Design Add and Search Words Data Structure

Write a C# program to implement a WordDictionary class that supports adding new words and finding if a word matches a given pattern. The pattern may contain the dot character '.' which can match any single letter.

Example 1

Input:
["WordDictionary","addWord","addWord","addWord","search","search","search","search"]

[[],["bad"],["dad"],["mad"],["pad"],["bad"],[".ad"],["b.."]]
Output: [null,null,null,null,false,true,true,true]
Explanation:

Step 1: Create a new WordDictionary instance.

WordDictionary wordDictionary = new WordDictionary();


Step 2: Add words to the dictionary.

wordDictionary.addWord("bad");
wordDictionary.addWord("dad");
wordDictionary.addWord("mad");


Step 3: Search for words in the dictionary.

wordDictionary.search("pad") returns false (not in dictionary).
wordDictionary.search("bad") returns true (exact match).
wordDictionary.search(".ad") returns true (matches "bad", "dad", or "mad").
wordDictionary.search("b..") returns true (matches "bad").


Step 4: Return the results of all operations.

Example 2

Input:
["WordDictionary","addWord","addWord","search","search","search","search"]

[[],["at"],["bat"],["bat"],["at"],[".at"],["an"]]
Output: [null,null,null,true,true,true,false]
Explanation:

Step 1: Create a new WordDictionary instance.

WordDictionary wordDictionary = new WordDictionary();


Step 2: Add words to the dictionary.

wordDictionary.addWord("at");
wordDictionary.addWord("bat");


Step 3: Search for words in the dictionary.

wordDictionary.search("bat") returns true (exact match).
wordDictionary.search("at") returns true (exact match).
wordDictionary.search(".at") returns true (matches "bat" or "at").
wordDictionary.search("an") returns false (not in dictionary).


Step 4: Return the results of all operations.

Constraints

1 ≤ word.length ≤ 25
Words consist of lowercase English letters only
The dot character '.' may be used to represent any letter
At most 10^4 calls will be made to addWord and search
Time Complexity: O(M) for adding words and O(M * 26^N) for searching words with wildcards, where M is the word length
Space Complexity: O(M) where M is the total number of characters in all words