LeetCode 208. Implement Trie (Prefix Tree)

原题链接在这里：https://leetcode.com/problems/implement-trie-prefix-tree/

题目：

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

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

题解：

Trie 是一种数据结构，用来做字典查找，是一种用于快速检索的多叉数结构。例如，英文字母的字典树是26叉数，数字的字典树是10叉树。 

Trie树的基本性质有三点，归纳为：

1. 根节点不包含字符，根节点外每一个节点都只包含一个字符。
2. 从根节点到某一节点，路径上经过的字符连接起来，为该节点对应的字符串。
3. 每个节点的所有子节点包含的字符串不相同。

下面有两种方法，第一种相对简洁

Time Complexity: insert, O(m). search, O(m). startsWith, O(m). m = word.length().

Space: O(n*m). n是总共有多少词.

AC Java:

class Trie {
    TrieNode root;
    
    /** Initialize your data structure here. */
    public Trie() {
        root = new TrieNode();
    }
    
    /** Inserts a word into the trie. */
    public void insert(String word) {
        TrieNode p = root;
        for(char c : word.toCharArray()){
            if(p.next[c-'a'] == null){
                p.next[c-'a'] = new TrieNode();
            }
            
            p = p.next[c-'a'];
        }
        
        p.val = word;
    }
    
    /** Returns if the word is in the trie. */
    public boolean search(String word) {
        TrieNode p = root;
        for(char c : word.toCharArray()){
            if(p.next[c-'a'] == null){
                return false;
            }
            
            p = p.next[c-'a'];
        }
        
        return p.val.equals(word);
    }
    
    /** Returns if there is any word in the trie that starts with the given prefix. */
    public boolean startsWith(String prefix) {
        TrieNode p = root;
        for(char c : prefix.toCharArray()){
            if(p.next[c-'a'] == null){
                return false;
            }
            
            p = p.next[c-'a'];
        }
        
        return true;
    }
}

class TrieNode{
    String val;
    TrieNode [] next;
    
    public TrieNode(){
        val = "";
        next = new TrieNode[26];
    }
}

/**
 * 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);
 */

AC Python:

class Trie:

    def __init__(self):
        """
        Initialize your data structure here.
        """
        self.root = TrieNode()
        

    def insert(self, word: str) -> None:
        """
        Inserts a word into the trie.
        """
        p = self.root
        for c in word:
            if c not in p.next:
                p.next[c] = TrieNode()
            p = p.next[c]
        p.val = word
        

    def search(self, word: str) -> bool:
        """
        Returns if the word is in the trie.
        """
        p = self.root
        for c in word:
            if c not in p.next:
                return False
            p = p.next[c]
        return p.val == word
        

    def startsWith(self, prefix: str) -> bool:
        """
        Returns if there is any word in the trie that starts with the given prefix.
        """
        p = self.root
        for c in prefix:
            if c not in p.next:
                return False
            p = p.next[c]
        return True
    
class TrieNode:
    def __init__(self):
        self.val = ""
        self.next = {}


# 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)

第二种方法用的是存是否为叶子节点. 与第一种方法的存val不同，但本质上都是一回事。

Note: search() 和 startsWith() 有所不同，search时还需要注意跳出loop时是否已经打了Trie树的叶子节点.

AC Java:

class TrieNode {
    //Mark if this node is the end of the word
    boolean isLeaf;
    HashMap<Character,TrieNode> nexts;
    public TrieNode() {
        nexts = new HashMap<Character,TrieNode>();
    }
}

public class Trie {
    private TrieNode root;
    
    public Trie() {
        root = new TrieNode();
    }

    // Inserts a word into the trie.
    public void insert(String word) {
        TrieNode p = root;
        char [] s = word.toCharArray();
        int len = s.length;
        int i = 0;
        //traverse the existing character
        while(i<len){
            if(p.nexts.containsKey(s[i])){
                p = p.nexts.get(s[i]);
                i++;
            }else{
                break;
            }
        }
        //append new nodes
        while(i<len){
            TrieNode newNode = new TrieNode();
            p.nexts.put(s[i],newNode);
            p = newNode;
            i++;
        }
        //Set the end of the word
        p.isLeaf = true;
    }

    // Returns if the word is in the trie.
    public boolean search(String word) {
        TrieNode p = root;
        char [] s = word.toCharArray();
        int len = s.length;
        int i = 0;
        while(i<len){
            TrieNode nextNode = p.nexts.get(s[i]);
            if(nextNode == null){
                return false;
            }
            p = nextNode;
            i++;
        }
        //return if this is a leaf node
        return p.isLeaf;
    }

    // Returns if there is any word in the trie
    // that starts with the given prefix.
    public boolean startsWith(String prefix) {
        TrieNode p = root;
        char [] s = prefix.toCharArray();
        int len = s.length;
        int i = 0;
        while(i<len){
            TrieNode nextNode = p.nexts.get(s[i]);
            if(nextNode == null){
                return false;
            }
            p = nextNode;
            i++;
        }
        return true;
    }
}

// Your Trie object will be instantiated and called as such:
// Trie trie = new Trie();
// trie.insert("somestring");
// trie.search("key");

Reference: http://blog.csdn.net/wzy_1988/article/details/45744067#trie树基本实现