Top-K Frequent Words: Hash Maps & Min-Heap Fundamentals — Questions & Answers

Test your knowledge of finding the top-K frequent words in a text corpus using hash maps and min-heaps. This quiz covers key concepts, usage scenarios, and time-space trade-offs in designing efficient solutions for word frequency analysis.

This quiz contains 10 questions. Below is a complete reference of all questions, answer choices, and correct answers. You can use this section to review after taking the interactive quiz above.

1. Question 1: Identifying the Most Common Words

   When finding the top 3 most frequent words in the sentence 'apple apple orange banana banana banana', which data structure is best to first count the frequency of each word?

   • Trie
   • Hash Map
   • Stack
   • Queue
   Show correct answer

   Correct answer: Hash Map

2. Question 2: Purpose of the Min-Heap

   Why is a min-heap commonly used after building a hash map of word frequencies to find the top-K frequent words in a large corpus?

   • It efficiently maintains the K largest elements seen so far
   • It deletes duplicate words automatically
   • It stores all possible substrings for searching
   • It sorts the entire list of words in ascending order
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   Correct answer: It efficiently maintains the K largest elements seen so far

3. Question 3: Space Efficiency Concern

   What is the space complexity of storing all unique words and their counts from a text with N total words and W unique words using a hash map?

   • O(N^2)
   • O(K)
   • O(W)
   • O(log N)
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   Correct answer: O(W)

4. Question 4: Extracting Top-K Words

   After filling a hash map with word frequencies, inserting each entry into a min-heap of size K gives what worst-case time complexity for the heap operations?

   • O(W log K)
   • O(W log W)
   • O(K log W)
   • O(K log N)
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   Correct answer: O(W log K)

5. Question 5: Limitation of Using a Heap Only

   Why can't you use only a min-heap to count word frequencies in a corpus without a hash map first?

   • A heap overwrites all existing data upon insertion
   • A heap cannot track individual word counts before insertion
   • A heap is slower than a hash map for lookups
   • A heap does not allow any form of sorting
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   Correct answer: A heap cannot track individual word counts before insertion

6. Question 6: Big-O Lower Bound

   When analyzing all the words in a text of N words to find word frequencies, what is the minimum possible time complexity?

   • O(log N)
   • O(1)
   • O(N^2)
   • O(N)
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   Correct answer: O(N)

7. Question 7: Time Complexity of Building the Hash Map

   Given a text of length N, what is the time complexity to construct the hash map with counts for each unique word?

   • O(2^N)
   • O(N log N)
   • O(K^2)
   • O(N)
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   Correct answer: O(N)

8. Question 8: Choosing Data Structures for Top-K Extraction

   Which of the following combinations is most efficient for finding top 5 frequent words in a large dataset?

   • Array for counting, then bubble sort
   • Queue for input, then selection sort
   • Trie for storing, then stack for extraction
   • Hash map for counting, then min-heap of size 5
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   Correct answer: Hash map for counting, then min-heap of size 5

9. Question 9: Impact of K on Memory Usage

   In the two-step process, increasing the value of K (number of frequent words to retrieve) will affect the memory used by which data structure?

   • Input String
   • Min-Heap
   • Stack
   • Hash Map
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   Correct answer: Min-Heap

10. Question 10: Heap Size and Performance

    For the operation of keeping the top K frequent words, why is the min-heap typically set to size K rather than W (number of unique words)?

    • To avoid using a hash map at all
    • To limit memory usage and improve performance
    • So all words can be sorted alphabetically
    • Because K is always equal to W
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    Correct answer: To limit memory usage and improve performance