What is a ternary search tree, and how is it used?

A ternary search tree is a type of trie data structure that can store and retrieve strings efficiently.

A ternary search tree (TST) is a special type of trie (also known as a prefix tree) that is used to store strings in a way that allows for efficient retrieval. It is called a 'ternary' tree because each node in the tree has up to three children: a left child, a middle child, and a right child. The left child represents all the strings that are less than the current node, the right child represents all the strings that are greater than the current node, and the middle child represents all the strings that start with the current node.

Each node in a TST contains a character, and a string is represented by a path from the root of the tree to a special node known as a 'end of string' node. This means that a TST can store multiple strings that share the same prefix, which makes it particularly useful for tasks such as autocomplete, where you want to find all the strings that start with a given prefix.

The main advantage of a TST over other types of trie is that it uses less memory. This is because, unlike a standard trie, which has a child node for every possible character, a TST only has child nodes for the characters that are actually used in the strings it stores. This makes TSTs more space-efficient, especially when the set of possible characters is large.

In terms of time complexity, searching for a string in a TST takes O(log n) time in the average case and O(n) time in the worst case, where n is the length of the string. This makes it faster than a binary search tree for most string-based tasks.

In conclusion, a ternary search tree is a powerful data structure that can store and retrieve strings efficiently. It is particularly useful for tasks that involve finding all the strings that start with a given prefix, such as autocomplete.