Prim算法的最坏情况图
[英]Worst-Case Graph for Prim's Algorithm
问题描述
My Algorithms class is talking about Prim's Algorithm as a method of finding Minimum Spanning Trees of weighted graphs. 
我的算法课谈论的是Prim算法，它是一种找到加权图的最小生成树的方法。 Our professor asked us to try to think of an example of a graph that Prim's Algorithm takes N^2 time to solve (N = number of Vertices). 我们的教授要求我们尝试考虑一个图的示例，该图的基本算法需要N ^ 2的时间来解决（N =顶点数）。 No one in the class could think of one off the top of their head, so I'm asking you. 班上没人能想到一个人，所以我问你。 I'm pretty sure Prim's Algorithm = O(N^2), so this would be the worst-case scenario for the algorithm. 我很确定Prim的算法= O（N ^ 2），所以这将是该算法最坏的情况。
What's a good example of a graph that takes N^2 time for Prim's Algorithm to solve? 有什么很好的示例图需要花费N ^ 2的时间来求解Prim的算法？
1 个解决方案
解决方案1
2 2017-04-20 21:08:46
If I understand your question correctly, the example is trivial. 如果我正确理解了您的问题，那么这个例子很简单。
If the graph is complete, there're O(N^2) edges, so just reading the graph is O(N^2) . 如果图是完整的，则有O(N^2)边，因此仅读取图就是O(N^2) 。
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