图形由顶点/节点和连接这些顶点的边/线组成。
图可以是无向的(意味着在与每个双向边相关联的两个顶点之间没有区别)或者可以指向图(意味着其边缘从一个顶点指向另一个顶点但不一定在另一个方向上)。
可以对图形进行加权(通过向每个边缘分配权重,其表示与该连接相关联的数值)或者图形可以是未加权的(所有边缘具有单位权重1或者所有边缘具有相同的恒定权重)。

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.

🕑
我们在VisuAlgo中讨论的大多数图形问题都涉及简单图

在一个简单图中,没有(自 - )环边(连接顶点与自身的边),没有多边/平行边(同一对顶点之间的边)。换句话说:在一对不同的顶点之间最多只能有一条边。

简单图中的边E的数量范围仅为0到O(V2)。

简单图上的图算法比非简单图上的算法更容易。

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.

🕑
无向边e:(u,v)被认为是以其两个端点顶点入射:u和v。如果两个顶点与公共边缘一起入射,则它们被称为相邻(或邻居)。例如,边(0,2)入射到顶点0 + 2并且顶点0 + 2是相邻的。

如果两个边缘与公共顶点一起入射,则它们被称为相邻边缘。例如,边(0,2)和(2,4)是相邻的。

无向图中的顶点v的度数是与v一起入射的边的数量。度为0的顶点被称为孤立顶点。例如,顶点0/2/6分别具有2/3/1的度数。

图G的子图G'是包含G的顶点和边的子集的(较小的)图。例如,三角形{0,1,2}是当前显示的图的子图。

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.

🕑
(无向)图G中(长度为n)的路径是顶点序列{v0,v1,...,vn-1,vn},使得在vivi+1∀i∈[0..n-1]之间存在边缘。
如果路径上没有重复的顶点,我们称这样的路径为简单路径。
例如,{0,1,2,4,5}是当前显示的图形中的一个简单路径。

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.

🕑
如果在G的每对不同顶点之间存在路径,则能将无向图G称为连接图。例如,当前显示的图不是连接图。

如果要把无向图C称为无向图G的连通分量,它必须符合以下的条件。 1)CG的子图; 2) C是个连接图; 3)没有G的连通子图将C作为子图并且包含不在C中的顶点或边(即C是满足其他两个标准的最大子图)。

例如,当前显示的图形具有{0,1,2,3,4}和{5,6}作为其两个连接分量。
🕑
在有向图中,前面提到的一些术语有小的调整。

如果我们有一个有向边e:(u→v),我们说v与u相邻但不一定在另一个方向上。例如,1在当前显示的有向图中与0相邻但0与1不相邻。

在有向图中,我们必须进一步将顶点v的度数区分为度数和度数。度数/出度是分别从v进入/离开的边数。例如,顶点1的入度/出度分别为2/1。

在有向图中,我们定义了强连通分量(SCC)的概念。在当前显示的有向图中,我们将{0},{1,2,3}和{4,5,6,7}作为其三个SCC。
🕑
循环是以相同顶点开始和结束的路径。

非循环图是不包含循环的图。

在无向图中,每个无向边都会导致一个微不足道的循环,尽管我们通常不会将其归类为循环。

非循环的有向图具有特殊名称:有向无环图(DAG),如上所示。

我们可以在非循环图上执行有趣的算法,这些算法将在此可视化页面和VisuAlgo中的其他图形可视化页面中进行探索。
🕑
具有涉及其顶点和/或边结构的特定属性的图可以使用其特定名称来调用,如树(如当前所示),完整图,二分图,有向无环图(DAG),以及使用频率较低的图:平面图,线图,星图,轮图等

在此可视化中,我们将在稍后突出显示前四个特殊图表。
🕑
图表在现实生活中经常以各种形式出现。因此,解决图形问题的最重要部分是图形建模部分,即将手中的问题简化为图形术语:顶点,边,权重等。
🕑
社交网络:顶点可以代表人,边缘代表人与人之间的联系(通常是无向和未加权)。
例如,请参阅当前显示的无向图。此图显示了它们之间的7个顶点(人)和8个边(连接/关系)。也许我们可以提出这样的问题:
  1. 谁是0号的朋友?
  2. 谁拥有最多的朋友?
  3. 有没有孤立的人(那些没有朋友的人)?
  4. 两个陌生人之间是否有共同的朋友:3号人和5号人?
  5. 等等...
🕑
运输网络:顶点可以表示站点,边缘表示站点之间的连接(通常是加权的)。

例如,请参阅当前显示的有向加权图。该图显示了5个顶点(站点/位置)和6个边缘(站点之间的连接/道路,具有正的权重行进时间,如图所示)。假设我们正在开车。我们或许可以问一下从0号站到4号站的路径是什么,以便我们用最少的时间到达4号站?

讨论:想想其他一些可以建模为图形的现实生活场景。
🕑

The content of this interesting slide (the answer of the usually intriguing discussion point from the earlier slide) is hidden and only available for legitimate CS lecturer worldwide. This mechanism is used in the various flipped classrooms in NUS.


If you are really a CS lecturer (or an IT teacher) (outside of NUS) and are interested to know the answers, please drop an email to stevenhalim at gmail dot com (show your University staff profile/relevant proof to Steven) for Steven to manually activate this CS lecturer-only feature for you.


FAQ: This feature will NOT be given to anyone else who is not a CS lecturer.

🕑

要在图形绘制模式之间切换,请选择相应的标题。 我们有:

  1. U/U = 无向/不加权,
  2. U/W = 无向/加权,
  3. D/U = 有向/不加权, and
  4. D/W = 有向/加权.

我们根据所选模式限制您可以绘制的图形类型。

🕑

您可以单击任何一个示例图形并可视化上图。

您还可以直接在可视化区域中绘制图形:

  1. 点击空白区域添加顶点,
  2. 单击顶点,按住,将绘制的边缘拖动到另一个顶点,然后将其放在那里以添加边缘(PS:此操作不适用于移动用户;您需要鼠标),
  3. 选择顶点/边缘并按“删除”键删除该顶点/边,
  4. 选择边缘并按“Enter”以更改该边缘的权重[0..99],
  5. 按住“Ctrl”,然后您可以单击并拖动顶点。
🕑
我们将VisuAlgo中讨论的图形限制为简单图形。请参阅本幻灯片中的讨论。

我们还将可以在屏幕上绘制的顶点数限制为最多10个顶点,范围从顶点0到顶点9.这与上面的简单图形约束一起,将无向/有向边的数量限制为45 /分别为90。
🕑
所有示例图都可以在这里找到。
目前,我们为每个类别提供七个示例图表(U / U,U / W,D / U,D / W)。
请注意,在加载其中一个示例图表后,您可以进一步修改当前显示的图表以满足您的需要。
🕑
Tree,Complete,Bipartite,Directed Acyclic Graph(DAG)是特殊图的属性。在上面的可视化/绘图区域中修改图形时,会立即检查和更新这些属性。

还有其他不太常用的特殊图形:平面图,线图,星图,轮图等,但在绘制它们时,它们当前在此可视化中不会被自动检测到。
🕑
树是具有V顶点和E = V-1边的连通图,非循环,并且在任何顶点对之间具有一条唯一路径。通常,树在无向图上定义。

无向树(见上文)实际上包含琐碎的循环(由其双向边缘引起),但它不包含非平凡循环。有针对性的树显然是非循环的。

由于树只有V-1边,因此它通常被认为是稀疏图。

我们目前显示我们的U / U:Tree示例。您可以进入“探索模式”并绘制自己的树木。
🕑
并非所有树都具有相同的图形绘制布局,其顶部具有特殊根顶点,底部具有叶顶点(顶点为1)。上面显示的(星)图也是树,因为它满足树的属性。

将其顶点之一指定为根顶点的树称为有根树。

我们总是可以通过将特定顶点(通常是顶点0)指定为根来将任何树转换为根树,并从根运行DFS或BFS算法。
🕑
在有根树中,我们有层次结构(父,子,祖先,后代),子树,级别和高度的概念。我们将通过示例说明这些概念,因为它们的含义与现实生活中的对应物一样:
  1. 0/1/7/9/4的父级分别为none / 0 / 1 / 8 / 3,
  2. 0/1/7的子女分别为{1,8} / {2,3,6,7} / none,
  3. 4/8的祖先分别为{3,1,0} / {0},
  4. 1/8的后代分别是{2,3,4,5,6,7} / {9},
  5. 以1为根的子树包括1,其后代和所有相关边,
  6. 0/1/2/3级成员分别为{0} / {1,8} / {2,3,6,7,9} / {4,5},
  7. 这个有根树的高度是它的最高级别= 3。
🕑
对于有根树,我们还可以定义其他属性:
二叉树是一个有根树,其中一个顶点最多有两个孩子,它们被恰当地命名为:left和right child(左子节点和右子节点)。在讨论二叉搜索树二叉堆时,我们经常会看到这种形式。
满二叉树是一个其中每个非叶(也称为内部)顶点恰好有两个子节点的二叉树。上面显示的二叉树符合此标准。
一个完全二叉树的每个级别都被完全填充,除了最后一级可能尽可能地填充。我们经常会在讨论二叉堆时看到这种形式。
🕑
完整图是具有V个顶点和 E = V*(V-1)/2 个边(或E = O(V2)的图,即在任何顶点对之间存在边。通常,完整图表用KV表示。
完整图是最密集的简单图。
我们目前展示了我们的U/W: K5示例。您可以进入“探索模式”并绘制自己的完整图形(虽然对于较大的V来说有点单调乏味)。
🕑
二分图是具有V个顶点的无向图,其可以被划分为大小为mn的两个不相交的顶点集,其中V = m + n。同一组的成员之间没有边缘。二分图也没有奇数长度的圈(cycle)。
我们目前展示了我们的U / U:Bipartite示例。您可以进入“探索模式”并绘制自己的二分图。
二分图也可以是完整的,即来自一个不相交集的所有m个顶点都连接到来自另一个不相交集的所有n个顶点。当m = n = V / 2时,这样的完全二分图也具有E = O(V2
🕑

Directed Acyclic Graph (DAG) is a directed graph that has no cycle, which is very relevant for Dynamic Programming (DP) techniques.


Each DAG has at least one Topological Sort/Order which can be found with a simple tweak to DFS/BFS Graph Traversal algorithm. DAG will be revisited again in DP technique for SSSP on DAG.


We currently show our D/W: Four 0→4 Paths example. You can go to 'Exploration Mode' and draw your own DAGs.

🕑
有许多方法可以将图形信息存储到图形数据结构中。在此可视化中,我们显示了三个图形数据结构:邻接矩阵,邻接列表和边缘列表 - 每个都有自己的优点和缺点。
🕑
邻接矩阵(AM)是一个方阵,其中条目AM [i] [j]示出从顶点i到顶点j的边缘权重。对于未加权的图形,我们可以为所有边缘权重设置单位权重= 1。 'x'表示该顶点不存在(已删除)。

我们简单地使用大小为VxV的C ++/Python/Java原生2D数组来实现这种数据结构。
🕑
空间复杂度分析:不幸的是,AM需要O(V2)的大空间复杂度,即使图形实际上是稀疏的(边缘不多)。

讨论:了解AM的大空间复杂性,何时使用它是有益的?或者AM总是一个劣质的图形数据结构,永远不该使用?
🕑

The content of this interesting slide (the answer of the usually intriguing discussion point from the earlier slide) is hidden and only available for legitimate CS lecturer worldwide. This mechanism is used in the various flipped classrooms in NUS.


If you are really a CS lecturer (or an IT teacher) (outside of NUS) and are interested to know the answers, please drop an email to stevenhalim at gmail dot com (show your University staff profile/relevant proof to Steven) for Steven to manually activate this CS lecturer-only feature for you.


FAQ: This feature will NOT be given to anyone else who is not a CS lecturer.

🕑
邻接列表(AL)是有V个列表的数组,每个顶点一个(通常以递增的顶点数排序),其中对于每个顶点i,AL [i]存储i的邻居列表。对于加权图,我们可以存储(邻居顶点,此边的权重)对。
我们使用一个嵌套的Vector对(用于加权图)来实现此数据结构。在C++中:vector<vector<pair<int, int>>> AL; Python: AL = [[] for _ in range(N)] Java: Vector<Vector<IntegerPair>> AL; // Java 中的IntegerPair 类似于 C++中的pair<int, int>
🕑
class IntegerPair implements Comparable<IntegerPair> {
Integer _f, _s;
public IntegerPair(Integer f, Integer s) { _f = f; _s = s; }
public int compareTo(IntegerPair o) {
if (!this.first().equals(o.first())) // this.first() != o.first()
return this.first() - o.first(); // is wrong as we want to
else // compare their values,
return this.second() - o.second(); // not their references
}
Integer first() { return _f; }
Integer second() { return _s; }
}
// IntegerTriple is similar to IntegerPair, just that it has 3 fields
🕑
我们使用对,因为我们需要存储每条边的信息对:(邻居顶点,边权重),其中对于未加权图,权重可以设置为0或未使用。
由于Vector的自动调整大小功能,我们使用Vector来存储对。如果我们有一个顶点的k个邻居,我们只需将k个邻居添加到该顶点的最初为空的Vector对象(此Vector可以用Linked List替换)。

我们在外面再用一层Vector来储存Vector对,即如果我们想枚举顶点u的邻居,我们使用AL [u](C ++/Python)或AL.get(u)(Java)来访问正确的Vector。
🕑
空间复杂度分析:AL具有O(V + E)的空间复杂度,比AM效率高得多,并且通常是大多数图形算法中的默认图形数据结构。
讨论:AL是最常用的图形数据结构,但讨论AL哪种情况实际上不是最佳的图形数据结构?
🕑

The content of this interesting slide (the answer of the usually intriguing discussion point from the earlier slide) is hidden and only available for legitimate CS lecturer worldwide. This mechanism is used in the various flipped classrooms in NUS.


If you are really a CS lecturer (or an IT teacher) (outside of NUS) and are interested to know the answers, please drop an email to stevenhalim at gmail dot com (show your University staff profile/relevant proof to Steven) for Steven to manually activate this CS lecturer-only feature for you.


FAQ: This feature will NOT be given to anyone else who is not a CS lecturer.

🕑

边缘列表(EL)是具有连接顶点及其权重的边的集合。通常,这些边是按权重增加来排序的,例如, Kruskal's algorithm的一部分用于最小生成树(MST)的问题。但是,在此可视化中,我们通过增加第一个顶点数来对边进行排序,如果是连接,则通过增加第二个顶点数来对边进行排序请注意,无向/有向图中的双向边分别列出一次/两次。
我们使用三元组Vector来实现这种数据结构。C++:vector<tuple<int, int, int>> EL; Python: EL = [] Java: Vector<IntegerTriple> EL; // Java中的IntegerTriple类似于C++中的tuple<int, int, int>

🕑
空间复杂度分析:EL具有O(E)的空间复杂度,其比AM更有效并且与AL一样有效。

讨论:除了Kruskal的最小生成树(MST)算法之外,详细说明EL的潜在用法!
🕑

The content of this interesting slide (the answer of the usually intriguing discussion point from the earlier slide) is hidden and only available for legitimate CS lecturer worldwide. This mechanism is used in the various flipped classrooms in NUS.


If you are really a CS lecturer (or an IT teacher) (outside of NUS) and are interested to know the answers, please drop an email to stevenhalim at gmail dot com (show your University staff profile/relevant proof to Steven) for Steven to manually activate this CS lecturer-only feature for you.


FAQ: This feature will NOT be given to anyone else who is not a CS lecturer.

🕑

将图形信息存储到图形数据结构后,我们可以回答几个简单的问题。

  1. 计数 V,
  2. 计数 E,
  3. 枚举顶点u的邻居,
  4. 检查边缘(u,v)的存在等。
🕑
在AM和AL中,V只是数据结构的行数,可以在O(V中或甚至在O(1中获得 - 取决于实际实现。
讨论:如果图存储在EL中,如何计算V
PS:有时这个数字是存储/维护在一个单独的变量中,这样我们就不必每次都重新计算它 - 特别是如果图形在创建之后永远/很少改变,因此我们有O(1)性能,例如:对于上面显示的示例图,我们可以存储(在我们的AM / AL / EL数据结构中)有7个顶点。
🕑

The content of this interesting slide (the answer of the usually intriguing discussion point from the earlier slide) is hidden and only available for legitimate CS lecturer worldwide. This mechanism is used in the various flipped classrooms in NUS.


If you are really a CS lecturer (or an IT teacher) (outside of NUS) and are interested to know the answers, please drop an email to stevenhalim at gmail dot com (show your University staff profile/relevant proof to Steven) for Steven to manually activate this CS lecturer-only feature for you.


FAQ: This feature will NOT be given to anyone else who is not a CS lecturer.

🕑
在边表(EL)中,E只是行数,可以用O(E)计数。请注意,根据需要,我们可以在EL中存储一次双向边,但在其他情况下,我们将两个有向边存储在EL内。
在邻接表(AL)中,可以通过将所有V列表的长度相加来找到 E,并将最终答案除以2(对于无向图)。这需要O(V+E计算时间,因为每个顶点和每个边缘仅被处理一次。
讨论:如果图表存储在邻接矩阵(AM)中,如何计算E
PS:为了提高效率,有时将这个数字存储/维护在一个单独的变量中,例如:对于上面显示的示例图,我们可以记住(在我们的AM / AL / EL数据结构中)有8个无向边。
🕑

The content of this interesting slide (the answer of the usually intriguing discussion point from the earlier slide) is hidden and only available for legitimate CS lecturer worldwide. This mechanism is used in the various flipped classrooms in NUS.


If you are really a CS lecturer (or an IT teacher) (outside of NUS) and are interested to know the answers, please drop an email to stevenhalim at gmail dot com (show your University staff profile/relevant proof to Steven) for Steven to manually activate this CS lecturer-only feature for you.


FAQ: This feature will NOT be given to anyone else who is not a CS lecturer.

🕑
在AM中,如果AM [u],我们需要遍历AM [u] [j]∀j∈[0..V-1]的所有列并报告(j,AM [u] [j])是否[j]是零。这是 O(V) - 慢。
在AL中,我们只需要遍历AL [u]。如果顶点u只有k个邻居,那么我们只需要O(k来枚举它们 - 这被称为输出敏感时间复杂度,已经是最好的了。
我们通常按顶点数量递增的方式列出邻居。例如,上面的示例图中的顶点1的邻居是{0,2,3},按增加的顶点数顺序。
讨论:如果图形存储在EL中,如何执行此操作?
🕑

The content of this interesting slide (the answer of the usually intriguing discussion point from the earlier slide) is hidden and only available for legitimate CS lecturer worldwide. This mechanism is used in the various flipped classrooms in NUS.


If you are really a CS lecturer (or an IT teacher) (outside of NUS) and are interested to know the answers, please drop an email to stevenhalim at gmail dot com (show your University staff profile/relevant proof to Steven) for Steven to manually activate this CS lecturer-only feature for you.


FAQ: This feature will NOT be given to anyone else who is not a CS lecturer.

🕑
在AM中,我们可以简单地检查AM [u] [v]是否为非零。这是O(1) - 最快的。
在AL中,我们必须检查AL [u]是否包含顶点v。这是O(k) - 更慢。
例如,上面的示例图中存在边(2,4),但边不存在边(2,6)。
请注意,如果我们找到了edge(u,v),我们也可以访问和/或更新其权重。
讨论:如果图形存储在EL中,如何执行此操作?
🕑

The content of this interesting slide (the answer of the usually intriguing discussion point from the earlier slide) is hidden and only available for legitimate CS lecturer worldwide. This mechanism is used in the various flipped classrooms in NUS.


If you are really a CS lecturer (or an IT teacher) (outside of NUS) and are interested to know the answers, please drop an email to stevenhalim at gmail dot com (show your University staff profile/relevant proof to Steven) for Steven to manually activate this CS lecturer-only feature for you.


FAQ: This feature will NOT be given to anyone else who is not a CS lecturer.

🕑

Quiz: So, what is the best graph data structure?

Adjacency Matrix
Edge List
Adjacency List
It Depends

讨论: 为什么?

🕑

The content of this interesting slide (the answer of the usually intriguing discussion point from the earlier slide) is hidden and only available for legitimate CS lecturer worldwide. This mechanism is used in the various flipped classrooms in NUS.


If you are really a CS lecturer (or an IT teacher) (outside of NUS) and are interested to know the answers, please drop an email to stevenhalim at gmail dot com (show your University staff profile/relevant proof to Steven) for Steven to manually activate this CS lecturer-only feature for you.


FAQ: This feature will NOT be given to anyone else who is not a CS lecturer.

🕑
你已经完成了这个相对简单的图形数据结构的基本内容,我们鼓励你在探索模式中通过绘制你自己的图形进一步探索。
然而,我们仍然有一些更有趣的图形数据结构的挑战,在本节中概述。
请注意,图形数据结构通常只是解决较难的图形问题(如MST, SSSP, MF, Matching, MVC, ST, or TSP)的必要部分,而不是充分部分。
🕑

有关此数据结构的一些有趣问题,请练习Graph Data Structures培训模块(无需登录)。

🕑
请查看 C++/Python/Java/OCaml 对于此课中讲到的这三种图结构的实现:邻接矩阵(Adjacency Matrix),邻接表(Adjacency List),边表(Edge List):graph_ds.cpp | py | java | ml.
🕑

尝试解决两个基本的编程问题,这些问题需要使用图形数据结构,而不需要任何花哨的图形算法:

  1. UVa 10895 - Matrix Transpose and,
  2. Kattis - flyingsafely.
🕑

The content of this interesting slide (the answer of the usually intriguing discussion point from the earlier slide) is hidden and only available for legitimate CS lecturer worldwide. This mechanism is used in the various flipped classrooms in NUS.


If you are really a CS lecturer (or an IT teacher) (outside of NUS) and are interested to know the answers, please drop an email to stevenhalim at gmail dot com (show your University staff profile/relevant proof to Steven) for Steven to manually activate this CS lecturer-only feature for you.


FAQ: This feature will NOT be given to anyone else who is not a CS lecturer.


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.

🕑
V=0, E=0 • 树? No • 完成? No • 二部? No • DAG? No • 交叉? No
邻接矩阵
012
0010
1101
2010
邻接列表
0: 1
1: 02
2: 1
边缘列表
0: 01
1: 12

Edit Graph

>

We use cookies to improve our website.
By clicking ACCEPT, you agree to our use of Google Analytics for analysing user behaviour and improving user experience as described in our Privacy Policy.
By clicking reject, only cookies necessary for site functions will be used.

ACCEPT REJECT
关于 团队 使用条款 隐私政策

关于

VisuAlgo于2011年由Steven Halim博士创建,是一个允许学生以自己的速度自学基础知识,从而更好地学习数据结构与算法的工具。
VisuAlgo包含许多高级算法,这些算法在Steven Halim博士的书(“Competitive Programming”,与他的兄弟Felix Halim博士合作)和其他书中有讨论。今天,一些高级算法的可视化/动画只能在VisuAlgo中找到。
虽然本网站是专门为新加坡国立大学(NUS)学生学习各种数据结构和算法类(例如CS1010,CS2040,CS3230,CS3233,CS4234)而设,但我们作为在线学习的倡导者,我们非常希望世界各地的好奇的头脑能发现这些非常有用的算法可视化。
VisuAlgo不是从一开始就设计为在小触摸屏(例如智能手机)上工作良好,因为为了满足许多复杂算法可视化,需要大量的像素和点击并拖动手势进行交互。为得到良好的用户体验,最低屏幕分辨率应为1024x768,并且本网站只有首页相对适合移动设备。但是,我们正在测试一个准备在2022年4月发布的移动版本。
VisuAlgo是一个正在进行的项目,更复杂的可视化仍在开发中。
最令人兴奋的发展是自动问题生成器和验证器(在线测验系统),允许学生测试他们的基本数据结构和算法的知识。这些问题是通过一些随机生成的规则,学生的答案会在提交给我们的评分服务器后立即自动分级。这个在线测验系统,当它被更多的世界各地的CS教师采用,应该能从技术上消除许多大学的典型计算机科学考试手动基本数据结构和算法问题。通过在通过在线测验时设置小(但非零)的重量,CS教练可以(显着地)增加他/她的学生掌握这些基本问题,因为学生具有几乎无限数量的可以立即被验证的训练问题他们参加在线测验。培训模式目前包含12个可视化模块的问题。我们将很快添加剩余的12个可视化模块,以便VisuAlgo中的每个可视化模块都有在线测验组件。
VisuAlgo支持三种语言:英语,中文,印尼语。目前,我们还以各种语言写了有关VisuAlgo的公共注释:
id, kr, vn, th.

团队

项目领导和顾问(2011年7月至今)
Dr Steven Halim, Senior Lecturer, School of Computing (SoC), National University of Singapore (NUS)
Dr Felix Halim, Senior Software Engineer, Google (Mountain View)

本科生研究人员 1 (Jul 2011-Apr 2012)
Koh Zi Chun, Victor Loh Bo Huai

最后一年项目/ UROP学生 1 (Jul 2012-Dec 2013)
Phan Thi Quynh Trang, Peter Phandi, Albert Millardo Tjindradinata, Nguyen Hoang Duy

最后一年项目/ UROP学生 2 (Jun 2013-Apr 2014)
Rose Marie Tan Zhao Yun, Ivan Reinaldo

本科生研究人员 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

最后一年项目/ UROP学生 3 (Jun 2014-Apr 2015)
Erin Teo Yi Ling, Wang Zi

最后一年项目/ UROP学生 4 (Jun 2016-Dec 2017)
Truong Ngoc Khanh, John Kevin Tjahjadi, Gabriella Michelle, Muhammad Rais Fathin Mudzakir

最后一年项目/ UROP学生 5 (Aug 2021-Dec 2022)
Liu Guangyuan, Manas Vegi, Sha Long, Vuong Hoang Long

最后一年项目/ UROP学生 6 (Aug 2022-Apr 2023)
Lim Dewen Aloysius, Ting Xiao

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

致谢
本项目运营资金是由NUS教学与学习发展中心(CDTL)的教学增进款慷慨提供的。

使用条款

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.

隐私政策

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.