1 Trie 介绍

1.1 字典

• 如果有 n 个条目，使用树结构，查询的时间复杂度是 O(logn);
• 如果有100 万个条目（2^20），logn 大约数20

1.2 Trie

• 查询每个条目的时间复杂度和字典中的条目总数无关；
• 时间复杂度是 O(w),w 是查询单词的长度；

1.3 Trie 的查询

• Trie.java

package tree;

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;
    }

    public int getSize() {
        return size;
    }

    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++;
        }
    }

    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;
    }

}

1.4 Trie 前缀搜索

  // 查询是否在 Trie 中有单词以 prefix 为前缀
    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;

    }