結果

問題 No.2798 Multiple Chain
コンテスト
ユーザー hos.lyric
提出日時 2024-06-28 21:26:02
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 3 ms / 2,000 ms
コード長 4,727 bytes
コンパイル時間 1,356 ms
コンパイル使用メモリ 120,712 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-06-28 21:26:05
合計ジャッジ時間 2,484 ms
ジャッジサーバーID
（参考情報） 		judge4 / 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 * 51
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 <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")


template <class T> T power(T a, long long e, T m) {
  for (T b = 1; ; (a *= a) %= m) {
    if (e & 1) (b *= a) %= m;
    if (!(e >>= 1)) return b;
  }
}

long long gcd(long long a, long long b) {
  if (a < 0) a = -a;
  if (b < 0) b = -b;
  if (a == 0) return b;
  if (b == 0) return a;
  const int s = __builtin_ctzll(a | b);
  a >>= __builtin_ctzll(a);
  do {
    b >>= __builtin_ctzll(b);
    if (a > b) swap(a, b);
    b -= a;
  } while (b);
  return a << s;
}

bool isPrime(long long n) {
  if (n <= 1 || n % 2 == 0) return (n == 2);
  const int s = __builtin_ctzll(n - 1);
  const long long d = (n - 1) >> s;
  // http://miller-rabin.appspot.com/
  for (const long long base : {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {
    __int128 a = base % n;
    if (a == 0) continue;
    a = power<__int128>(a, d, n);
    if (a == 1 || a == n - 1) continue;
    bool ok = false;
    for (int i = 0; i < s - 1; ++i) {
      (a *= a) %= n;
      if (a == n - 1) {
        ok = true;
        break;
      }
    }
    if (!ok) return false;
  }
  return true;
}

// n >= 3, odd
void factorizeRec(long long n, vector<long long> &ps) {
  static constexpr int BLOCK = 256;
  if (isPrime(n)) {
    ps.push_back(n);
  } else {
    for (long long c = 2; ; ++c) {
      long long x, y = 2, y0, z = 1, d = 1;
      for (int l = 1; d == 1; l <<= 1) {
        x = y;
        for (int i = 0; i < l; ++i) y = (static_cast<__int128>(y) * y + c) % n;
        for (int i = 0; i < l; i += BLOCK) {
          y0 = y;
          for (int j = 0; j < BLOCK && j < l - i; ++j) {
            y = (static_cast<__int128>(y) * y + c) % n;
            z = (static_cast<__int128>(z) * (y - x)) % n;
          }
          if ((d = gcd(z, n)) != 1) break;
        }
      }
      if (d == n) {
        for (y = y0; ; ) {
          y = (static_cast<__int128>(y) * y + c) % n;
          if ((d = gcd(y - x, n)) != 1) break;
        }
      }
      if (d != n) {
        factorizeRec(d, ps);
        factorizeRec(n / d, ps);
        return;
      }
    }
  }
}

vector<pair<long long, int>> factorize(long long n) {
  vector<pair<long long, int>> pes;
  if (n >= 2) {
    const int s = __builtin_ctzll(n);
    if (s) pes.emplace_back(2, s);
    if (n >> s >= 2) {
      vector<long long> ps;
      factorizeRec(n >> s, ps);
      std::sort(ps.begin(), ps.end());
      const int psLen = ps.size();
      for (int i = 0, j = 0; i < psLen; i = j) {
        for (; j < psLen && ps[i] == ps[j]; ++j) {}
        pes.emplace_back(ps[i], j - i);
      }
    }
  }
  return pes;
}

vector<long long> divisors(long long n) {
  const auto pes = factorize(n);
  vector<long long> ds{1};
  for (const auto &pe : pes) {
    const int len0 = ds.size();
    const int len1 = len0 * (pe.second + 1);
    ds.resize(len1);
    for (int i = len0; i < len1; ++i) ds[i] = ds[i - len0] * pe.first;
  }
  std::sort(ds.begin(), ds.end());
  return ds;
}

////////////////////////////////////////////////////////////////////////////////


int main() {
  constexpr int M = 70;
  Int ps[M] = {};
  ps[0] = 1;
  for (int i = 1; i < M; ++i) {
    for (int j = +1, k; (k = j*(3*j+1)/2) <= i; ++j) ps[i] -= (j&1?-1:+1) * ps[i - k];
    for (int j = -1, k; (k = j*(3*j+1)/2) <= i; --j) ps[i] -= (j&1?-1:+1) * ps[i - k];
  }
cerr<<"ps = ";pv(ps,ps+M);
  
  Int N;
  for (; ~scanf("%lld", &N); ) {
    const auto pes = factorize(N);
    Int ans = 1;
    for (const auto &pe : pes) {
      ans *= ps[pe.second];
    }
    printf("%lld\n", ans);
  }
  return 0;
}
0