字典

如果有n个条目，使用树结构，查询的复杂度是O(logn)，假设要查询一百万个条目，则需要大约log2^20，也就是20。

Trie

查询每个条目的时间复杂度和字典中一共多少条目无关。时间复杂度为O(w)，w为单词的长度，大多数的单词的长度比10要小。

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;
    }

    // 获得Trie中存储的单词数量
    public int getSize(){
        return size;
    }

    // 向Trie中添加一个新的单词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);
        }

        if (!cur.isWord){
            cur.isWord = true;
            size++;
        }
    }

    // 查询单词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;
    }

    // 查询是否在Trie中有单词以prefix为前缀
    public boolean isPrefix(String perfix){

        Node cur = root;

        for (int i = 0; i < perfix.length(); i++){
            char c = perfix.charAt(i);
            if (cur.next.get(c) == null){
                return false;
            }
            cur = cur.next.get(c);
        }
        return true;
    }
}

对Trie和AVLSet和BSTSet进行测试

import java.util.ArrayList;

public class Main {

    public static void main(String[] args) {

        System.out.println("Pride and Prejudice");

        ArrayList<String> words = new ArrayList<>();
        if(FileOperation.readFile("pride-and-prejudice.txt", words)){

            long startTime = System.nanoTime();

            BSTSet<String> set = new BSTSet<>();
            for(String word: words)
                set.add(word);

            for(String word: words)
                set.contains(word);

            long endTime = System.nanoTime();

            double time = (endTime - startTime) / 1000000000.0;

            System.out.println("Total different words: " + set.getSize());
            System.out.println("BSTSet: " + time + " s");

            // ---

            startTime = System.nanoTime();

            Trie trie = new Trie();
            for(String word: words)
                trie.add(word);

            for(String word: words)
                trie.contains(word);

            endTime = System.nanoTime();

            time = (endTime - startTime) / 1000000000.0;

            System.out.println("Total different words: " + trie.getSize());
            System.out.println("Trie: " + time + " s");


            // ---

            startTime = System.nanoTime();

            AVLSet<String> avlSet = new AVLSet();
            for(String word: words)
                avlSet.add(word);

            for(String word: words)
                avlSet.contains(word);

            endTime = System.nanoTime();

            time = (endTime - startTime) / 1000000000.0;

            System.out.println("Total different words: " + avlSet.getSize());
            System.out.println("AVLSet: " + time + " s");
        }
    }
}

测试结果：

Pride and Prejudice
Total different words: 6530
BSTSet: 0.164487683 s
Total different words: 6530
Trie: 0.133619481 s
Total different words: 6530
AVLSet: 0.146618689 s