Tries

A Trie, also known as a prefix tree or digital tree, is a tree-like data structure that is used for efficient retrieval of a key in a large set of strings. Unlike a binary search tree, where keys are compared, the position of a node in a Trie is determined by the characters of the key. Each node in a Trie represents a common prefix. A node typically contains an array or map of pointers (one for each possible character in the alphabet) to its children and a boolean flag indicating whether the path from the root to this node represents a complete word. The root node represents an empty string. To insert a word, we traverse the Trie from the root, creating new nodes as needed for characters that don't have a path yet. When we reach the end of the word, we mark the final node as a word-ending node. Searching for a word or a prefix follows a similar traversal. The time complexity for insertion and search is O(L), where L is the length of the string, which is independent of the number of strings stored in the Trie. This makes Tries extremely fast for these operations. They are commonly used in applications like autocomplete features in search engines, spell checkers, and IP routing tables.