---
id: trie
title: Trie
toc_max_heading_level: 2
---

## Introduction

Tries are special trees (prefix trees) that make searching and storing strings more efficient. Tries have many practical applications, such as conducting searches and providing autocomplete. It is helpful to know these common applications so that you can easily identify when a problem can be efficiently solved using a trie.

Be familiar with implementing from scratch, a `Trie` class and its `add`, `remove` and `search` methods.

## Learning resources

- Readings
  - [Trying to Understand Tries](https://medium.com/basecs/trying-to-understand-tries-3ec6bede0014), basecs
  - [Implement Trie (Prefix Tree)](https://leetcode.com/articles/implement-trie-prefix-tree/), LeetCode
- Additional (only if you have time)
  - [Compressing Radix Trees Without (Too Many) Tears](https://medium.com/basecs/compressing-radix-trees-without-too-many-tears-a2e658adb9a0), basecs

## Time complexity

`m` is the length of the string used in the operation.

| Operation | Big-O | Note |
| --------- | ----- | ---- |
| Search    | O(m)  |      |
| Insert    | O(m)  |      |
| Remove    | O(m)  |      |

## Corner cases

- Searching for a string in an empty trie
- Inserting empty strings into a trie

## Techniques

Sometimes preprocessing a dictionary of words (given in a list) into a trie, will improve the efficiency of searching for a word of length k, among n words. Searching becomes O(k) instead of O(n).

## Recommended questions

- [Implement Trie (Prefix Tree)](https://leetcode.com/problems/implement-trie-prefix-tree)
- [Add and Search Word](https://leetcode.com/problems/add-and-search-word-data-structure-design)
- [Word Break](https://leetcode.com/problems/word-break)
- [Word Search II](https://leetcode.com/problems/word-search-ii/)

## Recommended courses

import AlgorithmCourses from '../\_courses/AlgorithmCourses.md'

<AlgorithmCourses />