#828409 (C++17) No.2173 Nightcord

• 問題: No.2173 Nightcord
• ユーザー: NyaanNyaan
• 提出日時: 2022-12-25 15:04:36
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 860 ms / 2,525 ms
• コード長: 14,628 bytes
• コンパイル時間: 2,783 ms
• コンパイル使用メモリ: 273,596 KB
• 最終ジャッジ日時: 2025-02-09 20:54:54
• ジャッジサーバーID （参考情報）: judge2 / judge3

ファイルパターン	結果
sample	AC * 3
other	AC * 54

ソースコード

/**
 *  date : 2022-12-25 15:04:27
 */

#define NDEBUG
using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  template <typename S>
  P &operator*=(const S &r) {
    first *= r, second *= r;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
  template <typename S>
  P operator*(const S &r) const {
    return P(*this) *= r;
  }
  P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N,F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

vector<int> mkiota(int n) {
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  return ret;
}

template <typename T>
T mkrev(const T &v) {
  T w{v};
  reverse(begin(w), end(w));
  return w;
}

template <typename T>
bool nxp(vector<T> &v) {
  return next_permutation(begin(v), end(v));
}

template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;

}  // namespace Nyaan

// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan

// inout
namespace Nyaan {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}

istream &operator>>(istream &is, __int128_t &x) {
  string S;
  is >> S;
  x = 0;
  int flag = 0;
  for (auto &c : S) {
    if (c == '-') {
      flag = true;
      continue;
    }
    x *= 10;
    x += c - '0';
  }
  if (flag) x = -x;
  return is;
}

istream &operator>>(istream &is, __uint128_t &x) {
  string S;
  is >> S;
  x = 0;
  for (auto &c : S) {
    x *= 10;
    x += c - '0';
  }
  return is;
}

ostream &operator<<(ostream &os, __int128_t x) {
  if (x == 0) return os << 0;
  if (x < 0) os << '-', x = -x;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
  if (x == 0) return os << 0;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

void outr() {}
template <typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
  cout << t;
  outr(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan

// debug

#ifdef NyaanDebug
#define trc(...) (void(0))
#else
#define trc(...) (void(0))
#endif

#ifdef NyaanLocal
#define trc2(...) (void(0))
#else
#define trc2(...) (void(0))
#endif

// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)

namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }

//

struct Point {
  using T = __int128_t;
  T x, y;
  Point() : x(0), y(0) {}
  Point(T x_, T y_) : x(x_), y(y_) {}

  Point &operator+=(const Point &p) {
    this->x += p.x;
    this->y += p.y;
    return *this;
  }

  Point &operator-=(const Point &p) {
    this->x -= p.x;
    this->y -= p.y;
    return *this;
  }

  int pos() const {
    if (y < 0) return -1;
    if (y == 0 && 0 <= x) return 0;
    return 1;
  }

  Point operator+(const Point &p) const { return Point(*this) += p; }
  Point operator-(const Point &p) const { return Point(*this) -= p; }
  Point operator-() const { return Point(-this->x, -this->y); }
  bool operator==(const Point &p) const { return x == p.x && y == p.y; }
  bool operator!=(const Point &p) const { return x != p.x || y != p.y; }
  bool operator<(const Point &p) const { return x == p.x ? y < p.y : x < p.x; }

  friend istream &operator>>(istream &is, Point &p) {
    long long x, y;
    is >> x >> y;
    p.x = x, p.y = y;
    return is;
  }

  friend ostream &operator<<(ostream &os, const Point &p) {
    os << (long long)(p.x) << " " << (long long)(p.y);
    return os;
  }
};
using Points = vector<Point>;

Point::T dot(const Point &a, const Point &b) { return a.x * b.x + a.y * b.y; }
Point::T cross(const Point &a, const Point &b) { return a.x * b.y - a.y * b.x; }

// sort by argument (-Pi ~ Pi)
void ArgumentSort(Points &v) {
  sort(begin(v), end(v), [](Point a, Point b) {
    if (a.pos() != b.pos()) return a.pos() < b.pos();
    return cross(a, b) > 0;
  });
}

// 1 ... counterclockwise / 0 straight / -1 clockwise
int ccw(const Point &a, const Point &b, const Point &c) {
  Point::T t = cross(b - a, c - a);
  return t < 0 ? -1 : t == 0 ? 0 : 1;
}

// v must have sorted by x-coordinate
Points LowerHull(const Points &ps) {
  int N = (int)ps.size();
  for (int i = 0; i < N - 1; i++) assert(ps[i].x <= ps[i + 1].x);
  if (N <= 2) return ps;
  Points convex(N);
  int k = 0;
  for (int i = 0; i < N; convex[k++] = ps[i++]) {
    while (k >= 2 && ccw(convex[k - 2], convex[k - 1], ps[i]) <= 0) --k;
  }
  convex.resize(k);
  return convex;
}

struct Line {
  Point a, b;
  Line() = default;
  Line(const Point &_a, const Point &_b) : a(_a), b(_b) {}
};

bool onto(Line l, Point m) {
  auto A = cross(l.b - l.a, m - l.a);
  if (A != 0) return false;
  auto d1 = dot(l.b - l.a, m - l.a);
  auto d2 = dot(l.b - l.a, l.b - l.a);
  if (0 <= d1 and d1 <= d2) return true;
  return false;
}

bool cross_point(Line l, Line m) {
  auto A = cross(l.b - l.a, m.a - l.a);
  auto B = cross(l.b - l.a, m.b - l.a);
  if (A == 0 and onto(l, m.a)) return true;
  if (B == 0 and onto(l, m.b)) return true;
  swap(l, m);
  auto C = cross(l.b - l.a, m.a - l.a);
  auto D = cross(l.b - l.a, m.b - l.a);
  if (C == 0 and onto(l, m.a)) return true;
  if (D == 0 and onto(l, m.b)) return true;
  if (A == 0 or B == 0 or C == 0 or D == 0) return false;
  if ((A > 0) == (B > 0)) return false;
  if ((C > 0) == (D > 0)) return false;
  return true;
}

Points UpperHull(const Points &ps) {
  int N = (int)ps.size();
  for (int i = 0; i < N - 1; i++) assert(ps[i].x <= ps[i + 1].x);
  if (N <= 2) return ps;
  Points convex(N);
  int k = 0;
  for (int i = 0; i < N; convex[k++] = ps[i++]) {
    while (k >= 2 && ccw(convex[k - 2], convex[k - 1], ps[i]) >= 0) --k;
  }
  convex.resize(k);
  return convex;
}

Points ConvexHull(const Points &ps) {
  int N = (int)ps.size();
  for (int i = 0; i < N - 1; i++) assert(ps[i].x <= ps[i + 1].x);
  if (N <= 2) return ps;
  Points convex(2 * N);
  int k = 0;
  for (int i = 0; i < N; convex[k++] = ps[i++]) {
    while (k >= 2 && ccw(convex[k - 2], convex[k - 1], ps[i]) <= 0) --k;
  }
  for (int i = N - 2, t = k + 1; i >= 0; convex[k++] = ps[i--]) {
    while (k >= t && ccw(convex[k - 2], convex[k - 1], ps[i]) <= 0) --k;
  }
  convex.resize(k - 1);
  return convex;
}

using namespace Nyaan;

void q() {
  inl(N, K);
  Points c1, c2;
  rep(i, N) {
    inl(x, y, c);
    (c == 1 ? c1 : c2).emplace_back(x, y);
  }

  rep(_, 2) {
    each(p, c2) {
      if (sz(c1) <= 1) continue;
      Points ps;
      each(q, c1) ps.push_back(q - p);
      ArgumentSort(ps);
      trc(ps);
      for (int i = 0, j = 1; i < sz(ps); i++) {
        while (j != i and cross(ps[i], ps[j]) > 0) {
          j++;
          if (j == sz(ps)) j = 0;
        }
        trc(ps[i], ps[j]);
        if (dot(ps[i], ps[j]) < 0 and cross(ps[i], ps[j]) == 0) die("Yes");
      }
    }
    swap(c1, c2);
  }
  trc("line end");

  sort(all(c1));
  sort(all(c2));
  c1 = ConvexHull(c1);
  c2 = ConvexHull(c2);
  trc(c1);
  trc(c2);

  rep(_, 2) {
    // p が凸包 c1 に接する/内包されるか？
    each(p, c2) {
      int ok = 1;
      int not_on = 0;
      rep(i, sz(c1)) {
        if (sz(c1) == 1) break;
        auto p1 = c1[i];
        auto p2 = c1[(i + 1) % sz(c1)];
        // (x2-x1,y2-y1) x (xp-x1,yp-y1)
        i128 cross = ::cross(p2 - p1, p - p1);
        if (cross == 0) {
          // 内部か？
          if (onto({p1, p2}, p)) {
            die("Yes");
          }
        } else if (cross < 0) {
          ok = 0;
        } else {
          not_on = 1;
        }
        if (ok == 0) break;
      }
      if (ok and not_on and K >= 4) die("Yes");
    }
    swap(c1, c2);
  }

  if (K == 3) die("No");

  rep(i, sz(c1)) {
    Line l1{c1[i], c1[(i + 1) % sz(c1)]};
    rep(j, sz(c2)) {
      Line l2{c2[j], c2[(j + 1) % sz(c2)]};
      if (cross_point(l1, l2)) die("Yes");
    }
  }
  out("No");
}

void Nyaan::solve() {
  int t = 1;
  // in(t);
  while (t--) q();
}