Tries

Overview

The word trie comes from the word retrieval. A trie is also known as a digital tree, radix tree or prefix tree.

Each node contains the following:

1. A value, which can be null.
2. An array of pointers to child nodes, where each one may optionally be null.

A trie usually has an empty root node (or ""). This root node contains a list of nodes, one for each character in the alphabet (e.g. 26 entries for English). The characters are mapped to pointers in the array by their index, were A = 0 and Z = 25.

The value is used to indicate whether or not the sequence of letters from the root node to the current node form a valid word (if they don't, they only exist because there is a larger word which contains these letters).

Complexity

The worst case time to construct a trie is dependent on the product of the longest word \( m \), and how many words the trie contains \(n\). This is written using Big-O notation as \( \mathcal{O}(mn) \). The time it takes for insertion, deletion and searching is dependent on the product of the length of the word you are inserting, deleting or searching for \(a\), and the total number of words \(n\). This is expressed as \(\mathcal{O}(an)\).

Uses

Tries are used in the following ways:

• Search engines
• Spell-checkers
• Auto-complete