Tries are a tree-like data structure that are primarily used for storing and retrieving strings efficiently. They are an important data structure for tasks such as spell-checking and autocomplete, as they allow for fast insertion, deletion, and search operations on large sets of strings.
In a trie, each node in the tree represents a single character in a string. The root node represents the empty string, and the children of a node represent the characters that come after the character represented by the parent node. For example, the string "cat" would be represented in a trie as a node with the character 'c' as its root, with two child nodes representing the characters 'a' and 't'.
One of the key advantages of tries is that they allow for efficient prefix searches. To search for a prefix in a trie, we simply start at the root node and traverse down the tree, following the path corresponding to each character in the prefix. If we reach a null node along the way, it means that the prefix is not present in the trie. If we reach a node that is marked as the end of a word, it means that the prefix is present as a standalone word in the trie.
To insert a new string into a trie, we simply follow the same process as searching for a prefix, but instead of stopping at the end of the string, we continue down the tree, creating new nodes for each character in the string that doesn't already have a corresponding node.
Here is an example of how you can implement a trie data structure in Swift. First we need `TrieNode` class, the TrieNode class represents a single node in the trie, and has a dictionary of children nodes and a flag to indicate whether it is the end of a word.