結果

問題 No.2602 Real Collider
ユーザー emthrm
提出日時 2024-01-12 23:34:51
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 203 ms / 2,000 ms
コード長 5,510 bytes
コンパイル時間 8,034 ms
コンパイル使用メモリ 402,528 KB
実行使用メモリ 6,948 KB
最終ジャッジ日時 2024-09-28 00:19:55
合計ジャッジ時間 14,008 ms
ジャッジサーバーID
（参考情報） 		judge1 / 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 * 78
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 <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 998244353;
// constexpr int MOD = 1000000007;
constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};
constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};
constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U>
inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U>
inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << fixed << setprecision(20);
  }
} iosetup;

namespace std {

__int128 gcd(__int128 x, __int128 y) {
  while (y != 0) std::swap(x %= y, y);
  return x;
}

}

template <typename T = long long>
struct Rational {
  T num, den;

  Rational() : num(0), den(1) {}
  Rational(const T num, const T den = 1) : num(num), den(den) {
    // assert(den != 0);
    reduce();
  }

  template <typename Real = long double>
  Real to_real() const { return static_cast<Real>(num) / den; }

  Rational& operator+=(const Rational& x) {
    const T g = std::gcd(den, x.den);
    num = num * (x.den / g) + x.num * (den / g);
    den *= x.den / g;
    reduce();
    return *this;
  }
  Rational& operator-=(const Rational& x) { return *this += -x; }

  Rational& operator*=(const Rational& x) {
    const T g1 = std::gcd(num, x.den), g2 = std::gcd(den, x.num);
    num = (num / g1) * (x.num / g2);
    den = (den / g2) * (x.den / g1);
    reduce();
    return *this;
  }
  Rational& operator/=(const Rational& x) {
    return *this *= Rational(x.den, x.num);
  }

  auto operator<=>(const Rational& x) const {
    return num * x.den <=> x.num * den;
  }
  bool operator==(const Rational& x) const {
    return num == x.num && den == x.den;
  }

  Rational& operator++() {
    if ((num += den) == 0) den = 1;
    return *this;
  }
  Rational operator++(int) {
    const Rational res = *this;
    ++*this;
    return res;
  }
  Rational& operator--() {
    if ((num -= den) == 0) den = 1;
    return *this;
  }
  Rational operator--(int) {
    const Rational res = *this;
    --*this;
    return res;
  }

  Rational operator+() const { return *this; }
  Rational operator-() const { return Rational(-num, den); }

  Rational operator+(const Rational& x) const { return Rational(*this) += x; }
  Rational operator-(const Rational& x) const { return Rational(*this) -= x; }
  Rational operator*(const Rational& x) const { return Rational(*this) *= x; }
  Rational operator/(const Rational& x) const { return Rational(*this) /= x; }

  friend std::ostream& operator<<(std::ostream& os, const Rational& x) {
    if (x.den == 1) return os << x.num;
    return os << x.num << '/' << x.den;
  }

 private:
  void reduce() {
    const T g = std::gcd(num, den);
    num /= g;
    den /= g;
    if (den < 0) {
      num = -num;
      den = -den;
    }
  }
};

using rational = Rational<__int128>;

using Point = pair<int, int>;
tuple<rational, rational, rational> smallest_enclosing_circle(
    const Point& p1, const Point& p2, const Point& p3) {
  const auto get_circle = [](const Point& p1, const Point& p2) -> tuple<rational, rational, rational> {
    const auto [p1x, p1y] = p1;
    const auto [p2x, p2y] = p2;
    return {rational(p1x + p2x, 2), rational(p1y + p2y, 2),
            rational((p2x - p1x) * (p2x - p1x) + (p2y - p1y) * (p2y - p1y), 4)};
  };
  auto [cx, cy, cr] = get_circle(p1, p2);
  const auto is_in = [&](const Point& p) -> bool {
    const auto [x, y] = p;
    return (cx - x) * (cx - x) + (cy - y) * (cy - y) <= cr;
  };
  if (!is_in(p3)) {
    tie(cx, cy, cr) = get_circle(p1, p3);
    if (!is_in(p2)) {
      tie(cx, cy, cr) = get_circle(p2, p3);
      if (!is_in(p1)) {
        const int a = (p3.first - p2.first) * (p3.first - p2.first) + (p3.second - p2.second) * (p3.second - p2.second);
        const int b = (p1.first - p3.first) * (p1.first - p3.first) + (p1.second - p3.second) * (p1.second - p3.second);
        const int c = (p2.first - p1.first) * (p2.first - p1.first) + (p2.second - p1.second) * (p2.second - p1.second);
        const int idx = p3.first - p1.first, idy = p3.second - p1.second;
        const int jdx = p2.first - p1.first, jdy = p2.second - p1.second;
        const int s = idx * jdy - idy * jdx;
        cx = rational(__int128{p1.first} * a * (b + c - a) + __int128{p2.first} * b * (c + a - b) + __int128{p3.first} * c * (a + b - c), 4LL * s * s);
        cy = rational(__int128{p1.second} * a * (b + c - a) + __int128{p2.second} * b * (c + a - b) + __int128{p3.second} * c * (a + b - c), 4LL * s * s);
        cr = (cx - p1.first) * (cx - p1.first) + (cy - p1.second) * (cy - p1.second);
      }
    }
  }
  return {cx, cy, cr};
}

#include <boost/multiprecision/cpp_int.hpp>
using namespace boost::multiprecision;

int main() {
  int q, xa, ya, xb, yb, xc, yc; cin >> q >> xa >> ya >> xb >> yb >> xc >> yc;
  const auto [cx, cy, cr] = smallest_enclosing_circle({xa, ya}, {xb, yb}, {xc, yc});
  while (q--) {
    int x, y; cin >> x >> y;
    const rational dx = cx - x, dy = cy - y;
    cout << ((int256_t{dx.num} * dx.num * dy.den * dy.den + int256_t{dy.num} * dy.num * dx.den * dx.den) * cr.den <= int256_t{cr.num} * dx.den * dx.den * dy.den * dy.den ? "Yes\n" : "No\n");
  }
  return 0;
}
0