alfadel's blog

By alfadel, history, 4 years ago, In English

I'v tried to solve this problem from 4 or 5 days, but the only solution that I'v wrote finish running in 84 seconds using Segmented Sieve.

So is there any hints or resources to start working on the correct solution?

 
 
 
 
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4 years ago, # |
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You don't actually need to find all primes to cimpute the sum. E.g.here is a description of an approach, that only takes O(n^0.75) time. Link

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    4 years ago, # ^ |
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    Thank you for the link, but can you explain the method used? because I don't understand it.

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      4 years ago, # ^ |
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      What exactly didn't you understand? The only method used here is DP.

      They just define a function that does a bit more than just a summation of the primes. S(v, p) is the sum of all numbers between 2 and v which are still in the sieve if you remove all multiples of all primes  ≤ p. Every non-prime number below n has a factor , so the answer to the problem is .

      And for this function it is not too hard to come up with a recursive definition. If you don't understand it, just try it with a few numbers. E.g. for S(25, 3), and see what numbers they sum up, and what numbers you sum up with S(25, 3), and which numbers with 3 * S(8, 2) and 3 * S(2, 2).

      Implementation was not described in the link. But I assume that a top-down DP approach is fast enough.