Editorial for Facebook Hacker Cup '15 Round 1 P1 - Homework

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If we precompute the primacity of each number, then answering test cases just takes a sweep over the precomputed results.

To compute the primacity, one option is to use a modified Sieve of Eratosthenes. In the normal sieve, we iterate upwards and whenever we find a prime number, we cross off all multiples of it from our list of primes. Rather than crossing off a multiple, we can add 1 to a counter that keeps track of its primacity.

For example, 2 is prime, so we add 1 to the primacity of 4, 6, 8, 10, etc. 3 is the next prime, so we add 1 to the primacity of 3, 6, 9, 12, etc.

The time complexity is the same as the standard sieve, \mathcal O(N \log \log N) for the integers 1 to N.


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