VisuAlgo.net/en
visualising data structures and algorithms through animation
Featured story: Visualizing Algorithms with a Click
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VisuAlgo is a trilingual site. Try visiting the other versions of VisuAlgo other than the default English version, e.g., Chinese or Indonesian. Users can see the translation statistics for these three pages (we strive to make all three near 100% soon). Unfortunately the translation progress with other languages are too far behind and they are thus redirected to English.
In VisuAlgo, you can use your own input for any algorithm instead of using only the provided sample inputs. This is one of the key feature of VisuAlgo. Try the graph drawing feature in these 9 graph-related visualizations: Graph DS, DFS/BFS, MST, SSSP, Max Flow, Matching, MVC, Steiner Tree, and TSP. You can also click tag 'graph' in any of these 9 graph-related visualization boxes or type in 'graph' in the search box.
On Wednesday, 22 December 2021, VisuAlgo moves to a new system. Here are some more noticeable visualization upgrades: /heap (try Compact Array mode plus PartialSort(), UpdateKey(i, newv), and Delete(i) operations), /bitmask (clearer this time), /ufds (more examples and new initialization mode).
To compare 2 related algorithms, e.g., Kruskal's vs Prim's on the same graph, or 2 related operations of the same data structure, e.g., visualizing Binary (Max) Heap as a Binary Tree or as a Compact Array, open 2 VisuAlgo pages in 2 windows and juxtapose them. Click here to see the screenshot. This juxtaposition technique can be used anytime you want to compare two similar data structures or algorithms.
You can visualize the recursion tree (or DAG, if there are overlapping subproblems and Dynamic Programming (DP) is applicable) of ANY valid recursive function that can be written in JavaScript. Click here to see the screenshot. Obviously do not try visualizing recursion with a gigantic recursion tree as doing so will crash your own web browser/computer.
VisuAlgo loads fast for first time visitors (we use Cloudflare global CDN), but it loads 'almost instantly' for returning visitors as we also cache lots of static content of VisuAlgo :). So, do not use incognito or private browsing mode to keep the cache. Moreover, for NUS students with VisuAlgo accounts, we will load VisuAlgo according to your preferences/class setup after you login.
Each visualization page has an 'e-Lecture Mode' that is accessible from that page's top right corner. This mode is automatically shown to first time (or non logged-in) visitors to showcase the data structure or algorithm being visualized. The quality of e-Lecture Mode will gradually be made to reach the lecture standard of algorithm classes in National University of Singapore :).
Please check the newest features of VisuAlgo: 1). User accounts system for NUS students and verified CS lecturers worldwide (and also read the latest Privacy Policy popup at the bottom right corner), 2). More mobile-friendly setup, 3). More polished e-Lecture notes to reach "NUS standard", and 4). Trilingual capability (/en, /zh, or /id).
VisuAlgo has two main components: The 24 visualization pages and their associated Online Quiz component (more questions are currently being added into the question bank). We do not script any of the questions in Online Quiz :O and all answers will be graded almost instantly :). You can this online quiz system by clicking the 'Training' button on the visualization module.
Search the term 'algorithm visualization' in your favorite Search Engine, do you see VisuAlgo in the first page of the search result :)? Next level: Search that term again, but in Chinese or Indonesian :). Lastly, search the name of your favorite data structure or algorithm without mentioning the keyword 'animation' or 'visualization'. Sometimes VisuAlgo is still listed in the first page :).
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array
algorithm
bubble
select
insert
selection
insertion
merge
quick
randomized quick
counting
radix
sort
cs1010
cs2040
cs3230
list
data structure
sorting
-
bit manipulation
set
cs3233
array
list
ds
data structure
bitmask
-
stack
queue
doubly
deque
cs2040
array
ds
data structure
linked
-
priority queue
recursive
cs2040
recursion
ds
data structure
binary
heap
-
open addressing
linear
quadratic
probing
cs2040
ds
data structure
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adelson velskii landis
set
table
avl
cs2040
recursion
recursive
ds
data structure
set
bst
binary
search
tree
priority
queue
-
tree
complete
bipartite
dag
cs2040
graph
ds
data structure
-
path compression
disjoint
set
data structure
union by rank
cs2040
cs3233
array
tree
find
ds
-
binary indexed tree
bit
dynamic
fenwick
range
sum
point
update
cs3233
binary
ds
data structure
-
dynamic
range
sum
min
max
cs3233
segment
tree
ds
data structure
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dynamic programming
dp
generic
cs1010
cs2040
cs3233
cs4234
recursive
algorithm
recursion
tree
dag
-
bfs
dfs
cs2040
bipartite
scc
cut vertex
articulation point
bridge
cs2020
graph
algorithm
-
mst
prim
kruskal
graph
min
spanning
cs2040
tree
algorithm
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sssp
single-source
bfs
dijkstra
bellman ford
cs2040
single source
shortest path
graph
algorithm
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floyd
tortoise-hare
math
cs3233
algorithm
-
string
matching
lrs
lcs
cs3233
suffix
tree
ds
data structure
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lcp
cs3233
matching
lrs
lcs
suffix
array
string
ds
data structure
-
convex
cut
winding
concave
cs3233
computational
geometry
algorithm
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andrew
monotone chain
graham
scan
jarvis
march
cs3233
computational
geometry
algorithm
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max flow
edmonds karp
min cut
dinic
ford fulkerson
graph
cs3233
cs4234
algorithm
-
augmenting path
bipartite
graph
cs3233
cs4234
matching
algorithm
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np-hard
graph
bipartite
tree
tree
dp
bipartite
matching
max flow
cs3233
cs4234
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np-hard
graph
dp
mst
cs3233
cs4234
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About
✕
VisuAlgo was conceptualised in 2011 by Dr Steven Halim as a tool to help his students better understand data structures and algorithms, by allowing them to learn the basics on their own and at their own pace.
VisuAlgo contains many advanced algorithms that are discussed in Dr Steven Halim's book ('Competitive Programming', co-authored with his brother Dr Felix Halim and his friend Dr Suhendry Effendy) and beyond. Today, a few of these advanced algorithms visualization/animation can only be found in VisuAlgo.
Though specifically designed for National University of Singapore (NUS) students taking various data structure and algorithm classes (e.g., CS1010/equivalent, CS2040/equivalent, CS3230, CS3233, and CS4234), as advocators of online learning, we hope that curious minds around the world will find these visualizations useful too.
VisuAlgo is not designed to work well on small touch screens (e.g., smartphones) from the outset due to the need to cater for many complex algorithm visualizations that require lots of pixels and click-and-drag gestures for interaction. The minimum screen resolution for a respectable user experience is 1024x768 and only the landing page is relatively mobile-friendly. However, we are currently experimenting with a mobile (lite) version of VisuAlgo to be ready by April 2022.
VisuAlgo is an ongoing project and more complex visualizations are still being developed.
The most exciting development is the automated question generator and verifier (the online quiz system) that allows students to test their knowledge of basic data structures and algorithms. The questions are randomly generated via some rules and students' answers are instantly and automatically graded upon submission to our grading server. This online quiz system, when it is adopted by more CS instructors worldwide, should technically eliminate manual basic data structure and algorithm questions from typical Computer Science examinations in many Universities. By setting a small (but non-zero) weightage on passing the online quiz, a CS instructor can (significantly) increase his/her students mastery on these basic questions as the students have virtually infinite number of training questions that can be verified instantly before they take the online quiz. The training mode currently contains questions for 12 visualization modules. We will soon add the remaining 12 visualization modules so that every visualization module in VisuAlgo have online quiz component.
We have translated VisuAlgo pages into three main languages: English, Chinese, and Indonesian. Currently, we have also written public notes about VisuAlgo in various languages:
id,
kr,
vn,
th.
Team
✕
Project Leader & Advisor (Jul 2011-present)
Dr Steven Halim, Senior Lecturer, School of Computing (SoC), National University of Singapore (NUS)
Dr Felix Halim, Senior Software Engineer, Google (Mountain View)
Undergraduate Student Researchers 1 (Jul 2011-Apr 2012)
Koh Zi Chun, Victor Loh Bo Huai
Final Year Project/UROP students 1 (Jul 2012-Dec 2013)
Phan Thi Quynh Trang, Peter Phandi, Albert Millardo Tjindradinata, Nguyen Hoang Duy
Final Year Project/UROP students 2 (Jun 2013-Apr 2014)
Rose Marie Tan Zhao Yun, Ivan Reinaldo
Undergraduate Student Researchers 2 (May 2014-Jul 2014)
Jonathan Irvin Gunawan, Nathan Azaria, Ian Leow Tze Wei, Nguyen Viet Dung, Nguyen Khac Tung, Steven Kester Yuwono, Cao Shengze, Mohan Jishnu
Final Year Project/UROP students 3 (Jun 2014-Apr 2015)
Erin Teo Yi Ling, Wang Zi
Final Year Project/UROP students 4 (Jun 2016-Dec 2017)
Truong Ngoc Khanh, John Kevin Tjahjadi, Gabriella Michelle, Muhammad Rais Fathin Mudzakir
Final Year Project/UROP students 5 (Aug 2021-Dec 2022)
Liu Guangyuan, Manas Vegi, Sha Long, Vuong Hoang Long
Final Year Project/UROP students 6 (Aug 2022-Apr 2023)
Lim Dewen Aloysius, Ting Xiao
List of translators who have contributed ≥100 translations can be found at statistics page.
Acknowledgements
This project is made possible by the generous Teaching Enhancement Grant from NUS Centre for Development of Teaching and Learning (CDTL).
Terms of use
✕
VisuAlgo is free of charge for Computer Science community on earth. If you like VisuAlgo, the only "payment" that we ask of you is for you to tell the existence of VisuAlgo to other Computer Science students/instructors that you know =) via Facebook/Twitter/Instagram/TikTok posts, course webpages, blog reviews, emails, etc.
If you are a data structure and algorithm student/instructor, you are allowed to use this website directly for your classes. If you take screen shots (videos) from this website, you can use the screen shots (videos) elsewhere as long as you cite the URL of this website (https://visualgo.net) and/or list of publications below as reference. However, you are NOT allowed to download VisuAlgo (client-side) files and host it on your own website as it is plagiarism. As of now, we do NOT allow other people to fork this project and create variants of VisuAlgo. Using the offline copy of (client-side) VisuAlgo for your personal usage is fine.
Note that VisuAlgo's online quiz component is by nature has heavy server-side component and there is no easy way to save the server-side scripts and databases locally. Currently, the general public can only use the 'training mode' to access these online quiz system. Currently the 'test mode' is a more controlled environment for using these randomly generated questions and automatic verification for real examinations in NUS.
List of Publications
This work has been presented briefly at the CLI Workshop at the ICPC World Finals 2012 (Poland, Warsaw) and at the IOI Conference at IOI 2012 (Sirmione-Montichiari, Italy). You can click this link to read our 2012 paper about this system (it was not yet called VisuAlgo back in 2012) and this link for the short update in 2015 (to link VisuAlgo name with the previous project).
This work is done mostly by my past students.
Bug Reports or Request for New Features
VisuAlgo is not a finished project. Dr Steven Halim is still actively improving VisuAlgo. If you are using VisuAlgo and spot a bug in any of our visualization page/online quiz tool or if you want to request for new features, please contact Dr Steven Halim. His contact is the concatenation of his name and add gmail dot com.
Privacy Policy
✕
Version 1.1 (Updated Fri, 14 Jan 2022).
Disclosure to all visitors: We currently use Google Analytics to get an overview understanding of our site visitors. We now give option for user to Accept or Reject this tracker.
Since Wed, 22 Dec 2021, only National University of Singapore (NUS) staffs/students and approved CS lecturers outside of NUS who have written a request to Steven can login to VisuAlgo, anyone else in the world will have to use VisuAlgo as an anonymous user that is not really trackable other than what are tracked by Google Analytics.
For NUS students enrolled in modules that uses VisuAlgo: By using a VisuAlgo account (a tuple of NUS official email address, NUS official student name as in the class roster, and a password that is encrypted on the server side — no other personal data is stored), you are giving a consent for your module lecturer to keep track of your e-lecture slides reading and online quiz training progresses that is needed to run the module smoothly. Your VisuAlgo account will also be needed for taking NUS official VisuAlgo Online Quizzes and thus passing your account credentials to another person to do the Online Quiz on your behalf constitutes an academic offense. Your user account will be purged after the conclusion of the module unless you choose to keep your account (OPT-IN). Access to the full VisuAlgo database (with encrypted passwords) is limited to Steven himself.
For other NUS students, you can self-register a VisuAlgo account by yourself (OPT-IN).
For other CS lecturers worldwide who have written to Steven, a VisuAlgo account (your (non-NUS) email address, you can use any display name, and encrypted password) is needed to distinguish your online credential versus the rest of the world. Your account will be tracked similarly as a normal NUS student account above but it will have CS lecturer specific features, namely the ability to see the hidden slides that contain (interesting) answers to the questions presented in the preceding slides before the hidden slides. You can also access Hard setting of the VisuAlgo Online Quizzes. You can freely use the material to enhance your data structures and algorithm classes. Note that there can be other CS lecturer specific features in the future.
For anyone with VisuAlgo account, you can remove your own account by yourself should you wish to no longer be associated with VisuAlgo tool.