208. Implement Trie (Prefix Tree) 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

Approach

Input: Initializing empty object sequence executing string mutations checking states.

Output: Boolean validity responses upon tracking.

This is a classic Trie (Prefix Tree) problem.

        (root)
    / / / | \ \ \ 
   a s x  f  z p b 
   ...

A Trie is a tree structure used for efficiently storing and retrieving a collection of strings.

1. Core Concept:

• Each node represents a character.
• Every path represents a prefix.
• At the last character of a word, use a flag (like isWord = true) to distinguish between a "complete word" and "just a prefix".

2. Operational Logic

   • insert(word): Build nodes character by character, eventually marking isWord=true.
   • search(word): Lookup character by character, finally isWord=true must be satisfied to return true.
   • startsWith(prefix): Lookup character by character, return true as long as the path exists.

3. Complexity

   • Insert / Search / Prefix Check: O(m), where m is the length of the string.
   • Trades space for time.

Implementation

python

class Trie:

    def __init__(self):
        # Initialize an empty dictionary to represent the root node of the Trie
        self.trie = {}
        
    def insert(self, word: str) -> None:
        # Start inserting words from the root node of the Trie
        node = self.trie
        for char in word:
            # If the current character is not in the current node, add it
            if char not in node:
                node[char] = {}
            # Move to the next node
            node = node[char]
        # Mark the end of the word within the node, using '#' 
        node['#'] = True  # '#' marks the end of a word

    def search(self, word: str) -> bool:
        # Start searching for the word from the root node
        node = self.trie
        for char in word:
            # If the current character is not found, return False
            if char not in node:
                return False
            # Move to the next node
            node = node[char]
        # Check if the current node is marked as the end of a word
        return '#' in node

    def startsWith(self, prefix: str) -> bool:
        # Check prefixes starting from the root node
        node = self.trie
        for char in prefix:
            # If the current character is not found, return False
            if char not in node:
                return False
            # Move to the next node
            node = node[char]
        # If the loop completes successfully, the prefix exists
        return True

javascript

// Define Trie (Prefix Tree)
class Trie {
    constructor() {
        // Root node, use an object to store children map
        this.root = {};
    }

    /** 
     * Insert a word into the Trie
     * @param {string} word
     * @return {void}
     */
    insert(word) {
        let curr = this.root;
        for (let ch of word) {
            // If the current node does not have this character, create a new child node
            if (!curr[ch]) {
                curr[ch] = {};
            }
            // Move to the child node
            curr = curr[ch];
        }
        // Mark this path to be representing a fully formed word
        curr.isWord = true;
    }

    /** 
     * Check if the completely formed word exists in the Trie
     * @param {string} word
     * @return {boolean}
     */
    search(word) {
        let curr = this.root;
        for (let ch of word) {
            // If character isn't found, return false
            if (!curr[ch]) return false;
            curr = curr[ch];
        }
        // Must be a complete word evaluating strictly to truthiness explicitly cast
        return !!curr.isWord;
    }

    /** 
     * Determine if there is any path with matching prefix internally structure
     * @param {string} prefix
     * @return {boolean}
     */
    startsWith(prefix) {
        let curr = this.root;
        for (let ch of prefix) {
            if (!curr[ch]) return false;
            curr = curr[ch];
        }
        return true;
    }
}

Complexity Analysis

• Time Complexity: O(m) depends exclusively upon the search string length
• Space Complexity: O(m) bounding structure creation matching character types

Links

208. Implement Trie (Prefix Tree) (English)

208. 实现 Trie (前缀树) (Chinese)