## tries
* 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.
```python 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.