208. Implement Trie (Prefix Tree)

https://leetcode.com/problems/implement-trie-prefix-tree/description/

Implement a trie with insert, search, and startsWith methods.

Example:

Trie trie = new Trie();

trie.insert("apple");
trie.search("apple");   // returns true
trie.search("app");     // returns false
trie.startsWith("app"); // returns true
trie.insert("app");   
trie.search("app");     // returns true

Note:

• You may assume that all inputs are consist of lowercase letters a-z.

• All inputs are guaranteed to be non-empty strings.

Thoughts

Trie是一棵树，每个子结点代表一个字符，当有单词包含它并后面还有字符时，相应的子节点指向后面的一个字符。每个结点还有一个flag用来记录它是否是某单词的终点。搜索一个单词时就顺着指针依次往下遍历, 当为null表明该单词不在里头。创建时也是这么遍历，为null时继续按照word往下插。搜索和创建时间复杂度为O(l), l为单词长度. 空间复杂度为O(lN)。Trie 并不一定比hash map快，但一般会有更高的memory。Trie的优势在于有很多相同prefix的词，有固定的查询时间 (hashmap 的collision不可预料)，以及能方便的实现自动完成等功能。

Code

# Implement a trie with insert, search, and startsWith methods. 
# 
#  Example: 
# 
#  
# Trie trie = new Trie();
# 
# trie.insert("apple");
# trie.search("apple");   // returns true
# trie.search("app");     // returns false
# trie.startsWith("app"); // returns true
# trie.insert("app");   
# trie.search("app");     // returns true
#  
# 
#  Note: 
# 
#  
#  You may assume that all inputs are consist of lowercase letters a-z. 
#  All inputs are guaranteed to be non-empty strings. 
#  
#  Related Topics Design Trie


# leetcode submit region begin(Prohibit modification and deletion)
class Trie(object):

    def __init__(self):
        """
        Initialize your data structure here.
        """
        self.trie = {}

    def insert(self, word):
        """
        Inserts a word into the trie.
        :type word: str
        :rtype: None
        """
        cur = self.trie
        for c in word:
            if c not in cur:
                cur[c] = {}
            cur = cur[c]
        cur['#'] = True

    def search(self, word):
        """
        Returns if the word is in the trie.
        :type word: str
        :rtype: bool
        """
        cur = self.trie
        for c in word:
            if c not in cur:
                return False
            cur = cur[c]
        return '#' in cur

    def startsWith(self, prefix):
        """
        Returns if there is any word in the trie that starts with the given prefix.
        :type prefix: str
        :rtype: bool
        """
        cur = self.trie
        for c in prefix:
            if c not in cur:
                return False
            cur = cur[c]
        return True


# Your Trie object will be instantiated and called as such:
# obj = Trie()
# obj.insert(word)
# param_2 = obj.search(word)
# param_3 = obj.startsWith(prefix)
# leetcode submit region end(Prohibit modification and deletion)

class Trie {
    static final int ALPHABET_SIZE = 26;

    static class TrieNode {
        TrieNode[] children = new TrieNode[ALPHABET_SIZE];
        boolean isEndOfWord;

        TrieNode() {
            isEndOfWord = false;
            for (int i = 0; i < ALPHABET_SIZE; i++) {
                children[i] = null;
            }
        }
    }

    static TrieNode root;

    /** Initialize your data structure here. */
    public Trie() {
        root = new TrieNode();
    }

    /** Inserts a word into the trie. */
    public void insert(String word) {
        int index;

        TrieNode node = root;
        for (int i = 0; i < word.length(); i++) {
            index = word.charAt(i) - 'a';
            if (node.children[index] == null) {
                node.children[index] = new TrieNode();
            }
            node = node.children[index];
        }

        node.isEndOfWord = true;
    }

    /** Returns if the word is in the trie. */
    public boolean search(String word) {
        TrieNode node = root;
        for (int i = 0; i < word.length(); i++) {
            int index = word.charAt(i) - 'a';
            if (node.children[index] == null) {
                return false;
            }
            node = node.children[index];
        }

        return node.isEndOfWord;
    }

    /** Returns if there is any word in the trie that starts with the given prefix. */
    public boolean startsWith(String prefix) {
        TrieNode node = root;
        for (int i = 0; i < prefix.length(); i++) {
            int index = prefix.charAt(i) - 'a';
            if (node.children[index] == null) {
                return false;
            }
            node = node.children[index];
        }

        return true;
    }
}

/**
 * Your Trie object will be instantiated and called as such:
 * Trie obj = new Trie();
 * obj.insert(word);
 * boolean param_2 = obj.search(word);
 * boolean param_3 = obj.startsWith(prefix);
 */

Analysis

搜索和创建时间复杂度为O(l), l为单词长度. 空间复杂度为O(lN).