meaningIess's blog

A Hard Problem on Topcoder
By meaningIess, history, 6 years ago, In English

You are given a number $$$n$$$ and a set $$$d$$$ that describe the graph. The graph has n vertices, numbered 0 through n-1. Vertices i and j are connected by an edge if and only if |i-j| is an element of d. Return the number of connected components of this graph.|d|<=50 and n<=1e18. In Topcoder its called "HugeGraph". I have searched for the editorial and I found nothing. Please anybody gives a editorial? Btw, for n,|d|<=1e5, if the problem can be solved? Sorry for my bad english:)

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6 years ago, # |
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I cannot search for this problem in Topcoder archive. Was this special round? If you know which srm it was you can check petr blog, I think he explains some problems from round he participated.

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6 years ago, # |
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Maybe from big $$$n$$$ you can find the answer with Berlekamp-Massey?

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    6 years ago, # ^ |
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    Ah, $$$d_i$$$ can be huge :(

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    6 years ago, # ^ |
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    For big N, wouldn't the answer be just gcd?

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      6 years ago, # ^ |
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      Yes, i think if $$$n > 2 \cdot \max{d}$$$.

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      6 years ago, # ^ |
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      But what the answer will be when $$$n$$$ and $$$d_i$$$ both huge?

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        6 years ago, # ^ |
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        Yeah, that's the question ;p

        I don't how to solve it. I only answered to 300iq's comment saying that BM is unnecessary.

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          6 years ago, # ^ |
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          For little $$$d_i$$$, it can be seemed $$$gcd$$$. For big $$$d_i$$$, it won't make a loop, every edge using big $$$d_i$$$ will minus the answer by 1? I guess that if all the $$$d_i>=n/2$$$ then the answer is $$$n - edges number$$$? I don't know if it's true.

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6 years ago, # |
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Please, anybody replies? I neeeeeed the editorial! I'm VERY interested in this problem :(

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