master-algorithms-py

tries, also called prefix tree, are a variant of n-ary tree in which characters are stored in each node.
each trie node represents a string (a prefix) and each path down the tree represents a word. note that not all the strings represented by trie nodes are meaningful.
the root is associated with the empty string.
the * nodes (null nodes) are often used to indicate complete words (usually represented by a special type of child) or a boolean flag that terminates the parent node.
a node can have anywhere from 1 through alphabet_size + 1 child.
can be used to store the entire english language for quick prefix lookup (O(k), where k is the length of the string). they are also widely used on autocompletes, spell checkers, and ip routing (longest prefix matching).
tries structures can be represented by arrays and maps or trees.

class Trie:

    def __init__(self):
        self.root = {}

    def insert(self, word: str) -> None:
        node = self.root
        for c in word:
            if c not in node:
                node[c] = {}
            node = node[c]
        node['$'] = None
        
    def match(self, seq, prefix=False):
        node = self.root
        for c in seq:
            if c not in node:
                return False
            node = node[c]
        return prefix or ('$' in node)
        
    def search(self, word: str) -> bool:
        return self.match(word)
        
    def starts_with(self, prefix: str) -> bool:
        return self.match(prefix, True)

insertion

similar to a bst, when we insert a value to a trie, we need to decide which path to go depending on the target value we insert.
the root node needs to be initialized before you insert strings.

search

all the descendants of a node have a common prefix of the string associated with that node, so it should be easy to search if there are any words in the trie that starts with the given prefix.
we go down the tree depending on the given prefix, once we cannot find the child node, the search fails.
we can also search for a specific word rather than a prefix, treating this word as a prefix and searching in the same way as above.
if the search succeeds, we need to check if the target word is only a prefix of words in the trie or if it's exactly a word (for example, by adding a boolean flag).

comparison with hash tables

hash table wins in terms of time complexity, as its insert is usually O(1) (worst case O(log(N)) and trie's are O(M) (where M is the maximum length of a key).
trie wins in terms of space complexity. both O(M *N) in theory, but tries can be much smaller as there will be a lot of words that have similar prefix.