Medium

A trie (pronounced as "try") or prefix tree is a tree data structure used to efficiently store and retrieve keys in a dataset of strings. There are various applications of this data structure, such as autocomplete and spellchecker.

Implement the Trie class:

• Trie() Initializes the trie object.
• void insert(String word) Inserts the string word into the trie.
• boolean search(String word) Returns true if the string word is in the trie (i.e., was inserted before), and false otherwise.
• boolean startsWith(String prefix) Returns true if there is a previously inserted string word that has the prefix prefix, and false otherwise.

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"); // return True
trie.search("app"); // return False
trie.startsWith("app"); // return True
trie.insert("app");
trie.search("app"); // return True 

Constraints:

• 1 <= word.length, prefix.length <= 2000
• word and prefix consist only of lowercase English letters.
• At most 3 * 104 calls in total will be made to insert, search, and startsWith.

To solve the task, here are the steps for implementing the Trie (Prefix Tree) problem:

1. Define the TrieNode Class:

   • Define a class named TrieNode to represent each node in the trie.
   • Each node will have a dictionary to store child nodes, indicating possible characters that can follow the current node.
   • Additionally, each node will have a boolean flag to mark whether it represents the end of a word.

2. Initialize the Trie Class:

   • Implement the __init__ method for the Trie class to initialize an empty trie with a root node.

3. Implement the Insert Method:

   • Implement the insert method to insert a word into the trie.
   • Start from the root node and iterate through each character in the word.
   • Check if the character exists as a child of the current node. If not, create a new node for it.
   • Move to the child node and repeat the process for the next character.
   • After processing all characters, mark the last node as the end of the word.

4. Implement the Search Method:

   • Implement the search method to check if a word exists in the trie.
   • Start from the root node and iterate through each character in the word.
   • If at any point, a character is not found as a child of the current node, return False.
   • If all characters are found and the last node is marked as the end of a word, return True.

5. Implement the StartsWith Method:

   • Implement the startsWith method to check if there is any word in the trie that starts with a given prefix.
   • Follow a similar process as the search method, but return True as soon as all characters of the prefix are found, regardless of whether it forms a complete word.

6. Return Results:

   • After implementing all methods, create an instance of the Trie class and perform the required operations according to the given input.

Here's a Python implementation:

class TrieNode:
    def __init__(self):
        self.children = {}
        self.is_end_of_word = False

class Trie:
    def __init__(self):
        self.root = TrieNode()

    def insert(self, word: str) -> None:
        node = self.root
        for char in word:
            if char not in node.children:
                node.children[char] = TrieNode()
            node = node.children[char]
        node.is_end_of_word = True

    def search(self, word: str) -> bool:
        node = self.root
        for char in word:
            if char not in node.children:
                return False
            node = node.children[char]
        return node.is_end_of_word

    def startsWith(self, prefix: str) -> bool:
        node = self.root
        for char in prefix:
            if char not in node.children:
                return False
            node = node.children[char]
        return True

# Example Usage
trie = Trie()
trie.insert("apple")
print(trie.search("apple")) # Output: True
print(trie.search("app")) # Output: False
print(trie.startsWith("app")) # Output: True
trie.insert("app")
print(trie.search("app")) # Output: True

This solution efficiently implements the Trie data structure and satisfies the requirements of the problem.