Tries, also known as digital radix or prefix trees, are tree-like data structures used for efficient retrieval of items, particularly strings or words. They excel in applications like auto-completion, where quick searches for words sharing a common prefix are required.

Introduction

• Tries are non-binary trees optimized for storing and retrieving words or strings.
• The name "trie" comes from "retrieval" or "tree".
• They efficiently store thousands or millions of words in minimal space and offer fast lookups.

Why Use Tries

• Arrays of strings waste space as many words share common prefixes.
• Looking up words starting with a prefix in arrays is relatively slow.

Structure

• Each node represents a character.
• Nodes can have multiple children, typically equal to the number of letters in the alphabet.
• The root node is either null or an empty character, representing the starting point for any word.
• Words are stored by traversing down the trie, with each level corresponding to a character in the word.

Operation Complexity

• Searching for a word in a trie takes O(L) time, where L is the length of the word.
• Adding or removing a word also runs in O(L) time, as each character in the word needs to be traversed and potentially added to the trie.

Example

• Suppose we have a trie containing words like "bag", "boy", and "cat".
• Both "bag" and "boy" share the common prefix "b", stored in a single place without duplicating characters.
• Adding a word like "baggage" simply extends the existing branch for "bag".

Conclusion

• Tries offer efficient storage and retrieval of words, making them suitable for applications like auto-completion.
• Their structure allows for minimal space usage and fast lookups, making them a valuable data structure in text processing and search applications.