danger1200's blog

By danger1200, 5 years ago, In English

Today I noticed some interesting facts about dfs and bfs algorithms.

Let's consider a complete graph consisting of N vertices. Do bfs and dfs algorithms over this graph. You may be surprised but the spanning tree formed by BFS algorithm looks like a sun so I called this tree "Solnyshko-tree" while the tree formed by DFS algorithms looks like a line so I called it "Bamboooo-tree".

For a better understanding I suggest you to have a look at provided pictures.

Hope you find this topic interesting and useful. Thanks for attention and good luck on the upcoming contest!

 
 
 
 
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5 years ago, # |
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"Solnyshko-tree" is called star graph. http://mathworld.wolfram.com/StarGraph.html

Some japanese call star graph "Uni"(ウニ). Uni is a Japanese word for sea urchins. (cf: http://agc009.contest.atcoder.jp/tasks/agc009_d#)

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    5 years ago, # ^ |
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    Oh, sorry, I didn't know about the star graph. But I think my discovery is still useful for science.

    Anyway thanks for informing about the star graph

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5 years ago, # |
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facepalm

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5 years ago, # |
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This is the answer to our everyday questions.

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5 years ago, # |
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Are you joking ? :/

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5 years ago, # |
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WOW. I never noticed that. Thanks for sharing your wisdom!!!!!

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5 years ago, # |
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Is this fact correct about the graphs with more than 7 vertices too?

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    5 years ago, # ^ |
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    Of course yes, it is correct for every integer N > 0. You can prove it by induction

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      5 years ago, # ^ |
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      Man, for N=1 it looks like a put out sun, I'm not buying this.

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        5 years ago, # ^ |
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        This is neither about sun nor line, it is about the structure of the spanning tree formed by bfs or dfs in a complete graph. N=1 is a special case

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          5 years ago, # ^ |
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          Ok but for N=2 the so-called sun looks like a bamboo. What u gonna say now? Is every single N a special case of its own? Why am I even trusting you?!?!?!

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            5 years ago, # ^ |
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            Hmm, I don't see anything wrong here. For example, in my country bamboo is associated with the Sun. No Sun — no bamboo

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              5 years ago, # ^ |
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              I don't care about the zodiac, we are talking about competitive programming here.

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                5 years ago, # ^ |
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                I don't mention any astrology here. As I said before, my topic is not about suns, lines, bamboos etc. I've just wanted to share with codeforces community my observations about the structure of these trees (not about pictures), but these comments are killing me

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5 years ago, # |
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Nice drawing!

Clear explanations!

Very exciting topic!

Well done.

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5 years ago, # |
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Cmon guys, what's wrong with this post? Sorry if it is a well-known fact but I didn't see it yet. Can you provide a link with this fact if it exists or explain your downvotes otherwise?

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    5 years ago, # ^ |
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    It's too advanced and complicated for this website

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      5 years ago, # ^ |
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      I don't see it complicated and some coders understand my observation. So guys, why are you laughing at me?

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5 years ago, # |
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if this blog wasn't a new idea, but it was a new perspective! so it was appreciable! thanks for writing this blog! keep up writing your new thoughts on cf :)

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    5 years ago, # ^ |
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    Ohh man, thank you! I've already thought I'm shitposting here :(

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4 years ago, # |
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Wrong observation. That is a new moon, not line.

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17 months ago, # |
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how is bambooa a tree its a grass