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.

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Most graph problems that we discuss in VisuAlgo involves simple graphs.


In a simple graph, there is no (self-)loop edge (an edge that connects a vertex with itself) and no multiple/parallel edges (edges between the same pair of vertices). In another word: There can only be up to one edge between a pair of distinct vertices.


The number of edges E in a simple graph can only range from 0 to O(V2).


Graph algorithms on simple graphs are easier than on non-simple graphs.


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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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.

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A path (of length n) in an (undirected) graph G is a sequence of vertices {v0, v1, ..., vn-1, vn} such that there is an edge between vi and vi+1i ∈ [0..n-1] along the path.


If there is no repeated vertex along the path, we call such path as a simple path.


For example, {0, 1, 2, 4, 5} is one simple path in the currently displayed graph.


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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An undirected graph G is called connected if there is a path between every pair of distinct vertices of G. For example, the currently displayed graph is not a connected graph.


An undirected graph C is called a connected component of the undirected graph G if 1). C is a subgraph of G; 2). C is connected; 3). no connected subgraph of G has C as a subgraph and contains vertices or edges that are not in C (i.e. C is the maximal subgraph that satisfies the other two criteria).


For example, the currently displayed graph have {0, 1, 2, 3, 4} and {5, 6} as its two connected components.

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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。
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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。
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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。
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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。
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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...
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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。
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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.

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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。

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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。
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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。
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所有示例图都可以在这里找到。

目前,我们为每个类别提供至少两个示例图表(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。
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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。
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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。
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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。
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在根树中,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:

0/1/7/2/4的父级分别为none / 0/0/1/3,
0/1/7的子女分别为{1,7} / {2,3,6} / {8,9},
4/8的祖先分别为{3,1,0} / {7,0},
1/7的后代分别是{2,3,4,5,6} / {8,9},
以1为根的子树包括1,其后代和所有相关边,
0/1/2/3级成员分别为{0} / {1,7} / {2,3,6,8,9} / {4,5},
这个有根树的高度是它的最高级别= 3。
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For rooted tree, we can also define additional properties:


A binary tree is a rooted tree in which a vertex has at most two children that are aptly named: left and right child. We will frequently see this form during discussion of Binary Search Tree and Binary Heap.


A full binary tree is a binary tree in which each non-leaf (also called the internal) vertex has exactly two children. The binary tree shown above fulfils this criteria.


A complete binary tree is a binary tree in which every level is completely filled, except possibly the last level may be filled as far left as possible. We will frequently see this form especially during discussion of Binary Heap.

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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)。
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二分图是具有V个顶点的无向图,其可以被划分为大小为m和n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。二分图也没有奇数周期。

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)。
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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.

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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。
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Adjacency Matrix (AM) is a square matrix where the entry AM[i][j] shows the edge's weight from vertex i to vertex j. For unweighted graphs, we can set a unit weight = 1 for all edge weights. An 'x' means that that vertex does not exist (deleted).


We simply use a C++/Java native 2D array of size VxV to implement this data structure.

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Space Complexity Analysis: An AM unfortunately requires a big space complexity of O(V2), even when the graph is actually sparse (not many edges).


Discussion: Knowing the large space complexity of AM, when is it beneficial to use it? Or is AM always an inferior graph data structure and should not be used at all times?

🕑

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.

🕑

Adjacency List (AL) is an array of V lists, one for each vertex (usually in increasing vertex number) where for each vertex i, AL[i] stores the list of i's neighbors. For weighted graphs, we can store pairs of (neighbor vertex number, weight of this edge) instead.


We use a Vector of Vector pairs (for weighted graphs) to implement this data structure.
In C++: vector<vector<pair<int,int>>> AL;
In Java: Vector < Vector < IntegerPair > > AL;
// class IntegerPair in Java is like pair<int,int> in C++, next slide

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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
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We use pairs as we need to store pairs of information for each edge: (neighbor vertex number, edge weight) where weight can be set to 0 or unused for unweighted graph.


We use Vector of Pairs due to Vector's auto-resize feature. If we have k neighbors of a vertex, we just add k times to an initially empty Vector of Pairs of this vertex (this Vector can be replaced with Linked List).


We use Vector of Vectors of Pairs for Vector's indexing feature, i.e. if we want to enumerate neighbors of vertex u, we use AL[u] (C++) or AL.get(u) (Java) to access the correct Vector of Pairs.

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Space Complexity Analysis: AL has space complexity of O(V+E), which is much more efficient than AM and usually the default graph DS inside most graph algorithms.


Discussion: AL is the most frequently used graph data structure, but discuss several scenarios when AL is actually not the best graph data structure?

🕑

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.

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边缘列表(EL)是具有连接顶点及其权重的边的集合。通常,这些边缘通过增加重量来分类,例如, Kruskal最小生成树(MST)问题算法的一部分。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。在C ++中:vector <tuple <int,int,int >> EL;在Java中:Vector <integertriple> EL; // Java中的IntegerTriple类似于C ++中的tuple <int,int,int>
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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!
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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.

🕑

After storing our graph information into a graph DS, we can answer a few simple queries.

  1. Counting V,
  2. Counting E,
  3. Enumerating neighbors of a vertex u,
  4. Checking the existence of edge (u, v), etc.
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In an AM and AL, V is just the number of rows in the data structure that can be obtained in O(V) or even in O(1) — depending on the actual implementation.


Discussion: How to count V if the graph is stored in an EL?


PS: Sometimes this number is stored/maintained in a separate variable so that we do not have to re-compute this every time — especially if the graph never/rarely changes after it is created, hence O(1) performance, e.g. we can store that there are 7 vertices (in our AM/AL/EL data structure) for the example graph shown above.

🕑

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.

🕑

In an EL, E is just the number of its rows that can be counted in O(E). Note that depending on the need, we may store a bidirectional edge just once in the EL but on other case, we store both directed edges inside the EL.


In an AL, E can be found by summing the length of all V lists and divide the final answer by 2 (for undirected graph). This requires O(V+E) computation time as each vertex and each edge is only processed once.


Discussion: How to count E if the graph is stored in an AM?


PS: Sometimes this number is stored/maintained in a separate variable for efficiency, e.g. we can store that there are 8 undirected edges (in our AM/AL/EL data structure) for the example graph shown above.

🕑

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.

🕑

In an AM, we need to loop through all columns of AM[u][j] ∀j ∈ [0..V-1] and report pair of (j, AM[u][j]) if AM[u][j] is not zero. This is O(V) — slow.


In an AL, we just need to scan AL[u]. If there are only k neighbors of vertex u, then we just need O(k) to enumerate them — this is called an output-sensitive time complexity and is already the best possible.


We usually list the neighbors in increasing vertex number. For example, neighbors of vertex 1 in the example graph above are {0, 2, 3}, in that increasing vertex number order.


Discussion: How to do this if the graph is stored in an EL?

🕑

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.

🕑

In an AM, we can simply check if AM[u][v] is non zero. This is O(1) — the fastest possible.


In an AL, we have to check whether AL[u] contains vertex v or not. This is O(k) — slower.


For example, edge (2, 4) exists in the example graph above but edge (2, 6) does not exist.


Note that if we have found edge (u, v), we can also access and/or update its weight.


Discussion: How to do this if the graph is stored in an EL?

🕑

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?

Edge List
Adjacency List
It Depends
Adjacency Matrix

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.

🕑

You have reached the end of the basic stuffs of this relatively simple Graph Data Structures and we encourage you to explore further in the Exploration Mode by drawing your own graphs.


However, we still have a few more interesting Graph Data Structures challenges for you that are outlined in this section.


Note that graph data structures are usually just the necessary but not sufficient part to solve the harder graph problems like MST, SSSP, Max Flow, Matching, etc.


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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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

>

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关于

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 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.

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-Apr 2022)
Liu Guangyuan, Manas Vegi, Sha Long

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

致谢
This project is made possible by the generous Teaching Enhancement Grant from NUS Centre for Development of Teaching and Learning (CDTL).

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 ACM 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).

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.