Implement Trie (Prefix Tree)

Write a C# program to implement a Trie (Prefix Tree). A trie is a tree-like data structure used to store a dynamic set of strings, where the keys are usually strings. You will need to implement the Trie class with the following operations: insert, search, and startsWith.

Example 1

  
Input: 
    ["Trie", "insert", "search", "search", "startsWith", "insert", "search"]

 [[], ["apple"], ["apple"], ["app"], ["app"], ["app"], ["app"]]
  
Output: 
    [null, null, true, false, true, null, true]
  
Explanation: 
    

      
Trie trie = new Trie();
      
trie.Insert("apple");
      
trie.Search("apple");   // returns true
      
trie.Search("app");     // returns false
      
trie.StartsWith("app"); // returns true
      
trie.Insert("app");
      
trie.Search("app");     // returns true
    
  

Example 2

  
Input: 
    ["Trie", "insert", "insert", "insert", "search", "startsWith", "search"]

 [[], ["hello"], ["world"], ["hell"], ["world"], ["he"], ["hello world"]]
  
Output: 
    [null, null, null, null, true, true, false]
  
Explanation: 
    

      
Trie trie = new Trie();
      
trie.Insert("hello");
      
trie.Insert("world");
      
trie.Insert("hell");
      
trie.Search("world");       // returns true
      
trie.StartsWith("he");      // returns true
      
trie.Search("hello world"); // returns false
    
  

Constraints

  
1 ≤ word.length, prefix.length ≤ 2000
  
word and prefix consist only of lowercase English letters
  
At most 3 * 10^4 calls will be made to insert, search, and startsWith
  
Time Complexity: O(m) where m is key length
  
Space Complexity: O(n * m) where n is number of keys and m is key length