Add and Search Word

Question

Design a data structure that supports the following two operations:

void addWord(word)
bool search(word)

search(word) can search a literal word or a regular expression string containing only letters a-z or .. A . means it can represent any one letter.

For example:

addWord("bad")
addWord("dad")
addWord("mad")
search("pad") -> false
search("bad") -> true
search(".ad") -> true
search("b..") -> true

Note:
You may assume that all words are consist of lowercase letters a-z.

Solution

This kind of problem (searching a String) can be solved by Trie.

We use DFS to implement search. Notice corner cases.

When we choose to implement it by recursion, think one step each time.

class TrieNode {
    public char value;
    public boolean isLeaf;
    public HashMap<Character, TrieNode> children;
    
    public TrieNode(char c) {
        value = c;
        children = new HashMap<Character, TrieNode>();
        isLeaf = false;
    }
}

public class WordDictionary {
    public TrieNode root;

    public WordDictionary() {
        root = new TrieNode('!');
    }

    // Adds a word into the data structure.
    public void addWord(String word) {
        TrieNode currentNode = root;
        for (int i = 0; i < word.length(); i++) {
            char tmp = word.charAt(i);
            HashMap<Character, TrieNode> children = currentNode.children;
            TrieNode nextNode;
            if (children.containsKey(tmp)) {
                nextNode = children.get(tmp);
            } else {
                nextNode = new TrieNode(tmp);
                children.put(tmp, nextNode);
            }
            currentNode = nextNode;
            // Check whether it's the last character
            if (i == word.length() - 1)
                currentNode.isLeaf = true;
        }
    }

    // Returns if the word is in the data structure. A word could
    // contain the dot character '.' to represent any one letter.
    public boolean search(String word) {
        return dfsSearch(word, 0, root);
    }
    
    private boolean dfsSearch(String word, int index, TrieNode prevNode) {
        // If prevNode is null but word has not been completely traversed, return fasle
        if (prevNode == null) {
            return false;
        }
        
        // If word has been completely traversed, check whether tree is at bottom
        if (index == word.length()) {
            return prevNode.isLeaf;
        }
        char target = word.charAt(index);
        HashMap<Character, TrieNode> currentMap = prevNode.children;
        
        if (target != '.') {
            if (!currentMap.containsKey(target))
                return false;
            else
                return dfsSearch(word, index + 1, currentMap.get(target));
        } else {
            boolean result = false;
            for (Character key : currentMap.keySet()) {
                if (dfsSearch(word, index + 1, currentMap.get(key))) {
                    result = true;
                }
            }
            return result;
        }
    }
}

// Your WordDictionary object will be instantiated and called as such:
// WordDictionary wordDictionary = new WordDictionary();
// wordDictionary.addWord("word");
// wordDictionary.search("pattern");