208-ImplementTrie(PrefixTree)

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

Constraints:

• $1$ <= word.length, prefix.length <= $2000$
• word and prefix consist only of lowercase English letters. At most $3 * 10^4$ calls in total will be made to insert, search, and startsWith.

Problem can be found in here!

Solution: Hash Table

class Trie:
    def __init__(self):
        self.memo = {}

    def insert(self, word: str) -> None:
        current_memo = self.memo
        for char in word:
            if char not in current_memo:
                current_memo[char] = {}

            current_memo = current_memo[char]

        current_memo["."] = None

    def search(self, word: str) -> bool:
        current_memo = self.memo
        for char in word:
            if char not in current_memo:
                return False

            current_memo = current_memo[char]

        return "." in current_memo

    def startsWith(self, prefix: str) -> bool:
        current_memo = self.memo
        for char in prefix:
            if char not in current_memo:
                return False

            current_memo = current_memo[char]

        return True

Time Complexity: $O(n)$, Space Complexity: $O(n)$, where n is the length of the word.