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View the Project on GitHub AlexanderNekrasov/Youthful-Passion-Fruit-teambook
/**
* Author: Iurii Pustovalov
* Date: 2022-11-08
* Description: counting number of primes below N
* Time: O(N^2/3)
*/
ll prime_pi(const ll N) {
if (N <= 1) return 0;
if (N == 2) return 1;
const int v = sqrt(N);
int s = (v + 1) / 2;
vector<int> smalls(s);
for (int i = 1; i < s; i++) smalls[i] = i;
vector<int> roughs(s);
for (int i = 0; i < s; i++) roughs[i] = 2 * i + 1;
vector<ll> larges(s);
for (int i = 0; i < s; i++) larges[i] = (N / (2 * i + 1) - 1) / 2;
vector<bool> skip(v + 1);
const auto divide = [](ll n, ll d) -> int { return n / d; };
const auto half = [](int n) -> int { return (n - 1) >> 1; };
int pc = 0;
for (int p = 3; p <= v; p += 2)
if (!skip[p]) {
int q = p * p;
if ((ll)q * q > N) break;
skip[p] = true;
for (int i = q; i <= v; i += 2 * p) skip[i] = true;
int ns = 0;
for (int k = 0; k < s; k++) {
int i = roughs[k];
if (skip[i]) continue;
ll d = (ll)i * p;
larges[ns] = larges[k] -
(d <= v ? larges[smalls[d >> 1] - pc]
: smalls[half(divide(N, d))]) +
pc;
roughs[ns++] = i;
}
s = ns;
for (int i = half(v), j = ((v / p) - 1) | 1; j >= p; j -= 2) {
int c = smalls[j >> 1] - pc;
for (int e = (j * p) >> 1; i >= e; i--) smalls[i] -= c;
}
pc++;
}
larges[0] += (ll)(s + 2 * (pc - 1)) * (s - 1) / 2;
for (int k = 1; k < s; k++) larges[0] -= larges[k];
for (int l = 1; l < s; l++) {
ll q = roughs[l];
ll M = N / q;
int e = smalls[half(M / q)] - pc;
if (e < l + 1) break;
ll t = 0;
for (int k = l + 1; k <= e; k++)
t += smalls[half(divide(M, roughs[k]))];
larges[0] += t - (ll)(e - l) * (pc + l - 1);
}
return larges[0] + 1;
}
#line 1 "math/PrimeCount.cpp"
/**
* Author: Iurii Pustovalov
* Date: 2022-11-08
* Description: counting number of primes below N
* Time: O(N^2/3)
*/
ll prime_pi(const ll N) {
if (N <= 1) return 0;
if (N == 2) return 1;
const int v = sqrt(N);
int s = (v + 1) / 2;
vector<int> smalls(s);
for (int i = 1; i < s; i++) smalls[i] = i;
vector<int> roughs(s);
for (int i = 0; i < s; i++) roughs[i] = 2 * i + 1;
vector<ll> larges(s);
for (int i = 0; i < s; i++) larges[i] = (N / (2 * i + 1) - 1) / 2;
vector<bool> skip(v + 1);
const auto divide = [](ll n, ll d) -> int { return n / d; };
const auto half = [](int n) -> int { return (n - 1) >> 1; };
int pc = 0;
for (int p = 3; p <= v; p += 2)
if (!skip[p]) {
int q = p * p;
if ((ll)q * q > N) break;
skip[p] = true;
for (int i = q; i <= v; i += 2 * p) skip[i] = true;
int ns = 0;
for (int k = 0; k < s; k++) {
int i = roughs[k];
if (skip[i]) continue;
ll d = (ll)i * p;
larges[ns] = larges[k] -
(d <= v ? larges[smalls[d >> 1] - pc]
: smalls[half(divide(N, d))]) +
pc;
roughs[ns++] = i;
}
s = ns;
for (int i = half(v), j = ((v / p) - 1) | 1; j >= p; j -= 2) {
int c = smalls[j >> 1] - pc;
for (int e = (j * p) >> 1; i >= e; i--) smalls[i] -= c;
}
pc++;
}
larges[0] += (ll)(s + 2 * (pc - 1)) * (s - 1) / 2;
for (int k = 1; k < s; k++) larges[0] -= larges[k];
for (int l = 1; l < s; l++) {
ll q = roughs[l];
ll M = N / q;
int e = smalls[half(M / q)] - pc;
if (e < l + 1) break;
ll t = 0;
for (int k = l + 1; k <= e; k++)
t += smalls[half(divide(M, roughs[k]))];
larges[0] += t - (ll)(e - l) * (pc + l - 1);
}
return larges[0] + 1;
}