Leetcode: Implement Trie (Prefix Tree) && Summary: Trie

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

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

参考百度百科：Trie树

a trie, also called digital tree and sometimes radix tree or prefix tree (as they can be searched by prefixes)

The time complexity to insert and to search is O(m), where m is the length of the string.

标准Trie树的应用和优缺点

(1) 全字匹配：确定待查字串是否与集合的一个单词完全匹配。如上代码fullMatch()。

(2) 前缀匹配：查找集合中与以s为前缀的所有串。

注意：Trie树的结构并不适合用来查找子串。这一点和前面提到的PAT Tree以及后面专门要提到的Suffix Tree的作用有很大不同。

优点： 查找效率比与集合中的每一个字符串做匹配的效率要高很多。在o(m)时间内搜索一个长度为m的字符串s是否在字典里。Predictable O(k) lookup time where k is the size of the key

缺点：标准Trie的空间利用率不高，可能存在大量结点中只有一个子结点，这样的结点绝对是一种浪费。正是这个原因，才迅速推动了下面所讲的压缩trie的开发。

什么时候用Trie?

It all depends on what problem you're trying to solve. If all you need to do is insertions and lookups, go with a hash table. If you need to solve more complex problems such as prefix-related queries, then a trie might be the better solution.

像word search II就是跟前缀有关，如果dfs发现当前形成的前缀都不在字典中，就没必要再搜索下去了，所以用trie不用hashSet

Easy version of implement Trie. TrieNode only contains TrieNode[] children, and boolean isWord two fields

 class Trie {
     class TrieNode {
         TrieNode[] children;
         boolean isWord;
         public TrieNode() {
             this.children = new TrieNode[26];
             this.isWord = false;
         }
     }

     TrieNode root;

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

     /** Inserts a word into the trie. */
     public void insert(String word) {
         if (word == null || word.length() == 0) return;
         TrieNode cur = this.root;
         for (int i = 0; i < word.length(); i ++) {
             if (cur.children[word.charAt(i) - 'a'] == null) {
                 cur.children[word.charAt(i) - 'a'] = new TrieNode();
             }
             cur = cur.children[word.charAt(i) - 'a'];
         }
         cur.isWord = true;
     }

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

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

Older version, TrieNode also has num and val fields, which might not be that useful.

 class TrieNode {
     // Initialize your data structure here.
     int num; //How many words go through this TrieNode
     TrieNode[] son; //collection of sons
     boolean isEnd;
     char val;

     public TrieNode() {
         this.num = 0;
         this.son = new TrieNode[26];
         this.isEnd = false;
     }
 }

 public class Trie {
     private TrieNode root;

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

     // Inserts a word into the trie.
     public void insert(String word) {
         if (word==null || word.length()==0) return;
         char[] arr = word.toCharArray();
         TrieNode node = this.root;
         for (int i=0; i<arr.length; i++) {
             int pos = (int)(arr[i] - 'a');
             if (node.son[pos] == null) {
                 node.son[pos] = new TrieNode();
                 node.son[pos].num++;
                 node.son[pos].val = arr[i];
             }
             else {
                 node.son[pos].num++;
             }
             node = node.son[pos];
         }
         node.isEnd = true;
     }

     // Returns if the word is in the trie.
     public boolean search(String word) {
         char[] arr = word.toCharArray();
         TrieNode node = this.root;
         for (int i=0; i<arr.length; i++) {
             int pos = (int)(arr[i] - 'a');
             if (node.son[pos] == null) return false;
             node = node.son[pos];
         }
         return node.isEnd;
     }

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

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