#823594 (C++17) No.186 中華風 (Easy)

• 問題: No.186 中華風 (Easy)
• ユーザー: suisen
• 提出日時: 2022-12-09 21:16:29
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 2 ms / 2,000 ms
• コード長: 4,070 bytes
• コンパイル時間: 2,270 ms
• コンパイル使用メモリ: 200,968 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-04-22 19:19:01
• 合計ジャッジ時間: 3,183 ms
• ジャッジサーバーID （参考情報）: judge2 / judge4

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	1 ms; 5,376 KB
testcase_05	AC	1 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	2 ms; 5,376 KB
testcase_11	AC	2 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	2 ms; 5,376 KB
testcase_14	AC	2 ms; 5,376 KB
testcase_15	AC	1 ms; 5,376 KB
testcase_16	AC	1 ms; 5,376 KB
testcase_17	AC	2 ms; 5,376 KB
testcase_18	AC	2 ms; 5,376 KB
testcase_19	AC	2 ms; 5,376 KB
testcase_20	AC	2 ms; 5,376 KB
testcase_21	AC	2 ms; 5,376 KB
testcase_22	AC	2 ms; 5,376 KB

ソースコード

#line 1 "test/math/crt/yuki447.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/447"

#line 2 "src/Template.hpp"

#define CUT
#include <bits/stdc++.h>

using namespace std;

#define rep(i, l, r) for (int i = (l); i < (r); ++i)
#define rrep(i, l, r) for (int i = (r); i --> (l);)
#define all(c) begin(c), end(c)

#ifdef LOCAL
#define debug(...) debug_impl(#__VA_ARGS__, __VA_ARGS__)
template <class H, class... Ts> void debug_impl(string s, H&& h, Ts&&... ts) {
  cerr << '(' << s << "): (" << forward<H>(h);
  ((cerr << ", " << forward<Ts>(ts)), ..., (cerr << ")\n"));
}
#else
#define debug(...) void(0)
#endif

template <class T> bool chmax(T& a, const T& b) { return b > a ? (a = b, true) : false; }
template <class T> bool chmin(T& a, const T& b) { return b < a ? (a = b, true) : false; }

template <class T> istream& operator>>(istream& in, vector<T>& v) {
  for (auto& e : v) in >> e;
  return in;
}
template <class ...Args> void read(Args&... args) {
  (cin >> ... >> args);
}
template <class T> ostream& operator<<(ostream& out, const vector<T>& v) {
  int n = v.size();
  rep(i, 0, n) {
    out << v[i];
    if (i + 1 != n) out << ' ';
  }
  return out;
}
template <class H, class ...Ts> void print(H&& h, Ts &&... ts) {
  cout << h, ((cout << ' ' << forward<Ts>(ts)), ..., (cout << '\n'));
}

struct io_setup_ {
  io_setup_() {
    ios::sync_with_stdio(false), cin.tie(nullptr);
    cout << fixed << setprecision(10);
  }
} io_setup{};
#undef CUT

#define NOTE compile command: \texttt{g++ -std=gnu++17 -Wall -Wextra -g -fsanitize=address -fsanitize=undefined \$\{file\} -o \$\{fileDirname\}/\$\{fileBasenameNoExtension\}}
#undef NOTE
#define NOTE \texttt{-DLOCAL} を加えると \texttt{debug(...)} による出力が有効となる
#undef NOTE
#line 3 "src/math/CRT.hpp"
#define CUT
#line 3 "src/math/ExtGCD.hpp"

#define CUT
constexpr long safe_mod(long long x, long long m) {
  return (x %= m) < 0 ? x + m : x;
}
// Returns `(x,g)` s.t. `g=\gcd(a,b)`, `xa\equiv g \pmod{b}`, and `0\leq x< \frac{b}{g}`
constexpr pair<long long, long long> inv_gcd(long long a, long long b) {
  assert(b > 0);
  a = safe_mod(a, b);
  if (a == 0) return { 0, b };
  long long s = b, t = a, x = 0, y = 1;
  while (t) {
    long long u = s / t;
    s -= t * u, swap(s, t);
    x -= y * u, swap(x, y);
  }
  if (x < 0) x += b / s;
  return { x, s };
}
// Returns `x` s.t. `xa\equiv 1 \pmod{m}`.
// Requirement: `\gcd(a, m) = 1`.
constexpr long long inv_mod(long long a, long long m) {
  auto [x, g] = inv_gcd(a, m);
  assert(g == 1);
  return x;
}
// Returns `(x_0,y_0,g)` s.t. `g=\gcd(a,b)`, `ax_0 + by_0 = g`, and `0\leq x_0<\frac{b}{g}`.
// 一般解は `(x,y)=(x_0+k\cdot\dfrac{b}{g}, y_0-k\cdot\dfrac{a}{g})\;(k\in\mathbb{Z})` なので、`(x_0,y_0)` は `x` が非負の下で最小の解
constexpr tuple<long long, long long, long long> ext_gcd(long long a, long long b) {
  auto [x, g] = inv_gcd(a, b);
  return { x, (g - x * a) / b, g };
}
#undef CUT
#line 5 "src/math/CRT.hpp"
// Returns the pair `(x, M)` s.t. `\forall i.\; x \equiv r_i \pmod{m_i}` and `M = \mathrm{lcm}(m_1,\ldots,m_k)`.
// If such `x` doesn't exists, then returns `(-1,-1)`
pair<long long, long long> crt(vector<long long> r, vector<long long> m) {
  assert(r.size() == m.size());
  int n = r.size();
  long long r0 = 0, m0 = 1;
  for (int i = 0; i < n; i++) {
    assert(1 <= m[i]);
    long long r1 = r[i] % m[i], m1 = m[i];
    if (r1 < 0) r1 += m[i];
    if (m0 < m1) swap(r0, r1), swap(m0, m1);
    if (m0 % m1 == 0) {
      if (r0 % m1 != r1) return { -1, -1 };
      continue;
    }
    auto [im, g] = inv_gcd(m0, m1);
    long long u1 = (m1 / g);
    if ((r1 - r0) % g) return { -1, -1 };
    long long x = (r1 - r0) / g % u1 * im % u1;
    r0 += x * m0;
    m0 *= u1;
    if (r0 < 0) r0 += m0;
  }
  return { r0, m0 };
}
#undef CUT
#line 4 "test/math/crt/yuki447.test.cpp"

int main() {
  bool all_zero = true;
  vector<long long> r(3), m(3);
  rep(i, 0, 3) {
    read(r[i], m[i]);
    all_zero &= r[i] == 0;
  }
  print(all_zero ? lcm(lcm(m[0], m[1]), m[2]) : crt(r, m).first);
}