結果

問題 No.1322 Totient Bound
ユーザー Min_25
提出日時 2020-12-19 13:08:55
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 353 ms / 5,000 ms
コード長 3,820 bytes
コンパイル時間 1,117 ms
コンパイル使用メモリ 86,324 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-09-21 10:13:05
合計ジャッジ時間 7,799 ms
ジャッジサーバーID
(参考情報)
judge2 / judge5
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 36
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <cstdio>
#include <ctime>
#include <cassert>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <map>
#include <vector>
#include <tuple>
#include <array>
#include <functional>
using namespace std;
using u8 = unsigned char;
using i64 = long long;
using u64 = long long unsigned;
int isqrt(i64 n) {
return sqrtl(n);
}
i64 divide(i64 n, i64 d) {
return double(n) / d;
}
__attribute__((target("avx"), optimize("O3", "unroll-loops")))
pair< vector<int>, vector<i64> > prime_counts(const i64 N) {
const int v = isqrt(N);
vector<int> smalls(v + 1);
vector<i64> larges(v + 1);
for (int i = 1; i <= v; ++i) smalls[i] = i - 1;
for (int i = 1; i <= v; ++i) larges[i] = N / i - 1;
for (int p = 2, pcnt = 0; p <= v; ++p) if (smalls[p] > smalls[p - 1]) {
const i64 M = N / p, q = i64(p) * p;
const int w = v / p, l = min<i64>(v, N / q);
for (int i = 1; i <= w; ++i) larges[i] -= larges[i * p] - pcnt;
const int t = min(isqrt(M), l);
for (int i = w + 1; i <= t; ++i) larges[i] -= smalls[divide(M, i)] - pcnt;
for (int i = l, j = M / l; i > t; ++j) {
int c = smalls[j];
while (j + 1 <= v && smalls[j + 1] == c) ++j;
c -= pcnt;
for (int e = max<int>(t, divide(M, j + 1)); i > e; --i) larges[i] -= c;
}
for (int i = v, j = v / p; j >= p; --j) {
const int c = smalls[j] - pcnt;
for (int e = j * p; i >= e; --i) smalls[i] -= c;
}
++pcnt;
}
return make_pair(smalls, larges);
}
using u8 = unsigned char;
vector<int> prime_sieve(int N) {
if (N <= 1) return vector<int>();
const int sieve_size = 32 << 10;
static u8 block[sieve_size];
const int v = sqrt(N), vv = sqrt(v);
vector<bool> is_prime(v + 1, 1);
vector<pair<int, int>> sprimes;
for (int i = 2; i <= vv; ++i) if (is_prime[i]) {
for (int j = i * i; j <= v; j += i) is_prime[j] = 0;
}
for (int i = 3; i <= v; i += 2) if (is_prime[i]) sprimes.emplace_back(i, i * i / 2);
const int rsize = N > 60184 ? N / (log(N) - 1.1)
: max(1., N / (log(N) - 1.11)) + 1;
vector<int> primes(1, 2); primes.resize(rsize);
int psize = 1;
auto* pblock = block - 1;
for (int beg = 1; beg < (N + 1) / 2; beg += sieve_size, pblock -= sieve_size) {
int end = min(beg + sieve_size, (N + 1) / 2);
fill(block, block + sieve_size, 1);
for (int i = 0; i < int(sprimes.size()); ++i) {
int p, next; tie(p, next) = sprimes[i];
if (p * p > N) break;
for (; next < end; next += p) pblock[next] = 0;
sprimes[i].second = next;
};
for (int i = beg; i < end; ++i) if (pblock[i]) primes[psize++] = 2 * i + 1;
}
assert(psize <= int(primes.size()));
primes.resize(psize);
return primes;
}
int main() {
u64 N;
while (~scanf("%llu", &N)) {
auto pc = prime_counts(N);
u64 v = isqrt(N);
auto primes = prime_sieve(v + 10);
auto isp = [&] (u64 n) -> bool {
if (n <= 1) return 0;
for (size_t j = 0; j < primes.size(); ++j) {
u64 p = primes[j];
if (p * p > n) return 1;
if (n % p == 0) return 0;
}
abort();
};
for (size_t i = 1; i <= v; ++i) pc.first[i] += isp(i + 1);
for (size_t i = 1; i <= v; ++i) pc.second[i] += isp(N / i + 1);
auto count = [&] (u64 n) -> u64 {
return (n <= v) ? pc.first[n] : pc.second[N / n];
};
function<u64(u64, size_t)> rec = [&] (u64 phi, size_t beg) -> u64 {
u64 ret = count(phi) - beg;
for (size_t i = beg; i < primes.size(); ++i) {
u64 p = primes[i];
if ((p - 1) * p > phi) break;
u64 nphi = phi / (p - 1);
while (nphi + 1 > u64(primes[i])) {
ret += rec(nphi, i + 1) + 1;
nphi /= p;
}
}
return ret;
};
u64 ans = rec(N, 0) + 1;
printf("%llu\n", ans);
}
return 0;
}
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