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nth_prime: exclude even numbers

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This commit is contained in:
Dmitry Kokorin 2016-03-30 16:39:23 +03:00
parent a02354a9eb
commit 2e77b43e48
1 changed files with 17 additions and 12 deletions
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29
cpp/nth-prime/nth_prime.cpp
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@ -15,31 +15,36 @@ number_t nth(size_t n, size_t sieve_size)
if (n < 1) if (n < 1)
throw domain_error("invalid prime number index"); throw domain_error("invalid prime number index");
vector<number_t> primes = {2, 3, 5, 7, 11, 13}; if (n == 1)
return 2;
if (n <= primes.size()) vector<number_t> primes = {3, 5, 7, 11, 13};
return primes[n - 1];
primes.reserve(n); if (n - 2 < primes.size())
return primes[n - 2];
primes.reserve(n - 1);
if (auto_sieve_size == sieve_size) { if (auto_sieve_size == sieve_size) {
sieve_size = min(size_t(32 * 1024), sieve_size = min(size_t(32 * 1024),
size_t(n * (log(n) + log(log(n))) + 0.5)); size_t(0.5*(n * (log(n) + log(log(n)))) + 0.5));
} }
vector<char> sieve(sieve_size, false); vector<char> sieve(sieve_size, false);
sieve[0] = sieve[1] = true; sieve[0] = true;
size_t first_number = 0; size_t first_number = 1;
while (true) { while (true) {
for (auto p : primes) { for (auto p : primes) {
size_t reminder = first_number % p; size_t reminder = (first_number % (2*p));
size_t begin = reminder ? p - reminder : 0; size_t begin = reminder > p ? 3*p - reminder : p - reminder;
begin /= 2;
for (size_t i = begin; i < sieve_size; i += p) { for (size_t i = begin; i < sieve_size; i += p) {
@ -52,10 +57,10 @@ number_t nth(size_t n, size_t sieve_size)
if (sieve[i]) if (sieve[i])
continue; continue;
number_t p = first_number + i; number_t p = first_number + 2*i;
primes.push_back(p); primes.push_back(p);
if (primes.size() == n) if (primes.size() == n - 1)
return p; return p;
for (size_t j = i; j < sieve_size; j += p) { for (size_t j = i; j < sieve_size; j += p) {
@ -64,7 +69,7 @@ number_t nth(size_t n, size_t sieve_size)
} }
} }
size_t next_first_number = first_number + sieve_size; size_t next_first_number = first_number + 2*sieve_size;
if (next_first_number < first_number) if (next_first_number < first_number)
throw runtime_error("failed to reach prime number"); throw runtime_error("failed to reach prime number");