結果

問題 No.1322 Totient Bound
コンテスト
ユーザー Min_25
提出日時 2020-12-19 12:55:14
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 339 ms / 5,000 ms
コード長 5,676 bytes
コンパイル時間 1,361 ms
コンパイル使用メモリ 91,188 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-09-21 10:12:09
合計ジャッジ時間 7,266 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
このコードへのチャレンジ
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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 # 

#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;
}

__attribute__((target("avx"), optimize("O3", "unroll-loops")))
i64 prime_pi(const i64 N) {
  if (N <= 1) return 0;
  if (N == 2) return 1;
  const int v = isqrt(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<i64> 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 = [] (i64 n, i64 d) -> int { return double(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 (i64(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;
      i64 d = i64(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] += i64(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) {
    int q = roughs[l];
    i64 M = N / q;
    int e = smalls[half(M / q)] - pc;
    if (e < l + 1) break;
    i64 t = 0;
    for (int k = l + 1; k <= e; ++k) t += smalls[half(divide(M, roughs[k]))];
    larges[0] += t - i64(e - l) * (pc + l - 1);
  }
  return larges[0] + 1;
}
int main() {
  u64 N;
  while (~scanf("%llu", &N)) {
    const auto pc = prime_counts(N + 1);
    u64 v = isqrt(N + 1);
    auto primes = prime_sieve(v + 10);
    std::vector<int> isp(v + 1, -1);
    auto count = [&] (u64 n) -> u64 {
      if (n <= v) return pc.first[n];
      else {
        size_t i = N / (n - 1); u64 q = (N + 1) / i;
        assert(q <= n && n <= q + 1);
        if (q == n || (n >= 4 && n % 2 == 0)) {
          return (i > v) ? pc.first[q] : pc.second[i];
        }
        if (isp[i] < 0) {
          isp[i] = 1;
          for (size_t j = 1; j < primes.size(); ++j) {
            u64 p = primes[j];
            if (p * p > n) break;
            if (n % p != 0) continue;
            isp[i] = 0;
            break;
          }
        }
        return pc.second[i] + isp[i];
      }
    };

    function<u64(u64, size_t)> rec = [&] (u64 phi, size_t beg) -> u64 {
      u64 ret = count(phi + 1) - 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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