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Word Subsets Solution Explanation

Problem Description

We are given two arrays of words: words1 and words2. Our goal is to find all words in words1 that are "universal" to all the words in words2. A word in words1 is considered universal if it contains all the letters and their frequencies of every word in words2.

Intuition

The challenge is to efficiently check if words in words1 contain the cumulative character requirements of all words in words2. Here's how we break it down:

  1. Combine Requirements from words2: Merge the character requirements of all words in words2 into a single frequency map. For example, if words2 = ["abc", "ab"], the combined requirement is {a: 1, b: 1, c: 1}.
  2. Validate Words in words1: For each word in words1, check if it satisfies the combined requirements.

Approach

The solution involves two main steps:

Step 1: Build a Global Character Requirement

  • Iterate through all words in words2.
  • For each word, calculate its character frequencies.
  • Maintain a global frequency map where the frequency of each character is the maximum frequency across all words in words2.

Step 2: Validate Words in words1

  • For each word in words1, calculate its character frequencies.
  • Check if the word meets or exceeds the global requirements from words2.
  • If the word meets the requirements, add it to the result list.

Complexity

  • Time Complexity:
    • Building the global requirement: $$O(n_2 \cdot m_2)$$, where (n_2) is the number of words in words2, and (m_2) is the average length of words in words2.
    • Validating words: $$O(n_1 \cdot m_1)$$, where (n_1) is the number of words in words1, and (m_1) is the average length of words in words1.
    • Overall: $$O(n_1 \cdot m_1 + n_2 \cdot m_2)$$.
  • Space Complexity: $$O(26) = O(1)$$ for character frequency arrays.

Step-by-Step Explanation for Each Language

C++ Code

  1. Global Frequency Calculation:
    • Use a vector of size 26 to store the maximum frequency of each character in words2.
    • Iterate through words2, updating the global frequency map as needed.
  2. Validation of Words:
    • For each word in words1, calculate its character frequencies.
    • Compare the frequencies with the global requirement from words2.
  3. Final Result:
    • If a word satisfies all character requirements, include it in the result list.

Java Code

  1. Global Frequency Calculation:
    • Use an integer array of size 26 for the maximum frequency of each character in words2.
    • Traverse through each word in words2, updating the array to reflect the highest frequency of each character.
  2. Validation of Words:
    • For every word in words1, compute its character frequencies.
    • Match these frequencies against the global frequency array.
  3. Final Result:
    • If all conditions are met, add the word to the output list.

JavaScript Code

  1. Global Frequency Calculation:
    • Use an array of size 26 to track the maximum frequency of characters in words2.
    • Loop through words2, calculating frequencies and updating the global array as necessary.
  2. Validation of Words:
    • For each word in words1, calculate its character counts.
    • Compare these counts with the global requirements from words2.
  3. Final Result:
    • Add words that meet the requirements to the result array.

Python Code

  1. Global Frequency Calculation:
    • Utilize a list of size 26 to store the maximum frequency for each character.
    • Iterate over words2, computing character frequencies for each word and updating the global list.
  2. Validation of Words:
    • For every word in words1, compute its character frequencies using a helper function.
    • Compare the frequencies against the global frequency list.
  3. Final Result:
    • Add valid words to the output list.

Go Code

  1. Global Frequency Calculation:
    • Use a fixed-size array of integers (size 26) for the maximum character frequencies from words2.
    • Process each word in words2, updating the array to capture the maximum frequencies.
  2. Validation of Words:
    • For each word in words1, compute character frequencies using a helper function.
    • Validate these frequencies against the global requirement array.
  3. Final Result:
    • Append words that satisfy the global character requirements to the result slice.

Example

Input

words1 = ["amazon", "apple", "facebook", "google", "leetcode"]
words2 = ["e", "o"]

Output

["facebook", "google", "leetcode"]

Additional Notes

  • Each language implementation uses character frequency arrays to optimize the solution, ensuring efficient comparison of character counts.
  • This approach minimizes unnecessary recomputation and ensures a clean, modular design across all implementations.

Feel free to adapt the solution to suit your specific needs or optimize further based on constraints! 🎉