Count Bowl Subarrays

Count Bowl Subarrays

What is this problem about?

The Count Bowl Subarrays interview question (likely a variation of a monotonic stack problem) asks you to count subarrays that satisfy a "bowl-like" property. Usually, this means the elements first decrease and then increase, or follow a specific relative height pattern where the ends are higher than the middle.

Why is this asked in interviews?

Amazon uses the Monotonic Stack interview pattern for this problem to test your ability to maintain state while traversing an array. It evaluates whether you can use a stack to find "next greater" or "next smaller" elements to identify bounds for the bowl property. It’s a "Medium" problem that requires identifying the relationship between an element and its nearest larger/smaller neighbors.

Algorithmic pattern used

This problem is solved using a Monotonic Stack.

1. Use a stack to find the nearest element to the left that is greater than the current element.
2. Use another stack (or pass) to find the nearest element to the right that is greater.
3. The count of "bowls" often relates to how many elements are trapped between these two boundaries.
4. A common variation involves counting subarrays where the minimum element is not at the endpoints.

Example explanation

nums = [5, 2, 4]

1. 2 is a local minimum.
2. To its left is 5, to its right is 4.
3. The subarray [5, 2, 4] forms a bowl. If we had [5, 4, 3, 4, 5], there are multiple overlapping bowls like [4, 3, 4] and [5, 4, 3, 4, 5].

Common mistakes candidates make

• Brute Force: Checking all O(N^2) subarrays individually.
• Duplicate Counting: Not properly defining the "representative" element of a bowl (usually the minimum), leading to counting the same subarray multiple times.
• Stack Type: Confusing a monotonic increasing stack with a monotonic decreasing stack.

Interview preparation tip

Monotonic stacks are the key to many "Count Subarrays" problems involving minimums or maximums. If you need to know "for which subarrays is this element the minimum?", a monotonic stack is the answer.