Bitmask provide an efficient way to manipulate a small set of Booleans that is stored as a 32-(or 64-)bit signed integer in base-10 but interpreted as a short 32-(or 64-) characters string.
By using bitwise operations, each bit of the integer can be checked, turned on (or turned off) easily and quickly. It can be used in various algorithms such as the Dynamic Programming solution for Travelling Salesman Problem to speed up crucial (small) set-based operations.
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The visualisation of a bitmask data structure and its operations are shown above.
The top row describes the indices of the bits of the input integer S starting from the 0-th bit as the rightmost bit. Note that we use 1-digit hexadecimal notation of A/B/../E for the 10/11/../14-th bit.
The second row describes the bits of the input integer S. In practical applications, this is usually a 32-bit signed integer (e.g., int in C++/most other programming languages in 2022). Sometimes, this is a 64-bit signed integer (e.g., long long in C++). For this visualization, we limit S to 16-bit signed integer.
The third row describes the bits of the (bit)mask that will be applied to S together with the associated bitwise operation.
The last row describes the result.
Pro-tip 1: Since you are not logged-in, you may be a first time visitor (or not an NUS student) who are not aware of the following keyboard shortcuts to navigate this e-Lecture mode: [PageDown]/[PageUp] to go to the next/previous slide, respectively, (and if the drop-down box is highlighted, you can also use [→ or ↓/← or ↑] to do the same),and [Esc] to toggle between this e-Lecture mode and exploration mode.
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In this visualization, we currently support 6 Bitmask operations (all run in O(1)):
Set S (several ways)
Set j-th Bit
Check j-th Bit
Clear j-th Bit
Toggle j-th Bit
Least Significant Bit
Pro-tip 2: We designed this visualization and this e-Lecture mode to look good on 1366x768 resolution or larger (typical modern laptop resolution in 2021). We recommend using Google Chrome to access VisuAlgo. Go to full screen mode (F11) to enjoy this setup. However, you can use zoom-in (Ctrl +) or zoom-out (Ctrl -) to calibrate this.
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We can enter a (small) Integer between [0..32767 (215-1)] in Decimal (base-10) and the Binary (base-2) form of S will be visualized.
Alternatively, we can select any random Integer between the same range [0..32767], a random powers of 2 (with specific pattern of '10...0'), or a random powers of 2 minus 1 (with specific pattern of '11...1').
Pro-tip 3: Other than using the typical media UI at the bottom of the page, you can also control the animation playback using keyboard shortcuts (in Exploration Mode): Spacebar to play/pause/replay the animation, ←/→ to step the animation backwards/forwards, respectively, and -/+ to decrease/increase the animation speed, respectively.
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We can enter the index of the j-th Bit of S to be set (turned on).
Note that index starts from 0 but counted from the rightmost bit (refer to the top row).
The bitwise operation is simple: S OR (1 << j).
Setting a bit that is already on will not change anything.
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We can enter the index of the j-th Bit of S to be checked (on whether it is on or off).
Note that index starts from 0 but counted from the rightmost bit (refer to the top row).
The bitwise operation is simple: S AND (1 << j).
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We can enter the index of the j-th Bit of S to be cleared (turned off).
Note that index starts from 0 but counted from the rightmost bit (refer to the top row).
The bitwise operation is simple: S AND ~(1 << j).
Clearing a bit that is already off will not change anything.
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We can enter the index of the j-th Bit of S to be toggled (on → off or off → on).
Note that index starts from 0 but counted from the rightmost bit (refer to the top row).
The bitwise operation is simple: S XOR (1 << j).
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This operation requires no input. It is a special operation to quickly identify the rightmost bit that is on in S.
Beyond these simple applications, bitmask frequently used as low-level optimizations in a few advanced algorithms, so get ready when you encounter bitmask as sub-component of the bigger algorithms.
You have reached the last slide. Return to 'Exploration Mode' to start exploring!
Note that if you notice any bug in this visualization or if you want to request for a new visualization feature, do not hesitate to drop an email to the project leader: Dr Steven Halim via his email address: stevenhalim at gmail dot com.
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Set S
Set j-th Bit
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Clear j-th Bit
Toggle j-th Bit
Least Significant Bit
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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:
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
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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
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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.
