Leetcode: Implement Trie (Prefix Tree)

## Blog link: https://code.dennyzhang.com/implement-trie-prefix-tree
## Basic Ideas: TrieNode: is_word(bool), children(dict)
##           For the root node, we don't store any characters. Only in children
##           Here we use defaultdict, thus we can avoid has_key check  
## Assumption: If one word in the Trie tree, we also treat it starts with the word.
## Complexity:

class TrieNode(object):
    def __init__(self):
        self.children = collections.defaultdict(TrieNode)
        self.is_word = False

class Trie(object):

    def __init__(self):
        """
        Initialize your data structure here.
        """
        self.root = TrieNode()

    def insert(self, word):
        """
        Inserts a word into the trie.
        :type word: str
        :rtype: void
        """
        node = self.root
        # check character by character
        for ch in word:
            node = node.children[ch]
        node.is_word = True

    def search(self, word):
        """
        Returns if the word is in the trie.
        :type word: str
        :rtype: bool
        """
        node = self.root
        for ch in word:
            if ch not in node.children:
                return False
            node = node.children[ch]
        return node.is_word

    def startsWith(self, prefix):
        """
        Returns if there is any word in the trie that starts with the given prefix.
        :type prefix: str
        :rtype: bool
        """
        node = self.root
        for ch in prefix:
            if ch not in node.children:
                return False
            node = node.children[ch]
        return True

# Your Trie object will be instantiated and called as such:
# obj = Trie()
# obj.insert(word)
# param_2 = obj.search(word)
# param_3 = obj.startsWith(prefix)