題目：

Implement a trie with insert, search, and startsWith methods.

Note:
You may assume that all inputs are consist of lowercase letters a-z.

解題思路：
這道題的考點是設計字首樹。
一開始並不知道什麼是字首樹，所以無法下手解決。

Trie樹，又稱為字典樹、單詞查詢樹或者字首樹，是一種用於快速檢索的多叉數結構。例如，英文字母的字典樹是26叉數，數字的字典樹是10叉樹。
Trie樹的基本性質有三點，歸納為：
1. 根節點不包含字元，根節點外每一個節點都只包含一個字元。
2. 從根節點到某一節點，路徑上經過的字元連線起來，為該節點對應的字串。
3. 每個節點的所有子節點包含的字串不相同。

使用 HashMap

class TrieNode {
    // Initialize your data structure here.
    char c;
    HashMap<Character, TrieNode> children = new HashMap();
    boolean isLeaf;

    public TrieNode() {}

    public TrieNode(char c) {
        this.c = c;
    }
}

public class Trie {
    private TrieNode root;

    public
 
 Trie() {
        root = new TrieNode();
    }

    // Inserts a word into the trie.
    public void insert(String word) {
        HashMap<Character, TrieNode> children = root.children;
        for(int i = 0; i < word.length(); i ++) {
            char c = word.charAt(i);
            TrieNode t;
            if
 
(children.containsKey(c)) {
                t = children.get(c);
            } else {
                t = new TrieNode(c);
                children.put(c, t);
            }
            children = t.children;
            if(i == word.length() - 1)
                t.isLeaf = true;
        }
    }

    // Returns if the word is in the trie.
    public boolean search(String word) {
        TrieNode t = searchNode(word);
        if(t != null && t.isLeaf == true )
            return true;
        else
            return false;
    }

    // Returns if there is any word in the trie
    // that starts with the given prefix.
    public boolean startsWith(String prefix) {
        if(searchNode(prefix) == null)
            return false;
        else
            return true;
    }

    public TrieNode searchNode(String word) {
        HashMap<Character, TrieNode> children = root.children;
        TrieNode t = null;
        for(int i = 0; i < word.length(); i ++) {
            char c = word.charAt(i);
            if(children.containsKey(c)) {
                t = children.get(c);
            } else {
                return null;
            }
            children = t.children;
        }
        return t;
    }
}

// Your Trie object will be instantiated and called as such:
// Trie trie = new Trie();
// trie.insert("somestring");
// trie.search("key");

14 / 14 test cases passed.
Status: Accepted
Runtime: 52 ms