數據結構學習之字典樹篇(Java)

字典樹(Trie) : 又稱前綴樹，是一種樹形結構，是一種哈希樹的變種。典型應用是用於統計，排序和保存大量的字符串（但不僅限於字符串），所以經常被搜索引擎系統用於文本詞頻統計。它的優點是：利用字符串的公共前綴來減少查詢時間，最大限度地減少無謂的字符串比較，查詢效率比哈希樹高。
如果有n個條目，Trie查詢每個條目的時間複雜度和字典中一共有多少條目無關，時間複雜度爲O(w),w爲查詢單詞的長度！而大多數單詞的長度小於10。
使用java中的TreeMap實現Trie:
有增加與查詢,刪除功能

import java.util.TreeMap;

public class Trie {

    private class Node{
        public boolean isWord;
        public TreeMap<Character,Node> next;

        public Node(boolean isWord){
            this.isWord = isWord;
            next = new TreeMap<>();
        }

        public Node(){
            this(false);
        }
    }

    private Node root;
    private int size;

    public Trie(){
        root = new Node();
        size = 0;
    }

    //獲得Trie中存儲的單詞數量
    public int getSize(){
        return size;
    }

    //向Trie中添加一個新的單詞word
    public void add(String word){
        Node cur = root;
        for (int i = 0; i < word.length(); i ++){
            char c = word.charAt(i);
            if (cur.next.get(c) == null){
                cur.next.put(c,new Node());
            }
            cur = cur.next.get(c);
        }
        //判斷是否是已存在的單詞
        if (!cur.isWord){
            cur.isWord = true;
            size ++;
        }
    }

    //查詢單詞word是否在Trie中
    public boolean contains(String word){
        Node cur = root;
        for (int i = 0; i < word.length(); i ++){
            char c = word.charAt(i);
            if (cur.next.get(c) == null)
                return false;
            cur = cur.next.get(c);
        }
        return cur.isWord;
    }

    //查詢是否在Trie中有單詞以prefix爲前綴
    public boolean isPrefix(String prefix){
        Node cur = root;
        for (int i = 0; i < prefix.length(); i ++){
            char c = prefix.charAt(i);
            if (cur.next.get(c) == null)
                return false;
            cur = cur.next.get(c);
        }
        return true;
    }
}
import java.util.TreeMap;
/**
 * @author ymn
 * @version 1.0
 * @date 2020\5\22 0022 15:39
 */
public class Trie {

    private class Node{
        public boolean isWord;
        public TreeMap<Character,Node> next;

        public Node(boolean isWord){
            this.isWord = isWord;
            next = new TreeMap<>();
        }

        public Node(){
            this(false);
        }
    }

    private Node root;
    private int size;

    public Trie(){
        root = new Node();
        size = 0;
    }

    //獲得Trie中存儲的單詞數量
    public int getSize(){
        return size;
    }

    //向Trie中添加一個新的單詞word
    public void add(String word){
        Node cur = root;
        for (int i = 0; i < word.length(); i ++){
            char c = word.charAt(i);
            if (cur.next.get(c) == null){
                cur.next.put(c,new Node());
            }
            cur = cur.next.get(c);
        }
        //判斷是否是已存在的單詞
        if (!cur.isWord){
            cur.isWord = true;
            size ++;
        }
    }

    //查詢單詞word是否在Trie中
    public boolean contains(String word){
        Node cur = root;
        for (int i = 0; i < word.length(); i ++){
            char c = word.charAt(i);
            if (cur.next.get(c) == null)
                return false;
            cur = cur.next.get(c);
        }
        return cur.isWord;
    }

    //查詢是否在Trie中有單詞以prefix爲前綴
    public boolean isPrefix(String prefix){
        Node cur = root;
        for (int i = 0; i < prefix.length(); i ++){
            char c = prefix.charAt(i);
            if (cur.next.get(c) == null)
                return false;
            cur = cur.next.get(c);
        }
        return true;
    }
    // 刪除word, 返回是否刪除成功, 遞歸算法
    public boolean remove(String word){
        if(word.equals(""))
            return false;
        return remove(root, word, 0);
    }

    // 在以Node爲根的Trie中刪除單詞word[index...end),返回是否刪除成功, 遞歸算法
    private boolean remove(Node node, String word, int index){

        if(index == word.length()){
            if(!node.isWord)
                return false;
            node.isWord = false;
            size --;
            return true;
        }

        char c = word.charAt(index);
        if(!node.next.containsKey(c))
            return false;

        boolean ret = remove(node.next.get(c), word, index + 1);
        Node nextNode = node.next.get(c);
        if(!nextNode.isWord && nextNode.next.size() == 0)
            node.next.remove(word.charAt(index));
        return ret;
    }
}

除了Trie外，還有壓縮字典樹(Compressed Trie)，三分搜索樹（Ternary Search Tire）等。