Tries: A Visual Guide

Tries

A trie (also known as a Prefix Tree) stores a set of strings in a tree-like data structure. The trie below stores the strings APPLE, APP, BAT, BALL, BATS, and BALL:

Strings with a common prefix share the same nodes in the trie. For example, the strings APPLE and APP share the nodes A, P, and P.

A trie allows us to efficiently search if a given word exists in the trie. For example, we can search for the word APPLE by starting at the root of the trie and following the nodes along the path animated below:

A trie is commonly used to implement features like spell checkers and auto-complete. For example, if we type in the string "BA", then our trie can suggest "BALL" and "BAT" as possible completions.

This section covers the basics of tries that you should know for the coding interview. In particular, we will learn how to visualize the most common operations on a trie: search, insert, and delete.

Basics

A trie consists of a series of nodes arranged in a tree. Each node in the trie represents a character in one of the strings in the trie, and its children represent the next character in the string.
Each node also has a boolean value that indicates whether the node represents the end of a word. Nodes where this boolean value is true are colored blue in this guide.
A trie supports 3 main operations: search(word), insert(word), and delete(word).

Trie Class

A trie is typically implemented as a class with a reference to root of the trie of type TrieNode. The class has methods to search, insert, and delete words from the trie.

class Trie:
    def __init__(self):
        self.root = TrieNode()
        
    def search(self, word):
        # return True if word is in trie, False otherwise
        pass
    
    def insert(self, word):
        # insert word into trie
        pass
    
    def delete(self, word):
        # delete word from trie
        pass

TrieNodes

The TrieNode class can be defined as:

class TrieNode:
    def __init__(self, children = {}, eow = False):
        self.children = children
        self.is_end_of_word = eow

The children dictionary is a mapping from characters to TrieNode objects. For example, the code snippet below shows what the children dictionary looks like for a node with two children, "A" and "B":

In practice, we won't be manually creating TrieNode objects. Instead, we'll use the Trie class to interact with the trie. This snippet is only included to help you understand the structure of a trie.


root = TrieNode()

root.children = {
    'A': TrieNode(),
    'B': TrieNode()
}

Next, we'll learn how to visualize the 3 main operations on a trie: search, insert, and delete.

Trie Operations

This section focuses on how to visualize each operation to get a feel for how they work. We'll cover the implementation in-depth in the first practice problem.

Search

The search operation takes a search term as input and returns whether the term exists in the trie.

We start from the root node and the first character of the search term. We then traverse down the trie by checking if any of the children of the current node match the next character in the search term. If they do, we move to that node and continue the search with the next character in the search term.

The animation below visualizes the search operation for an input (case sensitive) of your choice, with a trie storing APPLE, APP, BAT, BALL, BATS, and BALL.

Try different search terms to get a feel for how the search operation works.

BALL returns true BA returns false, as BA is not marked as the end of a word

search for BATH

0 / 5

Time Complexity

O(L), where L is the length of the word being searched in the worst case we need to traverse L nodes in the Trie to find the word. Each node traversal takes constant time O(1), for a total of O(L) operations.

Insertion

The insert operation takes a word as input and adds it to the trie.

We traverse the trie until we reach the last character of the search term. From there, we add the nodes that don't exist already in the trie, and mark the last node as the end of a word.

The animation visualizes the insert operation for a word of your choice (case-sensitive) into a trie containing APPLE, APP, BAT, BATS, and BALLET.

The animation resets back to the original trie after each insertion - the trie does not accumulate words as you insert them.

Some example words to insert:

APPLE (already exists) BALL (no new nodes created, but "L" is marked as the end of a word) COAL (creates a new branch in the trie from the root)

insert BALLOON

0 / 3

Time Complexity

O(L) where L is the length of the word being inserted. In the worst case, such as when the trie is empty or the word being inserted has no common prefixes with existing words, we need to insert L nodes, each of which takes constant time O(1).

Deletion

The delete operation deletes a word from the trie.

We traverse down to the last character of the word we want to delete, set the "end of word" flag to false, and then remove any nodes that are not part of any other words in the trie.

The animation visualizes a delete operation from a trie containing APPLE, APP, BAT, BATS, BALL, and BALLET.

The animation resets back to the original trie after each deletion - meaning the trie does not continuously shrink as you delete words.

Some example words to delete:

BALL (removes the EOW marker from the "L" node) COAL (does nothing, as the word does not exist in the trie) BATS (removes the "S" node)

delete BALLET

0 / 5

Time Complexity

O(L). In the worst case, such as when the word to delete is the only word in the trie, we need to first traverse L nodes in the trie to find the word to delete, and then delete L nodes. Each node traversal takes constant time O(1), for a total 2L operations, which is O(L).

Summary

Operation	Description	Time Complexity
Search	Search for a word in the trie	O(L)
Insert	Insert a word in the trie	O(L)
Delete	Delete a word from the trie	O(L)

Space Complexity

The space complexity of a trie is O(C), where C is the total number of characters between all the words stored in the trie. This is due to the worst case, which happens when there are no common prefixes between the words stored in the trie.

A trie in which there are no shared nodes.

Next: Implement Trie Methods

Your account is free and you can post anonymously if you choose.

Sort By

Loading comments...

Back to Home

Eliminating Pairs

Overview

Container With Most Water

3-Sum

Triangle Numbers

Pointers as Regions

Move Zeroes

Sort Colors

Trapping Rain Water

Variable-Length

Overview

Longest Substring Without Repeating Characters

Longest Repeating Character Replacement

Fixed-Length

Overview

Maximum Sum of Subarrays of Size K

Max Points You Can Obtain From Cards

Max Sum of Distinct Subarrays Length k

Overview

Can Attend Meetings

Insert Interval

Non-Overlapping Intervals

Merge Intervals

Employee Free Time

Overview

Valid Parentheses

Decode String

Longest Valid Parentheses

Monotonic Stack

Overview

Daily Temperatures

Largest Rectangle in Histogram

Overview

Linked List Cycle

Palindrome Linked List

Remove Nth Node From End of List

Reorder List

Swap Nodes in Pairs

Overview

Apple Harvest (Koko Eating Bananas)

Search in Rotated Sorted Array

Overview

Kth Largest Element in an Array

K Closest Points to Origin

Find K Closest Elements

Merge K Sorted Lists

Introduction

Binary Trees

Overview

Level Order Sum

Rightmost Node

Zigzag Level Order

Maximum Width of Binary Tree

Graphs

Overview

Minimum Knight Moves

Rotting Oranges

01-Matrix

Bus Routes

Overview

Word Search

Solution Space Trees

Subsets

Generate Parentheses

Combination Sum

Topological Sort

Overview

Course Schedule

Course Schedule II

Fundamentals

Solving a Question with Dynamic Programming

Counting Bits

Decode Ways

Maximal Square

Unique Paths

Longest Increasing Subsequence

Word Break

Maximum Profit in Job Scheduling

Overview

Best Time to Buy and Sell Stock

Gas Station

Jump Game

Overview

Implement Trie Methods

Prefix Matching

Overview

Count Vowels in Substrings

Subarray Sum Equals K

Spiral Matrix

Rotate Image

Set Matrix Zeroes

Greedy Algorithms: Jump Game

Implement Trie Methods

Tries

A trie (also known as a Prefix Tree) stores a set of strings in a tree-like data structure. The trie below stores the strings APPLE, APP, BAT, BALL, BATS, and BALL:

Strings with a common prefix share the same nodes in the trie. For example, the strings APPLE and APP share the nodes A, P, and P.

A trie is commonly used to implement features like spell checkers and auto-complete. For example, if we type in the string "BA", then our trie can suggest "BALL" and "BAT" as possible completions.

This section covers the basics of tries that you should know for the coding interview. In particular, we will learn how to visualize the most common operations on a trie: search, insert, and delete.

Basics

A trie consists of a series of nodes arranged in a tree. Each node in the trie represents a character in one of the strings in the trie, and its children represent the next character in the string.
Each node also has a boolean value that indicates whether the node represents the end of a word. Nodes where this boolean value is true are colored blue in this guide.
A trie supports 3 main operations: search(word), insert(word), and delete(word).

Trie Class

A trie is typically implemented as a class with a reference to root of the trie of type TrieNode. The class has methods to search, insert, and delete words from the trie.

class Trie:
    def __init__(self):
        self.root = TrieNode()
        
    def search(self, word):
        # return True if word is in trie, False otherwise
        pass
    
    def insert(self, word):
        # insert word into trie
        pass
    
    def delete(self, word):
        # delete word from trie
        pass

TrieNodes

The TrieNode class can be defined as:

class TrieNode:
    def __init__(self, children = {}, eow = False):
        self.children = children
        self.is_end_of_word = eow

The children dictionary is a mapping from characters to TrieNode objects. For example, the code snippet below shows what the children dictionary looks like for a node with two children, "A" and "B":

In practice, we won't be manually creating TrieNode objects. Instead, we'll use the Trie class to interact with the trie. This snippet is only included to help you understand the structure of a trie.


root = TrieNode()

root.children = {
    'A': TrieNode(),
    'B': TrieNode()
}

Next, we'll learn how to visualize the 3 main operations on a trie: search, insert, and delete.

Trie Operations

This section focuses on how to visualize each operation to get a feel for how they work. We'll cover the implementation in-depth in the first practice problem.

Search

The search operation takes a search term as input and returns whether the term exists in the trie.

The animation below visualizes the search operation for an input (case sensitive) of your choice, with a trie storing APPLE, APP, BAT, BALL, BATS, and BALL.

Try different search terms to get a feel for how the search operation works.

BALL returns true BA returns false, as BA is not marked as the end of a word

search for BATH

0 / 5

Time Complexity

Insertion

The insert operation takes a word as input and adds it to the trie.

We traverse the trie until we reach the last character of the search term. From there, we add the nodes that don't exist already in the trie, and mark the last node as the end of a word.

The animation visualizes the insert operation for a word of your choice (case-sensitive) into a trie containing APPLE, APP, BAT, BATS, and BALLET.

The animation resets back to the original trie after each insertion - the trie does not accumulate words as you insert them.

Some example words to insert:

APPLE (already exists) BALL (no new nodes created, but "L" is marked as the end of a word) COAL (creates a new branch in the trie from the root)

insert BALLOON

0 / 3

Time Complexity

Deletion

The delete operation deletes a word from the trie.

We traverse down to the last character of the word we want to delete, set the "end of word" flag to false, and then remove any nodes that are not part of any other words in the trie.

The animation visualizes a delete operation from a trie containing APPLE, APP, BAT, BATS, BALL, and BALLET.

The animation resets back to the original trie after each deletion - meaning the trie does not continuously shrink as you delete words.

Some example words to delete:

BALL (removes the EOW marker from the "L" node) COAL (does nothing, as the word does not exist in the trie) BATS (removes the "S" node)

delete BALLET

0 / 5

Time Complexity

Summary

Operation	Description	Time Complexity
Search	Search for a word in the trie	O(L)
Insert	Insert a word in the trie	O(L)
Delete	Delete a word from the trie	O(L)

Space Complexity

A trie in which there are no shared nodes.

Next: Implement Trie Methods

Your account is free and you can post anonymously if you choose.

Sort By

Loading comments...

BlogBehavioral Interview Examples Interviewing for Experienced SWEs All Blog Posts

Compare UsCompare to Interviewing.io

LinksFAQ Schedule Mock Interviews Pricing Become a Coach Our Coaches Learn System Design Learn DSA Guided Practice Hello Interview Premium

LegalTerms and Conditions Privacy Policy

Contactsupport@hellointerview.com7511 Greenwood Ave North
Unit #4238 Seattle, WA 98103