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# VisuAlgo.net/en
## visualising data structures and algorithms through animation

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Featured story: Visualizing Algorithms with a Click



Featured blog: Digitising **as many** static Computer Science textbooks examples into equivalent VisuAlgo animation



VisuAlgo project continues to be funded by Optiver (started mid 2023, to continue to mid 2025 and possibly beyond).
The focus this AY24/25 is to make VisuAlgo much more mobile-friendly and to improve the online quiz capabilities.

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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 aim to make all three has near 100% translation rate. 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.

Here are some of the newer visualization features: ability to show two visualization scales (1.0x and 0.5x), the zoom-out scale is used to show operations of a slightly bigger test cases, /list (the linked list are no longer automatically re-layout for most cases to strengthen the O(1) impression of almost all Linked List operations).

Breaking news \[Fri, 09 Jun 23\]: VisuAlgo project is funded by Optiver starting today. We now open VisuAlgo account registration to every Computer Science students/teachers worldwide. Go to the login page and follow the on-screen instructions to create a new VisuAlgo account (no longer restricted to 'nus.edu'-related emails).

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 for many visualization pages have reached 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.

Preferred layout: Default View CS1010 or equivalent IT5003 CS2040 or equivalent CS3230 CS3233 CS4234

- Click to View

Array Training

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cs1010 it5003 cs2040 cs3230 cs3233
- Click to View

Sorting Training

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array algorithm bubble select insert selection insertion merge quick randomized quick counting radix sort cs1010 it5003 cs2040 cs3230 list data structure sorting
- Click to View

Bitmask Training

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bit manipulation set cs3233 array list ds data structure bitmask
- Click to View

Linked List Training

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stack queue doubly deque it5003 cs2040 array ds data structure linked
- Click to View

Binary Heap Training

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priority queue recursive it5003 cs2040 recursion ds data structure binary heap
- Click to View

Hash Table Training

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open addressing linear quadratic probing it5003 cs2040 ds data structure
- Click to View

Binary Search Tree Training

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adelson velskii landis set table avl it5003 cs2040 recursion recursive ds data structure set bst binary search tree priority queue
- Click to View

Graph Structures Training

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tree complete bipartite dag it5003 cs2040 graph ds data structure
- Click to View

Union-Find DS Training

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path compression disjoint set data structure union by rank cs2040 cs3233 array tree find ds
- Click to View

Fenwick Tree Training

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binary indexed tree bit dynamic fenwick range sum point update cs3233 binary ds data structure
- Click to View

Segment Tree Training

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dynamic range sum min max cs3233 segment tree ds data structure
- Click to View

Recursion Tree/DAG Training

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dynamic programming dp generic cs1010 it5003 cs2040 cs3233 cs4234 recursive algorithm recursion tree dag
- Click to View

Graph Traversal Training

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bfs dfs it5003 cs2040 bipartite scc cut vertex articulation point bridge cs2020 graph algorithm
- Click to View

Min Spanning Tree Training

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mst prim kruskal graph min spanning cs2040 tree algorithm
- Click to View

SS Shortest Paths Training

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sssp single-source bfs dijkstra bellman ford it5003 cs2040 single source shortest path graph algorithm
- Click to View

Cycle Finding Training

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floyd tortoise-hare math cs3233 algorithm
- Click to View

Suffix Tree Training

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string matching lrs lcs cs3233 suffix tree ds data structure
- Click to View

Suffix Array Training

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lcp cs3233 matching lrs lcs suffix array string ds data structure
- Click to View

Geometry (Polygon) Training

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convex cut winding concave cs3233 computational geometry algorithm
- Click to View

Convex Hull Training

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andrew monotone chain graham scan jarvis march cs3233 computational geometry algorithm
- Click to View

Network Flow Training

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max flow edmonds karp min cut dinic ford fulkerson graph cs3233 cs4234 algorithm
- Click to View

Graph Matching Training

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augmenting path bipartite graph cs3233 cs4234 matching algorithm
- Click to View

Min Vertex Cover Training

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np-hard graph bipartite tree tree dp bipartite matching max flow cs3233 cs4234
- Click to View

Steiner Tree Training

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np-hard graph mst cs4234
- Click to View

Traveling Salesperson Problem Training

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np-hard graph dp mst cs3233 cs4234
- Click to View

NP-complete Reductions

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cs3230 cs4234

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1.0x Share About Team Terms of use Privacy Policy Open in Browser

#### About
✕

Initially conceived in 2011 by Associate Professor Steven Halim, VisuAlgo aimed to facilitate a deeper understanding of data structures and algorithms for his students by providing a self-paced, interactive learning platform.

Featuring numerous advanced algorithms discussed in Dr. Steven Halim's book, 'Competitive Programming' — co-authored with Dr. Felix Halim and Dr. Suhendry Effendy — VisuAlgo remains the exclusive platform for visualizing and animating several of these complex algorithms even after a decade.

While primarily designed for National University of Singapore (NUS) students enrolled in various data structure and algorithm courses (e.g., CS1010/equivalent, CS2040/equivalent (including IT5003), CS3230, CS3233, and CS4234), VisuAlgo also serves as a valuable resource for inquisitive minds worldwide, promoting online learning.

Initially, VisuAlgo was not designed for small touch screens like smartphones, as intricate algorithm visualizations required substantial pixel space and click-and-drag interactions. For an optimal user experience, a minimum screen resolution of 1366x768 is recommended. However, since April 2022, a mobile (lite) version of VisuAlgo has been made available, making it possible to use a subset of VisuAlgo features on smartphone screens.

VisuAlgo remains a work in progress, with the ongoing development of more complex visualizations. At present, the platform features 24 visualization modules.

Equipped with a built-in question generator and answer verifier, VisuAlgo's "online quiz system" enables students to test their knowledge of basic data structures and algorithms. Questions are randomly generated based on specific rules, and students' answers are automatically graded upon submission to our grading server. As more CS instructors adopt this online quiz system worldwide, it could effectively eliminate manual basic data structure and algorithm questions from standard Computer Science exams in many universities. By assigning a small (but non-zero) weight to passing the online quiz, CS instructors can significantly enhance their students' mastery of these basic concepts, as they have access to an almost unlimited number of practice questions that can be instantly verified before taking the online quiz. Each VisuAlgo visualization module now includes its own online quiz component.

VisuAlgo has been translated into three primary languages: English, Chinese, and Indonesian. Additionally, we have authored public notes about VisuAlgo in various languages, including Indonesian, Korean, Vietnamese, and Thai:

id, kr, vn, th.

#### Team
✕

**Project Leader & Advisor (Jul 2011-present)**
Associate Professor Steven Halim, School of Computing (SoC), National University of Singapore (NUS)
Dr Felix Halim, Senior Software Engineer, Google (Mountain View)

**Undergraduate Student Researchers 1**
**CDTL TEG 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
**Jun 2013-Apr 2014** Rose Marie Tan Zhao Yun, Ivan Reinaldo

**Undergraduate Student Researchers 2**
**CDTL TEG 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 2**
**Jun 2014-Apr 2015**: Erin Teo Yi Ling, Wang Zi
**Jun 2016-Dec 2017**: Truong Ngoc Khanh, John Kevin Tjahjadi, Gabriella Michelle, Muhammad Rais Fathin Mudzakir
**Aug 2021-Apr 2023**: Liu Guangyuan, Manas Vegi, Sha Long, Vuong Hoang Long, Ting Xiao, Lim Dewen Aloysius

**Undergraduate Student Researchers 3**
**Optiver: Aug 2023-Oct 2023**: Bui Hong Duc, Oleh Naver, Tay Ngan Lin

**Final Year Project/UROP students 3**
**Aug 2023-Apr 2024**: Xiong Jingya, Radian Krisno, Ng Wee Han, Tan Chee Heng
**Aug 2024-Apr 2025**: Edbert Geraldy Cangdinata, Huang Xing Chen, Nicholas Patrick

List of translators who have contributed ≥ 100 translations can be found at statistics page.

**Acknowledgements**
NUS CDTL gave Teaching Enhancement Grant to kickstart this project.

For Academic Year 2023/24, a generous donation from Optiver will be used to further develop VisuAlgo.

#### Terms of use
✕

VisuAlgo is generously offered at no cost to the global Computer Science community. If you appreciate VisuAlgo, we kindly request that you **spread the word about its existence to fellow Computer Science students and instructors**. You can share VisuAlgo through social media platforms (e.g., Facebook, YouTube, Instagram, TikTok, Twitter, etc), course webpages, blog reviews, emails, and more.

Data Structures and Algorithms (DSA) students and instructors are welcome to use this website directly for their classes. If you capture screenshots or videos from this site, feel free to use them elsewhere, provided that you cite the URL of this website (https://visualgo.net) and/or the list of publications below as references. However, please refrain from downloading VisuAlgo's client-side files and hosting them on your website, as this constitutes plagiarism. At this time, we do not permit others to fork this project or create VisuAlgo variants. Personal use of an offline copy of the client-side VisuAlgo is acceptable.

Please note that VisuAlgo's online quiz component has a substantial server-side element, and it is not easy to save server-side scripts and databases locally. Currently, the general public can access the online quiz system only through the 'training mode.' The 'test mode' offers a more controlled environment for using randomly generated questions and automatic verification in real examinations at NUS.

**List of Publications**

This work has been presented 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).

**Bug Reports or Request for New Features**

VisuAlgo is not a finished project. Associate Professor 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 Associate Professor Steven Halim. His contact is the concatenation of his name and add gmail dot com.

#### Privacy Policy
✕

**Version 1.2 (Updated Fri, 18 Aug 2023).**

Since Fri, 18 Aug 2023, we no longer use Google Analytics. Thus, all cookies that we use now are solely for the operations of this website. The annoying cookie-consent popup is now turned off even for first-time visitors.

Since Fri, 07 Jun 2023, thanks to a generous donation by Optiver, anyone in the world can self-create a VisuAlgo account to store a few customization settings (e.g., layout mode, default language, playback speed, etc).

Additionally, for NUS students, by using a VisuAlgo account (a tuple of NUS official email address, 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 course lecturer to keep track of your e-lecture slides reading and online quiz training progresses that is needed to run the course 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 course unless you choose to keep your account (OPT-IN). Access to the full VisuAlgo database (with encrypted passwords) is limited to Prof Halim himself.

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 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.