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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