Recently, our team encountered this question during an interview. At first glance, many might think this is just a basic stack operation and even joke that Google is “lowering the bar.” But is that really the case? If we analyze it in depth, this question not only involves fundamental data structures but also tests algorithmic optimization strategies and efficient data handling skills, making it far more complex than it initially appears.

The interview officially started with the interviewer introducing the problem and explaining the requirements.

Enhanced Stack

• push(x): x is an integer, pushed onto the stack.
• pop(): Remove the most frequent element. If multiple elements have the same frequency, remove the one closest to the top.

After hearing the question, CSOAHelp immediately provided an approach, and the candidate then reiterated it: This problem is not just a simple stack operation; it involves frequency tracking combined with stack structure.

CSOAHelp’s Guidance:

1. Maintain a main stack to store elements in order while using a hash table to track the occurrence count of each element.
2. Since pop() needs to remove the most frequent element, we can use grouped stacks organized by frequency to efficiently retrieve and remove elements.
3. When executing push(x), update the frequency map first, then place x in the appropriate frequency stack.
4. When executing pop(), retrieve the top element from the highest frequency stack and update the frequency map accordingly.

Following CSOAHelp’s structured logic, the candidate accurately reiterated the solution and explained the design approach to the interviewer.

The interviewer then asked: What is the time complexity of this data structure?

CSOAHelp’s Guidance:

• push() operates in O(1) time since all actions, including updating the frequency and pushing to the stack, occur in constant time.
• pop() also operates in O(1) time as it directly retrieves the top element from the highest frequency stack without any additional traversal.

The candidate restated: Since a hash table is used to store frequencies and stacks are layered by frequency, all operations run in O(1) time without unnecessary traversals.

The interviewer then asked: If we wanted to extend this data structure to support removing any element, how would we approach it?

CSOAHelp’s Guidance:

• Maintain an inverse index to track the position of each element within the grouped stacks, allowing quick access and removal.
• Ensure pop() maintains the highest frequency order by implementing a lazy deletion mechanism, handling flagged deletions during pop() execution.

The candidate reiterated: If we need to support remove(x), we can use a hash table to track the position of x in the grouped stacks while employing a lazy deletion mechanism to ensure correctness during pop() operations.

The interviewer acknowledged the answer and followed up: In what real-world scenarios could this data structure be applied?

CSOAHelp’s Guidance:

• Frequent queries for popular elements, such as ranking hot topics on social media or managing hotspot data in caching systems.
• Applications requiring stack-like behavior while prioritizing frequency-based operations, such as task scheduling in operating systems.

The candidate reiterated: This data structure is well-suited for scenarios where frequently accessed elements must be retrieved quickly, such as recommending trending posts on social media or prioritizing high-frequency tasks in an operating system.

The interviewer expressed satisfaction with the answer, recognizing the candidate’s clarity of thought and precise responses under CSOAHelp’s guidance.

So, is this Google question really that simple? For algorithm experts, it might seem like an easy win, but for most candidates, efficiently solving it and handling follow-up questions requires a solid foundation and strong problem-solving skills. What do you think?

经过csoahelp的面试辅助，候选人获取了良好的面试表现。如果您需要面试辅助或面试代面服务，帮助您进入梦想中的大厂，请随时联系我。

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