strictly increasing.

Why is this asked in interviews?

Apple and Microsoft use this "Easy" version to test a candidate's ability to implement a brute-force enumeration pattern correctly. It checks for basic array slicing, validation logic, and loop management. It serves as a precursor to the "Hard" version, evaluating if you can first solve the problem simply before looking for $O(N)$ optimizations.

Algorithmic pattern used

This problem uses Enumeration.

1. Iterate through every possible start index i from 0 to $n-1$.
2. Iterate through every possible end index j from i to $n-1$.
3. For each pair $(i, j)$, create a temporary list of elements excluding the range $[i, j]$.
4. Verify if this temporary list is strictly increasing.
5. Count the number of pairs that pass the test.

Example explanation

nums = [1, 3, 2]

1. Remove [1]: Remains [3, 2] (False).
2. Remove [3]: Remains [1, 2] (True).
3. Remove [2]: Remains [1, 3] (True).
4. Remove [1, 3]: Remains [2] (True).
5. Remove [3, 2]: Remains [1] (True).
6. Remove [1, 3, 2]: Remains [] (True). Total count = 5.

Common mistakes candidates make

• Empty result: Forgetting that removing the entire array is a valid move (leaving an empty sequence, which is vacuously strictly increasing).
• Strict vs. Non-strict: Treating [1, 1] as valid when the problem specifies strictly increasing.
• Index errors: Messing up the boundaries when constructing the "remaining" array.

Interview preparation tip

In "Version I" of any problem, prioritize correctness and clarity over speed. If $N$ is small (e.g., $\le 50$), a $O(N^3)$ brute force is perfectly fine and often preferred because it's harder to make logic errors.