Pythonic Implementations of Trie (Prefix Tree)

This post proposes a Pythonic implementation of Trie data structure, with insert, search, and starts_with methods. With careful design, the Pythonic improvements reduced the lines of code from 27 lines to 8 lines.

class Trie(dict):
    def insert(self, word: str) -> None:
        reduce(lambda node, c: node.setdefault(c, {}), word, self)['$'] = True

    def search(self, word: str) -> bool:
        return self.starts_with(word + '$')

    def starts_with(self, prefix: str) -> bool:
        node = self
        return all(node := node.get(char) for char in prefix)

See this LeetCode problem for more info.

Basic Implementation

The most basic implementation has separated TrieNode and Trie classes, and marks the end of the word with the is_end_of_word attribute in TrieNode.

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

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

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

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

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

Improved

There are multiple improvements we can make to this basic implementation.

• We can mark the end of word by inserting a character out of the alphabet into the dictionary.
• If end-of-word marker is used, searching a full word is becomes to searching the word with end-of-word marker suffixed.
• We can merge the Trie and TrieNode classes into one class, since each of the TrieNode is also the root of a "sub-trie".
• We can simplify the searching and inserting code with higher-order functions such as reduce, all, and any.
• Since each trie is a dict, we can make Trie extendsdict.

class Trie(dict):
    def insert(self, word: str) -> None:
        reduce(lambda node, c: node.setdefault(c, {}), word, self)['$'] = True

    def search(self, word: str) -> bool:
        return self.starts_with(word + '$')

    def starts_with(self, prefix: str) -> bool:
        node = self
        return all(node := node.get(char) for char in prefix)

Now let's go into details of the implementation.

insert

reduce(lambda node, c: node.setdefault(c, {}), word, self)['$'] = True

When inserting a word into the trie, we start from the root, iterate over the word and insert the characters into the dictionary at each level. This can be done in a Pythonic functional programming style using reduce. We leverage dict.setdefault to create a new level of trie for unseen word sequences before.

The final return value of reduce is the leave of trie. By inserting {'$': True} in this dictionary, we marked it as a full word.

The whole inserting process takes only one line, isn't it beautiful?

starts_with

node = self
return all(node := node.get(char) for char in prefix)

Let's go over starts_with first since search relies on this method. Recall that in Python, many built-in data structures have default boolean value, which is True when they are non-empty. We can utilize this property to convert the searching process into a series of boolean and operations.

To avoid the redundant declarative style, we leverage the walrus operator := to update the node as we iterate. When a character isn't found, the expression is short-circuited and False is returned immediately.

search

return self.starts_with(word + '$')

With the use of end-of-word marker, searching 'word' is now equivalent to searching a word that starts with 'word$'!

Bonus: Implementation of WordDictionary

https://leetcode.com/problems/design-add-and-search-words-data-structure/

class WordDictionary(dict):
    def add_word(self, word: str) -> None:
        reduce(lambda node, c: node.setdefault(c, {}), word, self)['$'] = True

    def search(self, word: str) -> bool:
        return self.search_helper(word + '$', self)

    def search_helper(self, word: str, node: dict) -> bool:
        for i, c in enumerate(word):
            if c == ".":
                return any(
                    self.search_helper(word[i + 1:], node)
                    for node in node.values() if node is not True
                )
            else:
                if not (node := node.get(c)):
                    return False
        return True