Block sieving
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| #include <bits/stdc++.h> | |
| using namespace std; | |
| #define INF 1<<30 | |
| #define maxn 100000005 | |
| #define FASTIO ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0); | |
| typedef long long ll; | |
| ///Here we have an implementation that counts the number of primes | |
| ///smaller than or equal to n using block sieving. | |
| int count_primes(int n) | |
| { | |
| const int s = 10000; | |
| vector<int> primes; | |
| int nsqrt = sqrt(n); | |
| vector<char> is_prime(nsqrt+1, true); | |
| //for(auto x: is_prime) cerr << x<<endl; | |
| for(int i = 2; i <= nsqrt; i++){ | |
| if(is_prime[i]){ | |
| primes.push_back(i); | |
| for(int j = i * i; j <= nsqrt; j += i) | |
| is_prime[j] = false; | |
| } | |
| } | |
| int res = 0; | |
| vector<char> block(s); | |
| for(int k = 0; k*s <= n; k++){ | |
| fill(block.begin(), block.end(), true); | |
| int start = k * s; | |
| for(int p: primes){ | |
| int start_idx = (start + p - 1) / p; | |
| int j = max(start_idx, p) * p - start; | |
| for(; j < s; j += p) | |
| block[j] = false; | |
| } | |
| if(k == 0) | |
| block[0] = block[1] = false; | |
| for(int i = 0; i < s && start + i <= n; i++){ | |
| if(block[i]) | |
| res++; | |
| } | |
| } | |
| return res; | |
| } | |
| int main() | |
| { | |
| FASTIO | |
| ///* | |
| //double start_time = clock(); | |
| #ifndef ONLINE_JUDGE | |
| freopen("in.txt", "r", stdin); | |
| freopen("out.txt", "w", stdout); | |
| freopen("error.txt", "w", stderr); | |
| #endif //*/ | |
| int n; | |
| cin >> n; | |
| cout << count_primes(n) << "\n"; | |
| //double end_time = clock(); | |
| //printf( "Time = %lf ms\n", ( (end_time - start_time) / CLOCKS_PER_SEC)*1000); | |
| return 0; | |
| } |
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