Yes, @Isaac_Haseley, that is indeed true, and I do appreciate your insights. We can solve this problem using either of the approaches: max heap and min heap, each with pros and cons.

Using a **max heap** (as currently required in the challenge lesson), we can insert all word-frequency pairs and then extract the top k most frequent words by popping from the heap k times at the end of the insertion process. This method focuses on directly finding the highest frequencies without maintaining a fixed heap size.

On the other hand, the **min heap** approach allows us to dynamically maintain a heap of size `k`

during the insertion process, ensuring it contains the top k most frequent words by removing the least frequent word when the heap size exceeds `k`

. I realize now that this approach is efficient regarding time complexity. The custom comparison logic, as discussed by @Ethan_Davis for the heap, ensures that the order is maintained by frequency and, for ties, by lexicographical order.

We’ll make the necessary changes as suggested by you, and I do apologize for the oversight earlier that the min heap approach may offer a more straightforward solution regarding time efficiency and adherence to the problem’s sorting criteria. Thank you for pointing out this out. Your feedback helps us improve our solutions and explanations.

Let me know if there’s more to discuss on this topic!