1x

Hull Konveks dari sebuah himpunan titik-titik P adalah poligon konveks terkecil CH(P) di mana tiap titik dalam P terletak antara di perbatasan dari CH(P) atau di dalamnya. Bayangkan titik-titik tersebut sebagai paku di sebuah bidang datar dan kita memiliki karet yang cukup panjang untuk mengelilingi keseluruh paku tersebut. Jika karet ini dilepas, maka karet tersebut akan mengelilingi paku-paku tersebut dengan luas sekecil mungkin. Luas tersebut adalah luas dari hull konveks dari titik-titik / paku-paku tersebut. Mencari hull konveks dari sekelompok titik memiliki banyak kegunaan dalam masalah pengepakan.

Remarks: By default, we show e-Lecture Mode for first time (or non logged-in) visitor.
If you are an NUS student and a repeat visitor, please login.

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In this visualization, we currently only support Graham's Scan algorithm.

We first pick a pivot point (bottom-most, left-most point) and then sort the other N-1 points in counter-clockwise order w.r.t. this pivot point.

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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This visualization is currently only used once a year in NUS (around early April each year, for CS3233), hence it only gets updated briefly once a year.

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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Buat

Example Points

Edit Points

Andrew_Chain(Pts)

CH_Graham(Pts)

Shamos(Pts)

>
N =

Acak

Square

Pentagon

Crescent

Circle

#### Tentang

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.

#### Tim

Pemimpin & Penasihat Proyek (Jul 2011-sekarang)
Associate Professor Steven Halim, School of Computing (SoC), National University of Singapore (NUS)
Dr Felix Halim, Senior Software Engineer, Google (Mountain View)

Murid-Murid S1 Peniliti 1
CDTL TEG 1: Jul 2011-Apr 2012: Koh Zi Chun, Victor Loh Bo Huai

Murid-Murid Proyek Tahun Terakhir/UROP 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

Murid-Murid S1 Peniliti 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

Murid-Murid Proyek Tahun Terakhir/UROP 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

Murid-Murid S1 Peniliti 3
Optiver: Aug 2023-Oct 2023: Bui Hong Duc, Oleh Naver, Tay Ngan Lin

Murid-Murid Proyek Tahun Terakhir/UROP 3
Aug 2023-Apr 2024: Xiong Jingya, Radian Krisno, Ng Wee Han

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

Ucapan Terima Kasih
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.

#### Syarat Guna

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.

#### Kebijakan Privasi

Versi 1.2 (Dimutakhirkan Jum, 18 Aug 2023).
Sejak Jumat, 18 Aug 2023, kami tidak lagi menggunakan Google Analytics. Semua cookie yang kami gunakan sekarang hanya untuk operasi situs web ini. Popup persetujuan cookie yang mengganggu sekarang dimatikan bahkan untuk pengunjung pertama kali.
Sejak Jumat, 07 Jun 2023, berkat sumbangan yang murah hati dari Optiver, siapa pun di dunia bisa membuat akun VisuAlgo sendiri untuk menyimpan beberapa pengaturan kustomisasi (seperti mode layout, bahasa default, kecepatan pemutaran, dll).
Selain itu, untuk mahasiswa NUS, dengan menggunakan akun VisuAlgo (sebuah tupel dari alamat email NUS resmi, nama murid resmi NUS seperti dalam daftar kelas, dan sebuah kata sandi yang dienkripsi pada sisi server — tidak ada data personal lainnya yang disimpan), anda memberikan ijin kepada dosen modul anda untuk melacak pembacaan slide-slide kuliah maya dan kemajuan latihan kuis online yang dibutuhkan untuk menjalankan modul tersebut dengan lancar. Akun VisuAlgo anda akan juga dibutuhkan untuk mengambil kuis-kuis VisuAlgo online resmi sehingga memberikan kredensial akun anda ke orang lain untuk mengerjakan Kuis Online sebagai anda adalah pelanggaran akademis. Akun pengguna anda akan dihapus setelah modul tersebut selesai kecuali anda memilih untuk menyimpan akun anda (OPT-IN). Akses ke basis data lengkap dari VisuAlgo (dengan kata-kata sandi terenkripsi) dibatasi kepada Prof Halim saja.
Untuk dosen-dosen Ilmu Komputer di seluruh dunia yang telah menulis kepada Steven, sebuah akun VisuAlgo (alamat email (bukan-NUS), anda dapat menggunakan nama panggilan apapun, dan kata sandi terenkripsi) dibutuhkan untuk membedakan kredensial online anda dibandingkan dengan orang-orang lain di dunia. Akun anda akan dilacak seperti seorang murid NUS biasa diatas tetapi akun anda akan mempunya fitur-fiture spesifik untuk dosen-dosen Ilmu Komputer, yaitu kemampuan untuk melihat slide-slide tersembunyi yang berisi jawaban-jawaban (menarik) dari pertanyaan-pertanyaan yang dipresentasikan di slide-slide sebelumnya sebelum slide-slide tersembunyi tersebut. Anda juga dapat mengakses setingan Susah dari Kuis-Kuis Online VisuAlgo. Anda dapat dengan bebas menggunakan materi-materia untuk memperkaya kelas-kelas struktur-struktur data dan algoritma-algoritma anda. Catat bahwa mungkin ada fitur-fitur khusus tambahan untuk dosen Ilmu Komputer di masa mendatang.
Untuk siapapun dengan akun VisuAlgo, anda dapat membuang akun anda sendiri bila anda tidak mau lagi diasosiasikan dengan tool VisuAlgo ini.