# 0208. Implement Trie (solutions/Prefix Tree)

<https://leetcode.com/problems/implement-trie-prefix-tree>

## Description

A [**trie**](https://en.wikipedia.org/wiki/Trie) (pronounced as "try") or **prefix tree** is a tree data structure used to efficiently store and retrieve keys in a dataset of strings. There are various applications of this data structure, such as autocomplete and spellchecker.

Implement the Trie class:

* `Trie()` Initializes the trie object.
* `void insert(String word)` Inserts the string `word` into the trie.
* `boolean search(String word)` Returns `true` if the string `word` is in the trie (i.e., was inserted before), and `false` otherwise.
* `boolean startsWith(String prefix)` Returns `true` if there is a previously inserted string `word` that has the prefix `prefix`, and `false` otherwise.

**Example 1:**

```
**Input**
["Trie", "insert", "search", "search", "startsWith", "insert", "search"]
[[], ["apple"], ["apple"], ["app"], ["app"], ["app"], ["app"]]
**Output**
[null, null, true, false, true, null, true]
**Explanation**
Trie trie = new Trie();
trie.insert("apple");
trie.search("apple");   // return True
trie.search("app");     // return False
trie.startsWith("app"); // return True
trie.insert("app");
trie.search("app");     // return True
```

**Constraints:**

* `1 <= word.length, prefix.length <= 2000`
* `word` and `prefix` consist only of lowercase English letters.
* At most `3 * 104` calls **in total** will be made to `insert`, `search`, and `startsWith`.

## ac

```java
class Trie {
    private TrieNode root;
    /** Initialize your data structure here. */
    public Trie() {
        root = new TrieNode();
    }

    /** Inserts a word into the trie. */
    public void insert(String word) {
        root.insert(word, 0);
    }

    /** Returns if the word is in the trie. */
    public boolean search(String word) {
        TrieNode node = root.find(word, 0);
        return node != null && node.hasWord;
    }

    /** Returns if there is any word in the trie that starts with the given prefix. */
    public boolean startsWith(String prefix) {
        TrieNode node = root.find(prefix, 0);
        return node != null;
    }
}

class TrieNode {
    private TrieNode[] children;
    public boolean hasWord;

    public TrieNode() {
        children = new TrieNode[26];
        hasWord = false;
    }

    public void insert(String word, int index) {
        if (index == word.length()) {
            this.hasWord = true;
            return;
        }

        int pos = word.charAt(index) - 'a';
        if (children[pos] == null) {
            children[pos] = new TrieNode();
        }
        children[pos].insert(word, index + 1);
    }

    public TrieNode find(String word, int index) {
        if (index == word.length()) return this;

        int pos = word.charAt(index) - 'a';
        if (children[pos] == null) return null;

        return children[pos].find(word, index + 1);
    }
}

/**
 * Your Trie object will be instantiated and called as such:
 * Trie obj = new Trie();
 * obj.insert(word);
 * boolean param_2 = obj.search(word);
 * boolean param_3 = obj.startsWith(prefix);
 */
```

more intuitive:

```java
class Trie {
    TrieNode root;
    /** Initialize your data structure here. */
    public Trie() {
        root = new TrieNode();
    }

    /** Inserts a word into the trie. */
    public void insert(String word) {
        TrieNode r = root;
        for (int i = 0; i < word.length(); i++) {
            int pos = word.charAt(i) - 'a';
            if (r.next[pos] == null) r.next[pos] = new TrieNode();
            r = r.next[pos];
        }
        r.isWord = true;
    }

    /** Returns if the word is in the trie. */
    public boolean search(String word) {
        TrieNode r = root;
        for (int i = 0; i < word.length(); i++) {
            int pos = word.charAt(i) - 'a';
            if (r.next[pos] == null) return false;
            r = r.next[pos];
        }
        return r.isWord;
    }

    /** Returns if there is any word in the trie that starts with the given prefix. */
    public boolean startsWith(String prefix) {
        TrieNode r = root;
        for (int i = 0; i < prefix.length(); i++) {
            int pos = prefix.charAt(i) - 'a';
            if (r.next[pos] == null) return false;
            r = r.next[pos];
        }

        // prefix is word
        if (r.isWord) return true;

        // iterate next[]
        for (TrieNode t : r.next) {
            if (t != null) return true;
        }

        return false;
    }
}

class TrieNode {
    TrieNode[] next;
    boolean isWord;
    public TrieNode() {
        next = new TrieNode[26];
    }
}

/**
 * Your Trie object will be instantiated and called as such:
 * Trie obj = new Trie();
 * obj.insert(word);
 * boolean param_2 = obj.search(word);
 * boolean param_3 = obj.startsWith(prefix);
 */
```


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