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");
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