Algorithm Visualization of USFCA

提供交互式动画展示复杂数据结构和算法,包括堆、搜索树、哈希表、排序算法等,适合自学和深入理解。

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Cited from http://www.cs.usfca.edu/~galles/visualization/Algorithms.html

 

Visualizing Algorithms

The best way to understand complex data structures is to see them in action. We've developed interactive animations for a variety of data structures and algorithms. Our visualization tool is written in javascript using the HTML5 canvas element, and run in just about any modern browser -- including iOS devices like the iPhone and iPad, and even the web browser in the Kindle! (The frame rate is low enough in the Kindle that the visualizations aren't terribly useful, but the tree-based visualizations -- BSTs and AVL Trees -- seem to work well enough)

Check the Algorithms menu for all of the latest javascript implementations.

How to Use the Visualizations

This visualizations are meant to be fairly self- explainitory, though there are some subleties for advanced usage. Take a look at a typical visualization, for Binary Search Trees:

BST Screenshot

Algorithm Specific Controls

At the top of the screen (boxed in red in the above screenshot) are the algorithm specific controls -- these will change depending upon what algorithm you are visualizing. In this example, you could insert, delete, or find an element in the BST by entering text in the appropriate field and either pressing return or clicking the relevant button. The tree can be printed by clicking the print button. Once you give a command, the visualiztion will start, and can be controlled by the general animation controls at the bottom of the screen.

General Animation Controls

  • Skip Back If you are in the middle of an animation, this button will completly undo the current command. If you are not in the middle of an animation, this button will undo the previous command
  • Step Back This button is only active if you have paused the current animation (using the play/pause button). Step back one step in the current animation. If you are not currently animating, step back into the previous command. You could use this button (with sufficient keypresses) to back up through the entire history of everything you've done
  • Play/Pause Toggle between play mode (in which the algorithm runs free until it completes) and paused mode (where you need to press the Step Forward or Step Back button to advance the animation)
  • Step Forward This button is only active if you have paused the current animation (using the play/pause button), and the current animation has not yet completed. Step forward one step in the current animation.
  • Skip Forward This button is only active if the current animation has not completed. Skip to the end of the current animation
  • Animation Speed (slider) Change the speed of the animation. The value of this slider is saved in a cookie, so you should only need to set it once if you have a preferred speed
  • w, h, Chnage Canvas Size Change the width / height of the display area. While the change is immediate, the animations will not be centered in this new field until you reload the page. This will clear out the currnet animation, but the width and hight values are also saved in a cookie, so you should only need to change this field once, and then everything should work well if you are on a smart phone or a desktop with loads of screen real estate.
    Note that it can be easy to confuse yourself by stepping forward an backwards through an animation -- you can confuse the next step in the animation with the previous step, and misunderstand how the algorithm works. You may wish to only step forward when you are first delving into a particular algorithm.

Java/Swing Version

This work is based on visualizations that we created in Java using Swing -- that code is still available here , though that code is no longer being maintained. There are a few algorithms that we have not yet ported to the new system, so the older version may still be of use.

Flash Version

We have also developed a flash version of the visualizations, which currently also contains some algorithms that are not in the HTML version, though we should port everything over to javascript soon. We will keep the flash version available for those who may get a better frameate out of flash than javascript (and the flash version is a bit easier to download and use offline). However, the javascript versions are the preferred ones, and will get updates and bug fixes the quickest.

Writing your Own

The code is written to be easy to extend with your own visualizations -- look for a tutorial for how to create your own, with examples, to be up by some time in Summer 2011.

 

Currently, we have visualizations for the following data structures and algorithms:
### 关于克鲁斯卡尔算法生成最小生成树的可视化工具 对于希望理解克鲁斯卡尔算法如何构建最小生成树的学习者来说,存在多种在线资源可以提供帮助。一种有效的学习方式是通过交互式的动画展示来观察每一步骤的变化过程[^1]。 #### 可视化网站推荐 - **USFCA Visualization Tool**: 提供了一个直观的方式去探索不同数据结构与算法的工作原理,包括克鲁斯卡尔算法在内的多个图论算法均被囊括其中。该平台允许用户自定义输入并实时查看计算进展。 ```html <a href="http://www.cs.usfca.edu/~galles/visualization/Kruskal.html">访问 USFCA Kruskal Algorithm Visualizer</a> ``` 此链接指向一个专门针对克鲁斯卡尔算法设计的教学辅助页面,在这里可以通过拖拽节点创建图形,并设置边权重以模拟实际应用场景下的操作流程。 #### Python 实现示例 除了利用现有的网络工具外,编程爱好者也可以尝试自己动手实现这一经典算法: ```python from collections import defaultdict class Graph: def __init__(self, vertices): self.V = vertices self.graph = [] def addEdge(self, u, v, w): self.graph.append([u, v, w]) # A utility function to find set of an element i (uses path compression technique) def find(self, parent, i): if parent[i] == i: return i return self.find(parent , parent[i]) # A function that does union of two sets of x and y (uses union by rank) def union(self, parent, rank, x, y): rootX = self.find(parent, x) rootY = self.find(parent, y) if rank[rootX] < rank[rootY]: parent[rootX] = rootY elif rank[rootX] > rank[rootY]: parent[rootY] = rootX # If ranks are same, then make one as root and increment its rank by one else : parent[rootY] = rootX rank[rootX] += 1 # The main function to construct MST using Kruskal's algorithm def kruskalMST(self): result =[] # This will store the resultant MST i = 0 # An index variable, used for sorted edges e = 0 # An index variable, used for result[] # Step 1: Sort all the edges in non-decreasing order of their weight. self.graph = sorted(self.graph,key=lambda item:item[2]) parent = [] rank = [] # Create V subsets with single elements for node in range(self.V): parent.append(node) rank.append(0) while e < self.V -1 : # Step 2: Pick the smallest edge. And increment the index for next iteration u,v,w = self.graph[i] i = i + 1 x = self.find(parent, u) y = self.find(parent ,v) if x != y: e = e + 1 result.append([u,v,w]) self.union(parent, rank, x, y) minimumCost = 0 print ("Edges in the constructed MST") for u,v,weight in result: minimumCost += weight print("%d -- %d == %d" % (u,v,weight)) print("Minimum Spanning Tree",minimumCost) g = Graph(4) g.addEdge(0, 1, 10) g.addEdge(0, 2, 6) g.addEdge(0, 3, 5) g.addEdge(1, 3, 15) g.addEdge(2, 3, 4) g.kruskalMST() ``` 上述代码展示了完整的克鲁斯卡尔算法逻辑及其Python实现方法,能够作为理解和实践的良好起点。
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