208. Implement Trie (Prefix Tree)

1. Description

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.

2. Example

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

3. 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.

4. Solutions

Trie

class Trie {
public:
    Trie() : root(make_unique<Node>()) {}

    void insert(const string &word) {
        Node *iter = root.get();
        for (char letter : word) {
            int idx = index(letter);
            if (!iter->children[idx]) {
                iter->children[idx] = make_unique<Node>();
            }

            iter = iter->children[idx].get();
        }

        iter->is_end = true;
    }

    bool search(const string &word) const {
        const Node *iter = walk(word);
        return iter != nullptr && iter->is_end;
    }

    bool startsWith(const string &prefix) const {
        return walk(prefix) != nullptr;
    }

private:
    struct Node {
        array<unique_ptr<Node>, 26> children{};
        bool is_end = false;
    };

    unique_ptr<Node> root;

    static int index(char letter) {
        return letter - 'a';
    }

    const Node *walk(const string &word) const {
        const Node *iter = root.get();
        for (char letter : word) {
            int idx = index(letter);
            if (!iter->children[idx]) {
                return nullptr;
            }

            iter = iter->children[idx].get();
        }

        return iter;
    }
};