Design Add and Search Word Data Structure

Problem

Design a data structure that supports adding new words and searching for existing words.

Implement the WordDictionary class:

• void addWord(word) Adds word to the data structure.
• bool search(word) Returns true if there is any string in the data structure that matches word or false otherwise. word may contain dots '.' where dots can be matched with any letter.

Examples

Example 1:

Input:
["WordDictionary","addWord","addWord","addWord","search","search","search","search"]
[[],["day"],["bay"],["may"],["say"],["day"],[".ay"],["b.."]]

Output:
[null, null, null, null, false, true, true, true]

Explanation:
WordDictionary wordDictionary = new WordDictionary();
wordDictionary.addWord("day");
wordDictionary.addWord("bay");
wordDictionary.addWord("may");
wordDictionary.search("say"); // return false
wordDictionary.search("day"); // return true
wordDictionary.search(".ay"); // return true
wordDictionary.search("b.."); // return true

Constraints

• 1 <= word.length <= 20
• word in addWord consists of lowercase English letters.
• word in search consist of '.' or lowercase English letters.
• There will be at most 2 dots in word for search queries.
• At most 10,000 calls will be made to addWord and search.

You should aim for a solution with O(n) time for each function call and O(t + n) space, where n is the length of the string and t is the total number of nodes created in the Trie.

Solution

struct Node {
    std::unordered_map<char, Node*> children;
    bool end_of_word;
    Node() = default;
    ~Node() {
        for (auto &[_, child] : children) {
            delete child;
        }
    }
};
 
class WordDictionary {
    Node *root;
public:
    WordDictionary() {
        root = new Node();
    }
    ~WordDictionary() { delete root; }
    
    void addWord(const string &word) {
        Node *current = root;
        for (const auto &c : word) {
            if (!current->children.contains(c)) {
                current->children[c] = new Node();
            }
            current = current->children[c];
        }
        current->end_of_word = true;
    }
    
    bool search(const string &word) {
        std::function<bool(Node*, std::size_t)> dfs;
        // DFS checks if word[i:] matches any path starting from this node
        dfs = [&](Node *node, std::size_t i) -> bool {
            // Reached end of word, check if we are at terminal node
            if (i == word.size()) { return node->end_of_word; }
 
            char c = word[i];
            if (c == '.') {
                // Wildcard, check if any child has solution
                for (auto &[_, child] : node->children) {
                    if (dfs(child, i + 1)) {
                        return true;
                    }
                }
                return false;
            }
 
            if (!node->children.contains(c)) {
                return false;
            }
 
            return dfs(node->children[c], i + 1);
        };
        return dfs(root, 0);
    }
};