Ahmad_Elsagheer's blog

Counting successors in DAGs
By Ahmad_Elsagheer, 8 years ago, In English

Hello,

I have tried to solve this problem [Promotions]. It was in SWERC 2015. This problem is reduced to counting successors of every node in a DAG. My best algorithm to solve it is to make a dfs for every node and count the number of reachable nodes. So, the complexity is O(VE), but I got TLE with Java. I checked online solutions and found nothing different (except they are in C++). I wonder if there is a more efficient algorithm, maybe O(V^2) or if someone can provide an efficient AC Java implementation for it.

Thanks!

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8 years ago, # |
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There is no known algorithm with complexity better than O(VE/32). That one is achieved using bitsets.

In RAM model it is actually O(VE/log(V+E)).

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    8 years ago, # ^ |
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    That's interesting. Thanks!

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      8 years ago, # ^ |
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      Note that with 64-bit integers used as bitsets, you have V / 64 instead and under the given constraints, that's something like O(80E) per test case. Bitsets are a very useful thing.

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