Solution Explanation for Vowel Spellchecker

This problem requires implementing a spellchecker that corrects query words based on capitalization and vowel errors, adhering to specific precedence rules. The optimal solution uses hash tables for efficient lookups.

Approach:

1. Data Structures: We employ three hash tables:

   • s: A set (or unordered_set in C++) to store all words from wordlist for case-sensitive exact matches. This provides O(1) lookup time.
   • low: A map (or unordered_map in C++) to store lowercase versions of words as keys, with the original (case-preserving) word as the value. This handles capitalization errors.
   • pat: A map to store words with vowels replaced by '*' as keys and the original word as the value. This handles vowel errors.

2. Preprocessing: We iterate through wordlist once:

   • Add each word to s.
   • Convert each word to lowercase and add it to low, overwriting if a lowercase duplicate exists (we only need the first occurrence).
   • Replace vowels with '*' in the lowercase word and add it to pat, again overwriting duplicates.

3. Query Processing: For each query word:

   • Case-Sensitive Check: Check if the query is in s. If it is, this is the exact match, and we use it.
   • Case-Insensitive Check: Convert the query to lowercase. If it's in low, we've found a capitalization match; use the value from low.
   • Vowel-Insensitive Check: Replace vowels with '*' in the lowercase query. If it's in pat, we have a vowel error match; use the value from pat.
   • No Match: If none of the above conditions are met, there's no match, and we return an empty string.

Time Complexity:

• Preprocessing: O(N * L), where N is the length of wordlist and L is the maximum length of a word. The vowel replacement in the preprocessing step is linear to the length of the word.
• Query processing: O(M * L), where M is the length of queries. Each query involves a constant number of lookups in hash tables (O(1) on average), and potentially a linear-time vowel replacement in the worst case.

Therefore, the overall time complexity is O(N * L + M * L). Since L is relatively small and constant compared to N and M, it can be considered O(N + M).

Space Complexity:

• O(N) to store the three hash tables. The space used is proportional to the number of words in wordlist.

Code Implementation (Python):

class Solution:
    def spellchecker(self, wordlist, queries):
        s = set(wordlist)
        low = {}
        pat = {}
        vowels = "aeiou"
 
        def replace_vowels(word):
            return "".join(['*' if c in vowels else c for c in word])
 
        for word in wordlist:
            lower_word = word.lower()
            low[lower_word] = word  # Overwrite duplicates
            pat[replace_vowels(lower_word)] = word # Overwrite duplicates
 
        ans = []
        for query in queries:
            if query in s:
                ans.append(query)
            elif query.lower() in low:
                ans.append(low[query.lower()])
            elif replace_vowels(query.lower()) in pat:
                ans.append(pat[replace_vowels(query.lower())])
            else:
                ans.append("")
 
        return ans

The code in other languages (Java, C++, Go) follows a similar structure and logic, differing primarily in syntax and specific data structure implementations. The core idea of using hash tables for efficient lookups remains consistent across all languages.