trie.md

trie

intro

class TrieNode:
    def __init__(self):
        self.children = {}
        self.is_word = False

class Trie:
    def __init__(self):
        self.root = TrieNode()

    def insert(self, word: str) -> None:
        node = self.root
        for c in word:
            if c not in node.children:
                node.children[c] = TrieNode()
            node = node.children[c]
        node.is_word = True

    def search(self, word: str) -> bool:
        node = self.root
        for c in word:
            if c not in node.children:
                return False
            node = node.children[c]
        return node.is_word

    def startsWith(self, prefix: str) -> bool:
        node = self.root
        for c in prefix:
            if c not in node.children:
                return False
            node = node.children[c]
        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)

# time O(L) for insert(), search(), startsWith(), L is the word's length
# space O(nL), n is the number of words, L is the max len

• concepts
  • trie is a prefix tree
    • can insert word, search word, and search prefix efficiently in O(L)
    • a tree of character nodes
    • every node has a hashmap for children nodes
  • prune
    • think about when we can stop finding deeper nodes
    • think about remove certain node which no longer need to be considered
  • trie's variation can happen in
    • trie node
    • inserting way
    • searching way

pattern

• standard trie
  • insert word, search word, and search prefix
• custom trie node
  • the information to store in TrieNode can be different, depends on different problems
  • like store a list, boolean, string inside each trie node
    • notice the space complexity could increase
      • when disucss about complexity need to mention that only count for number of nodes or consider the content inside
  • store more info can improve time complexity sometimes
• perform dfs inside trie
  • can use dfs as assistance for searching (eg. args: node, idx)
  • could increase the time complexity for searching