# Trie
## Trie Node & Dictionary Search Tree
Refere to https://leetcode.com/problems/implement-trie-prefix-tree/

Let's consider a problem that we want to search an word from a dictionary.
For example,

**dictionary = {apple, ball, boat, code, command, coworker, zebra}
words = command**

*M : the length of the word we want to search
N : number of words in the dictionary*
* **Brute-Force**
Firstly, we come up with an idea that store the dictionary into a hash set. Then, compare each **"command"** to all the words in the dictionary.
The time complexity here will become **M x N**.
* **Well arrange BST**
To reduce the complexity, we can use binary search if we sort the dictionary in ascending order.
Here, the time complexity become **M x log(N)**.
* **Trie Node**
Using Trie, we can search the key in **O(M)** time. However the penalty is on Trie storage requirements.

class TrieNode{
public:
    bool isword;
    vector<TrieNode*> child;
    TrieNode() : isword(false){
        for(int i = 0; i < 26; ++i)
        {
            child.push_back(NULL);
        }
    };
};
class Trie {
TrieNode* root;
public:
    /** Initialize your data structure here. */
    Trie() {
        root = new TrieNode();
    }
    
    /** Inserts a word into the trie. */
    void insert(string word) {
        TrieNode* curr = root;
        for(auto c : word)
        {
            int tmp = c - 'a';
            // this child node has not been construct
            if(!curr->child[tmp])
            {
                curr->child[tmp] = new TrieNode();
            }
            curr = curr->child[tmp];
        }
        curr->isword = true;
    }
    
    /** Returns if the word is in the trie. */
    bool search(string word) {
        TrieNode* curr = root;
        for(auto c : word)
        {
            int tmp = c - 'a';
            if(!curr -> child[tmp]) return false;
            curr = curr -> child[tmp];
        }
        return curr->isword;
    }
    
    /** Returns if there is any word in the trie that starts with the given prefix. */
    bool startsWith(string prefix) {
        TrieNode* curr = root;
        for(auto c : prefix)
        {
            int tmp = c - 'a';
            if(!curr -> child[tmp]) return false;
            curr = curr -> child[tmp];
        }  
        return true;
    }
};