What is tries?

Tries: A Comprehensive Overview

A Trie (also known as a prefix tree) is a tree-like data structure used for storing a dynamic set or associative array where the keys are usually strings. Unlike a binary search tree, no node in the tree stores the key associated with that node; instead, its position in the tree defines the key with which it is associated. All the descendants of a node have a common prefix of the string associated with that node, and the root represents the empty string.

Key Features and Properties:

• Prefix-Based: Tries are inherently prefix-based, meaning that they efficiently retrieve and store strings based on their prefixes. This makes them extremely useful for applications like auto-completion, spell checking, and IP routing.

• Structure: The root node represents an empty string. Each node can have a maximum of n children (where n is the size of the alphabet – e.g., 26 for lowercase English letters). Each node stores a character or part of character of the string. Each node along the path from root to a node represents the prefix of the string.

• Space Complexity: The space complexity of a trie can be significant. In the worst-case, if there are no common prefixes between the strings, the trie can take space proportional to the sum of lengths of all strings.

• Time Complexity: Searching, inserting, and deleting operations in a trie generally take O(m) time, where m is the length of the key being searched, inserted, or deleted. This is a significant advantage over other data structures for certain operations.

Common Operations:

• Insertion: Inserting a string into a trie involves traversing the tree from the root, creating new nodes as needed for the characters in the string.

• Search: Searching for a string in a trie is similar to insertion. We traverse the tree based on the characters of the search string. If we reach a leaf node or a point where the next character is not present in the children of the current node, the string is not present in the trie.

• Deletion: Deleting a string involves traversing the tree to find the string's end node and then removing the nodes that are not part of any other strings.

Applications:

• Auto-Completion: Suggesting possible words or phrases as the user types.

• Spell Checking: Identifying and suggesting corrections for misspelled words.

• IP Routing: Used in network routers to determine the next hop for a given IP address.

• Dictionary Implementation: Storing and searching for words in a dictionary.

• Longest Prefix Matching: Finding the longest prefix of a given string that exists in a set of strings.

Advantages:

• Fast lookup times (O(m), where m is the key length).
• Efficient prefix-based searching.
• Can store a large number of strings efficiently if they share common prefixes.

Disadvantages:

• Can have high memory consumption, especially with long and diverse strings.
• The space usage can be inefficient if the strings have little or no common prefixes.