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");