Editorial for Facebook Hacker Cup '15 Round 1 P1 - Homework
Remember to use this editorial only when stuck, and not to copy-paste code from it. Please be respectful to the problem author and editorialist.
Submitting an official solution before solving the problem yourself is a bannable offence.
Submitting an official solution before solving the problem yourself is a bannable offence.
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 to a counter that keeps track of its primacity.
For example, is prime, so we add
to the primacity of
,
,
,
, etc.
is the next prime, so we add
to the primacity of
,
,
,
, etc.
The time complexity is the same as the standard sieve, for the integers
to
.
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