论文题
1e11内找素数个数。
Meissel-Lehmer 黑科技板子
#pragma warning(disable:4996) #include<iostream> #include<algorithm> #include<bitset> #include<tuple> #include<unordered_map> #include<fstream> #include<iomanip> #include<string> #include<cmath> #include<cstring> #include<vector> #include<map> #include<set> #include<list> #include<queue> #include<stack> #include<sstream> #include<cstdio> #include<ctime> #include<cstdlib> #define INF 0x3f3f3f3f #define inf 0x7FFFFFFF #define MOD 1000000007 #define moD 1000000003 #define pii pair<int,int> #define eps 1e-7 #define equals(a,b) (fabs(a-b)<eps) #define bug puts("bug") #define re register #define fi first #define se second #define pb push_back const int maxn = 2e5 + 5; const double Inf = 10000.0; const double PI = acos(-1.0); typedef long long ll; typedef unsigned long long ull; using namespace std; const int N = 5e6 + 5; const int M = 7; const int PM = 2 * 3 * 5 * 7 * 11 * 13 * 17; int np[N]; int prime[N], pi[N]; int phi[PM + 1][M + 1], sz[M + 1]; int getprime() { int cnt = 0; np[0] = np[1] = 1; pi[0] = pi[1] = 0; for (int i = 2; i < N; ++i) { if (!np[i]) prime[++cnt] = i; pi[i] = cnt; for (int j = 1; j <= cnt && i * prime[j] < N; ++j) { np[i * prime[j]] = 1; if (i % prime[j] == 0) break; } } return cnt; } void init() { getprime(); sz[0] = 1; for (int i = 0; i <= PM; ++i) phi[i][0] = i; for (int i = 1; i <= M; ++i) { sz[i] = prime[i] * sz[i - 1]; for (int j = 1; j <= PM; ++j) phi[j][i] = phi[j][i - 1] - phi[j / prime[i]][i - 1]; } } int sqrt2(ll x) { ll r = (ll)sqrt(x - 0.1); while (r * r <= x) ++r; return (int)(r - 1); } int sqrt3(ll x) { ll r = (ll)cbrt(x - 0.1); //cbrt(x): x的立方根 while (r * r * r <= x) ++r; return (int)(r - 1); } ll getphi(ll x, int s) { if (s == 0) return x; if (s <= M) return phi[x % sz[s]][s] + (x / sz[s]) * phi[sz[s]][s]; if (x <= prime[s] * prime[s]) return pi[x] - s + 1; if (x <= prime[s] * prime[s] * prime[s] && x < N) { int s2x = pi[sqrt2(x)]; ll ans = pi[x] - (s2x + s - 2) * (s2x - s + 1) / 2; for (int i = s + 1; i <= s2x; ++i) ans += pi[x / prime[i]]; return ans; } return getphi(x, s - 1) - getphi(x / prime[s], s - 1); } ll getpi(ll x) { if (x < N) return pi[x]; ll ans = getphi(x, pi[sqrt3(x)]) + pi[sqrt3(x)] - 1; for (int i = pi[sqrt3(x)] + 1, ed = pi[sqrt2(x)]; i <= ed; ++i) ans -= getpi(x / prime[i]) - i + 1; return ans; } ll lehmer_pi(ll x) { if (x < N) return pi[x]; int a = (int)lehmer_pi(sqrt2(sqrt2(x))); int b = (int)lehmer_pi(sqrt2(x)); int c = (int)lehmer_pi(sqrt3(x)); ll sum = getphi(x, a) + (ll)(b + a - 2) * (b - a + 1) / 2; for (int i = a + 1; i <= b; ++i) { ll w = x / prime[i]; sum -= lehmer_pi(w); if (i > c) continue; ll lim = lehmer_pi(sqrt2(w)); for (int j = i; j <= lim; ++j) sum -= lehmer_pi(w / prime[j]) - (j - 1); } return sum; } int main() { ll n; init(); while (~scanf("%lld", &n)) { printf("%lld\n", lehmer_pi(n)); } return 0; }