algoadvance

Given a list of words, you need to encode these words by using the shortest reference string and a list of indices. The reference string should be composed of all the words concatenated together with ‘#’ as the delimiter between words. The goal is to find the shortest possible reference string that can encode all the words.

Clarifying Questions

  1. What are the constraints on the input?
    • The words list will have at most 2000 words.
    • Each word will have at most 7 characters.
  2. Can there be duplicate words in the input list?
    • Yes, there can be duplicates.
  3. What should we do with duplicate words?
    • Duplicate words should be considered the same, and handling them optimally means only encoding them once.
  4. What kind of characters do the words contain?
    • The words consist of lowercase English letters.

Strategy

To minimize the length of the encoding string, we can leverage suffixes. If one word is a suffix of another, we can avoid encoding it separately.

  1. Sort words by descending length: This way we handle the longest words first.
  2. Use a set to keep track of unique words: This helps us to automatically ignore duplicates and suffixes.
  3. Check while adding words: For each word, before adding it to the encoding string, check if any suffix of it is already in the set.

Solution Steps

  1. Sort the words in decreasing order of length.
  2. Initialize an empty set to store suffixes.
  3. For each word in the sorted list:
    • Check if it’s already encoded (exists in the set).
    • If not, add all suffixes of the word to the set and increase the length of the encoding string by the word length + 1 (for the # character).

By the end of this process, the length of the encoding string will be our answer.

Time Complexity

The time complexity is approximately (O(N \cdot L^2)), where (N) is the number of words and (L) is the maximum length of the words. This is because for each word, we may need to add all suffixes (up to L operations per word), and checking membership in the set is (O(1)) on average.

Code

Here’s the Python implementation of the described strategy:

def minimumLengthEncoding(words):
    # Sort words by length in descending order
    words.sort(key=len, reverse=True)
    
    # Initialize set to keep track of suffixes
    unique_suffixes = set()
    
    # Result length
    encoding_length = 0
    
    # Iterate over each word
    for word in words:
        if word not in unique_suffixes:
            # If word is not in suffixes, add all its suffixes to the set
            for i in range(len(word)):
                unique_suffixes.add(word[i:])
            # Increase the encoding length by this word length + 1 for the '#'
            encoding_length += len(word) + 1
    
    return encoding_length

# Example usage:
words = ["time", "me", "bell"]
print(minimumLengthEncoding(words))  # Output: 10

Explanation of the Example:

In the example, [“time”, “me”, “bell”]:

Try our interview co-pilot at AlgoAdvance.com