結果
| 問題 |
No.2173 Nightcord
|
| コンテスト | |
| ユーザー |
 nok0
|
| 提出日時 | 2022-12-23 21:51:08 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 29,145 bytes |
| コンパイル時間 | 2,670 ms |
| コンパイル使用メモリ | 225,328 KB |
| 最終ジャッジ日時 | 2025-02-09 19:27:17 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | WA * 1 RE * 2 |
| other | AC * 18 WA * 10 RE * 26 |
コンパイルメッセージ
a.cpp: In function ‘void main_()’: a.cpp:366:23: warning: narrowing conversion of ‘x’ from ‘int’ to ‘long double’ [-Wnarrowing] a.cpp:366:26: warning: narrowing conversion of ‘y’ from ‘int’ to ‘long double’ [-Wnarrowing] a.cpp:368:23: warning: narrowing conversion of ‘x’ from ‘int’ to ‘long double’ [-Wnarrowing] a.cpp:368:26: warning: narrowing conversion of ‘y’ from ‘int’ to ‘long double’ [-Wnarrowing] /home/nok0/documents/programming/library/template/input.hpp: In function ‘void scanner::scan(char*)’: /home/nok0/documents/programming/library/template/input.hpp:29:33: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
ソースコード
#line 2 "/home/nok0/documents/programming/library/template/header.hpp"
#include <bits/stdc++.h>
#line 3 "/home/nok0/documents/programming/library/template/def_const.hpp"
const int inf = 1000000000;
const long long INF = 1000000000000000000ll;
#line 4 "/home/nok0/documents/programming/library/template/debug.hpp"
namespace viewer {
void view(const long long &e) {
if(e == INF)
std::cerr << "INF";
else if(e == -INF)
std::cerr << "-INF";
else
std::cerr << e;
}
void view(const int &e) {
if(e == inf)
std::cerr << "inf";
else if(e == -inf)
std::cerr << "-inf";
else
std::cerr << e;
}
template <typename T>
void view(const T &e) {
std::cerr << e;
}
template <typename T, typename U>
void view(const std::pair<T, U> &p) {
std::cerr << "(";
view(p.first);
std::cerr << ", ";
view(p.second);
std::cerr << ")";
}
template <class T0, class T1, class T2>
void view(const std::tuple<T0, T1, T2> &p) {
std::cerr << "(";
view(std::get<0>(p));
std::cerr << ", ";
view(std::get<1>(p));
std::cerr << ", ";
view(std::get<2>(p));
std::cerr << ")";
}
template <class T0, class T1, class T2, class T3>
void view(const std::tuple<T0, T1, T2, T3> &p) {
std::cerr << "(";
view(std::get<0>(p));
std::cerr << ", ";
view(std::get<1>(p));
std::cerr << ", ";
view(std::get<2>(p));
std::cerr << ", ";
view(std::get<3>(p));
std::cerr << ")";
}
template <typename T>
void view(const std::set<T> &s) {
if(s.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << "{ ";
for(auto &t : s) {
view(t);
std::cerr << ", ";
}
std::cerr << "\b\b }";
}
template <typename T>
void view(const std::unordered_set<T> &s) {
if(s.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << "{ ";
for(auto &t : s) {
view(t);
std::cerr << ", ";
}
std::cerr << "\b\b }";
}
template <typename T>
void view(const std::multiset<T> &s) {
if(s.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << "{ ";
for(auto &t : s) {
view(t);
std::cerr << ", ";
}
std::cerr << "\b\b }";
}
template <typename T>
void view(const std::unordered_multiset<T> &s) {
if(s.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << "{ ";
for(auto &t : s) {
view(t);
std::cerr << ", ";
}
std::cerr << "\b\b }";
}
template <typename T>
void view(const std::vector<T> &v) {
if(v.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << "{ ";
for(const auto &e : v) {
view(e);
std::cerr << ", ";
}
std::cerr << "\b\b }";
}
template <typename T, std::size_t ary_size>
void view(const std::array<T, ary_size> &v) {
if(v.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << "{ ";
for(const auto &e : v) {
view(e);
std::cerr << ", ";
}
std::cerr << "\b\b }";
}
template <typename T>
void view(const std::vector<std::vector<T>> &vv) {
std::cerr << "{\n";
for(const auto &v : vv) {
std::cerr << "\t";
view(v);
std::cerr << '\n';
}
std::cerr << "}";
}
template <typename T, typename U>
void view(const std::vector<std::pair<T, U>> &v) {
std::cerr << "{\n";
for(const auto &c : v) {
std::cerr << "\t(";
view(c.first);
std::cerr << ", ";
view(c.second);
std::cerr << ")\n";
}
std::cerr << "}";
}
template <class T0, class T1, class T2>
void view(const std::vector<std::tuple<T0, T1, T2>> &v) {
if(v.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << '{';
for(const auto &t : v) {
std::cerr << "\n\t";
view(t);
std::cerr << ",";
}
std::cerr << "\n}";
}
template <class T0, class T1, class T2, class T3>
void view(const std::vector<std::tuple<T0, T1, T2, T3>> &v) {
if(v.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << '{';
for(const auto &t : v) {
std::cerr << "\n\t";
view(t);
std::cerr << ",";
}
std::cerr << "\n}";
}
template <typename T, typename U>
void view(const std::map<T, U> &m) {
std::cerr << "{\n";
for(const auto &t : m) {
std::cerr << "\t[";
view(t.first);
std::cerr << "] : ";
view(t.second);
std::cerr << '\n';
}
std::cerr << "}";
}
template <typename T, typename U>
void view(const std::unordered_map<T, U> &m) {
std::cerr << "{\n";
for(const auto &t : m) {
std::cerr << "\t[";
view(t.first);
std::cerr << "] : ";
view(t.second);
std::cerr << '\n';
}
std::cerr << "}";
}
} // namespace viewer
// when compiling : g++ foo.cpp -DLOCAL
#ifdef LOCAL
void debug_out() {}
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
viewer::view(H);
std::cerr << ", ";
debug_out(T...);
}
#define debug(...) \
do { \
std::cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \
debug_out(__VA_ARGS__); \
std::cerr << "\b\b]\n"; \
} while(0)
#define dump(x) \
do { \
std::cerr << __LINE__ << " " << #x << " : "; \
viewer::view(x); \
std::cerr << '\n'; \
} while(0)
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif
#line 3 "/home/nok0/documents/programming/library/template/def_name.hpp"
#define pb push_back
#define eb emplace_back
#define SZ(x) ((int)(x).size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define popcnt(x) __builtin_popcountll(x)
template<class T = int>
using V = std::vector<T>;
template<class T = int>
using VV = std::vector<std::vector<T>>;
template<class T>
using pqup = std::priority_queue<T, std::vector<T>, std::greater<T>>;
using ll = long long;
using ld = long double;
using int128 = __int128_t;
using pii = std::pair<int, int>;
using pll = std::pair<long long, long long>;
#line 3 "/home/nok0/documents/programming/library/template/fast_io.hpp"
struct fast_io {
fast_io() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
std::cout << std::fixed << std::setprecision(15);
}
} fast_io_;
#line 3 "/home/nok0/documents/programming/library/template/input.hpp"
template<class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template<class T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
for (T &i : v) is >> i;
return is;
}
std::istream &operator>>(std::istream &is, __int128_t &a) {
std::string s;
is >> s;
__int128_t ret = 0;
for (int i = 0; i < (int)s.length(); i++)
if ('0' <= s[i] and s[i] <= '9')
ret = 10 * ret + s[i] - '0';
a = ret * (s[0] == '-' ? -1 : 1);
return is;
}
namespace scanner {
void scan(int &a) { std::cin >> a; }
void scan(long long &a) { std::cin >> a; }
void scan(std::string &a) { std::cin >> a; }
void scan(char &a) { std::cin >> a; }
void scan(char a[]) { std::scanf("%s", a); }
void scan(double &a) { std::cin >> a; }
void scan(long double &a) { std::cin >> a; }
template<class T, class U>
void scan(std::pair<T, U> &p) { std::cin >> p; }
template<class T>
void scan(std::vector<T> &a) { std::cin >> a; }
void INPUT() {}
template<class Head, class... Tail>
void INPUT(Head &head, Tail &...tail) {
scan(head);
INPUT(tail...);
}
} // namespace scanner
#define VEC(type, name, size) \
std::vector<type> name(size); \
scanner::INPUT(name)
#define VVEC(type, name, h, w) \
std::vector<std::vector<type>> name(h, std::vector<type>(w)); \
scanner::INPUT(name)
#define INT(...) \
int __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define LL(...) \
long long __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define STR(...) \
std::string __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define DOUBLE(...) \
double __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define LD(...) \
long double __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#line 3 "/home/nok0/documents/programming/library/template/math.hpp"
template <class T, class U>
inline bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; }
template <class T, class U>
inline bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; }
template <class T>
T divup(T x, T y) { return (x + y - 1) / y; }
template <class T>
T POW(T a, long long n) {
T ret = 1;
while(n) {
if(n & 1) ret *= a;
a *= a;
n >>= 1;
}
return ret;
}
long long POW(long long a, long long n, const int mod) {
long long ret = 1;
a = (a % mod + mod) % mod;
while(n) {
if(n & 1) (ret *= a) %= mod;
(a *= a) %= mod;
n >>= 1;
}
return ret;
}
template <class T, class F>
T bin_search(T ok, T ng, const F &f) {
while(abs(ok - ng) > 1) {
T mid = (ok + ng) >> 1;
(f(mid) ? ok : ng) = mid;
}
return ok;
}
template <class T, class F>
T bin_search(T ok, T ng, const F &f, int loop) {
for(int i = 0; i < loop; i++) {
T mid = (ok + ng) / 2;
(f(mid) ? ok : ng) = mid;
}
return ok;
}
#line 3 "/home/nok0/documents/programming/library/template/output.hpp"
template<class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template<class T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &a) {
for (int i = 0; i < int(a.size()); ++i) {
if (i) os << " ";
os << a[i];
}
return os;
}
std::ostream &operator<<(std::ostream &dest, __int128_t &value) {
std::ostream::sentry s(dest);
if (s) {
__uint128_t tmp = value < 0 ? -value : value;
char buffer[128];
char *d = std::end(buffer);
do {
--d;
*d = "0123456789"[tmp % 10];
tmp /= 10;
} while (tmp != 0);
if (value < 0) {
--d;
*d = '-';
}
int len = std::end(buffer) - d;
if (dest.rdbuf()->sputn(d, len) != len) {
dest.setstate(std::ios_base::badbit);
}
}
return dest;
}
template<class T>
void print(const T a) { std::cout << a << '\n'; }
template<class Head, class... Tail>
void print(Head H, Tail... T) {
std::cout << H << ' ';
print(T...);
}
template<class T>
void printel(const T a) { std::cout << a << '\n'; }
template<class T>
void printel(const std::vector<T> &a) {
for (const auto &v : a)
std::cout << v << '\n';
}
template<class Head, class... Tail>
void printel(Head H, Tail... T) {
std::cout << H << '\n';
printel(T...);
}
void Yes(const bool b = true) { std::cout << (b ? "Yes\n" : "No\n"); }
void No() { std::cout << "No\n"; }
void YES(const bool b = true) { std::cout << (b ? "YES\n" : "NO\n"); }
void NO() { std::cout << "NO\n"; }
#line 2 "/home/nok0/documents/programming/library/template/rep.hpp"
#define foa(v, a) for (auto &v : a)
#define repname(a, b, c, d, e, ...) e
#define rep(...) repname(__VA_ARGS__, rep3, rep2, rep1, rep0)(__VA_ARGS__)
#define rep0(x) for (int rep_counter = 0; rep_counter < (x); ++rep_counter)
#define rep1(i, x) for (int i = 0; i < (x); ++i)
#define rep2(i, l, r) for (int i = (l); i < (r); ++i)
#define rep3(i, l, r, c) for (int i = (l); i < (r); i += (c))
#define repsname(a, b, c, ...) c
#define reps(...) repsname(__VA_ARGS__, reps1, reps0)(__VA_ARGS__)
#define reps0(x) for (int reps_counter = 1; reps_counter <= (x); ++reps_counter)
#define reps1(i, x) for (int i = 1; i <= (x); ++i)
#define rrepname(a, b, c, ...) c
#define rrep(...) rrepname(__VA_ARGS__, rrep1, rrep0)(__VA_ARGS__)
#define rrep0(x) for (int rrep_counter = (x)-1; rrep_counter >= 0; --rrep_counter)
#define rrep1(i, x) for (int i = (x)-1; i >= 0; --i)
#line 3 "/home/nok0/documents/programming/library/template/vector.hpp"
template <class T>
int lb(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::lower_bound((a).begin(), (a).end(), (x))); }
template <class T>
int ub(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::upper_bound((a).begin(), (a).end(), (x))); }
template <class T>
void UNIQUE(std::vector<T> &a) {
std::sort(a.begin(), a.end());
a.erase(std::unique(a.begin(), a.end()), a.end());
}
template <class T>
std::vector<T> press(std::vector<T> &a) {
auto res = a;
UNIQUE(res);
for(auto &v : a)
v = lb(res, v);
return res;
}
#define SORTname(a, b, c, ...) c
#define SORT(...) SORTname(__VA_ARGS__, SORT1, SORT0, ...)(__VA_ARGS__)
#define SORT0(a) std::sort((a).begin(), (a).end())
#define SORT1(a, c) std::sort((a).begin(), (a).end(), [](const auto x, const auto y) { return x c y; })
template <class T>
void ADD(std::vector<T> &a, const T x = 1) {
for(auto &v : a) v += x;
}
template <class T>
void SUB(std::vector<T> &a, const T x = 1) {
for(auto &v : a) v -= x;
}
template <class T>
struct cum_vector {
public:
cum_vector() = default;
template <class U>
cum_vector(const std::vector<U> &vec) : cum((int)vec.size() + 1) {
for(int i = 0; i < (int)vec.size(); i++)
cum[i + 1] = cum[i] + vec[i];
}
T prod(int l, int r) {
return cum[r] - cum[l];
}
private:
std::vector<T> cum;
};
std::vector<std::pair<char, int>> rle(const std::string &s) {
const int n = s.size();
std::vector<std::pair<char, int>> ret;
for(int l = 0; l < n;) {
int r = l + 1;
for(; r < n and s[l] == s[r]; r++) {}
ret.emplace_back(s[l], r - l);
l = r;
}
return ret;
}
template <class T>
std::vector<std::pair<T, int>> rle(const std::vector<T> &v) {
int n = v.size();
std::vector<std::pair<T, int>> ret;
for(int l = 0; l < n;) {
int r = l + 1;
for(; r < n and v[l] == v[r]; r++) {}
ret.emplace_back(v[l], r - l);
l = r;
}
return ret;
}
std::vector<int> iota(int n) {
std::vector<int> p(n);
std::iota(p.begin(), p.end(), 0);
return p;
}
#line 11 "/home/nok0/documents/programming/library/template/all"
using namespace std;
#line 2 "a.cpp"
using R = long double;
using point = std::complex<R>;
using arrow = point;
const R EPS(1e-10), PI(acosl(-1));
inline bool eq(const R &a, const R &b) { return fabsl(b - a) < EPS; }
inline bool same_point(const point &a, const point &b) { return abs(b - a) < EPS; }
/*
sign of x
-1: x < 0
0: x == 0
1: x > 0
*/
inline int sgn(const R &x) { return fabsl(x) < EPS ? 0 : (x < 0 ? -1 : 1); }
/*
sign of (a-b)
-1: a < b
0: a == b
1: a > b
*/
inline int compare(const R &a, const R &b) { return eq(a, b) ? 0 : a < b ? -1 :
1; }
std::istream &operator>>(std::istream &is, point &p) {
R a, b;
is >> a >> b;
p = point(a, b);
return is;
}
std::ostream &operator<<(std::ostream &os, point &p) { return os << '(' << p.real() << ", " << p.imag() << ')'; }
// rotate point 'p' for counter clockwise direction
point rotate(const point &p, const R &theta) {
return point(cosl(theta) * p.real() - sinl(theta) * p.imag(), sinl(theta) * p.real() + cosl(theta) * p.imag());
}
R radian_to_degree(const R &r) { return (r * 180.0 / PI); }
R degree_to_radian(const R &d) { return (d * PI / 180.0); }
// get angle a-b-c (<pi)
R get_angle(const point &a, const point &b, const point &c) {
const point v(a - b), w(c - b);
R theta = fabsl(atan2l(w.imag(), w.real()) - atan2l(v.imag(), v.real()));
return std::min(theta, 2 * PI - theta);
}
namespace std {
bool operator<(const point &a, const point &b) { return a.real() != b.real() ? a.real() < b.real() : a.imag() < b.imag(); }
} // namespace std
struct segment;
struct line {
point a, b;
line() = default;
line(const point &a, const point &b) : a(a), b(b) {}
// Ax + By + C = 0
line(const R &A, const R &B, const R &C) {
if(eq(A, 0)) {
assert(!eq(B, 0));
a = point(0, -C / B), b = point(1, -(A + C) / B);
} else {
a = point(-C / A, 0), b = point(-(B + C) / A, 1);
}
}
explicit line(const segment &seg);
friend std::ostream &operator<<(std::ostream &os, line &ln) { return os << '(' << ln.a << " -- " << ln.b << ')'; }
friend std::istream &operator>>(std::istream &is, line &a) { return is >> a.a >> a.b; }
};
struct segment {
point a, b;
segment() = default;
segment(const point &a, const point &b) : a(a), b(b) {}
explicit segment(const line &ln) : a(ln.a), b(ln.b) {}
friend std::ostream &operator<<(std::ostream &os, segment &seg) { return os << '[' << seg.a << " -- " << seg.b << ']'; }
friend std::istream &operator>>(std::istream &is, segment &a) { return is >> a.a >> a.b; }
};
line::line(const segment &seg) : a(seg.a), b(seg.b) {}
struct circle {
point center;
R radius;
circle() = default;
circle(const point ¢er, const R &radius) : center(center), radius(radius) {}
};
using points = std::vector<point>;
using polygon = std::vector<point>;
using segments = std::vector<segment>;
using lines = std::vector<line>;
using circles = std::vector<circle>;
R cross(const point &a, const point &b) { return real(a) * imag(b) - imag(a) * real(b); }
R dot(const point &a, const point &b) { return real(a) * real(b) + imag(a) * imag(b); }
enum CCW {
ONLINE_FRONT = -2,
CLOCKWISE = -1,
ON_SEGMENT = 0,
COUNTER_CLOCKWISE = 1,
ONLINE_BACK = 2,
};
int ccw(const point &a, point b, point c) {
b -= a, c -= a;
const R crs_b_c = cross(b, c);
if(crs_b_c > EPS) return CCW::COUNTER_CLOCKWISE;
if(crs_b_c < -EPS) return CCW::CLOCKWISE;
if(dot(b, c) < -EPS) return CCW::ONLINE_BACK;
if(norm(b) + EPS < norm(c)) return CCW::ONLINE_FRONT;
return CCW::ON_SEGMENT;
}
bool parallel(const arrow &a, const arrow &b) { return eq(cross(a, b), R(0)); }
bool parallel(const line &a, const line &b) { return parallel(a.b - a.a, b.b - b.a); }
bool parallel(const line &a, const segment &b) { return parallel(a.b - a.a, b.b - b.a); }
bool parallel(const segment &a, const line &b) { return parallel(a.b - a.a, b.b - b.a); }
bool parallel(const segment &a, const segment &b) { return parallel(a.b - a.a, b.b - b.a); }
bool orthogonal(const arrow &a, const arrow &b) { return eq(dot(a, b), R(0)); }
bool orthogonal(const line &a, const line &b) { return orthogonal(a.b - a.a, b.b - b.a); }
bool orthogonal(const line &a, const segment &b) { return orthogonal(a.b - a.a, b.b - b.a); }
bool orthogonal(const segment &a, const line &b) { return orthogonal(a.b - a.a, b.b - b.a); }
bool orthogonal(const segment &a, const segment &b) { return orthogonal(a.b - a.a, b.b - b.a); }
point projection(const line &l, const point &p) { return l.a + (l.a - l.b) * dot(p - l.a, l.a - l.b) / norm(l.a - l.b); }
point projection(const segment &s, const point &p) { return projection(line(s), p); }
point reflection(const line &l, const point &p) { return projection(l, p) * R(2) - p; }
point reflection(const segment &s, const point &p) { return projection(line(s), p); }
R distance(const point &p, const point &q);
R distance(const line &l, const point &p);
int number_of_common_tangents(const circle &c1, const circle &c2) {
const R r1 = std::min(c1.radius, c2.radius), r2 = std::max(c1.radius, c2.radius), d = distance(c1.center, c2.center);
int com = compare(r1 + r2, d);
return com == 1 ? compare(d + r1, r2) + 1 : 3 - com;
}
// number of common points (-1: infinite)
int intersect(const line &l, const point &p) { return int(abs(ccw(l.a, l.b, p)) != 1); }
int intersect(const point &p, const line &l) { return intersect(l, p); }
int intersect(const line &l, const line &m) {
if(intersect(l, m.a) && intersect(l, m.b)) return -1;
return int(!parallel(l, m));
}
int intersect(const segment &s, const point &p) { return int(ccw(s.a, s.b, p) == CCW::ON_SEGMENT); }
int intersect(const point &p, const segment &s) { return intersect(s, p); }
int intersect(const line &l, const segment &s) {
if(intersect(l, s.a) && intersect(l, s.b)) return -1;
return ccw(l.a, l.b, s.a) * ccw(l.a, l.b, s.b) != 1;
}
int intersect(const segment &s, const line &l) { return intersect(l, s); }
int intersect(const circle &c, const line &l) {
R d = c.radius - distance(l, c.center);
return fabsl(d) < EPS ? 1 : d > 0. ? 2 :
0;
}
int intersect(const line &l, const circle &c) { return intersect(c, l); }
int intersect(const circle &c, const point &p) { return int(eq(c.radius, distance(c.center, p))); }
int intersect(const point &p, const circle &c) { return intersect(c, p); }
int intersect(const segment &s, const segment &t) {
if(same_point(s.a, s.b)) return intersect(t, s.a);
if(intersect(line(s), t.a) && intersect(line(s), t.b) && std::max(std::min(s.a, s.b), std::min(t.a, t.b)) < std::min(std::max(s.a, s.b), std::max(t.a, t.b)))
return -1;
return int(ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 && ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0);
}
int intersect(const circle &c, const segment &s) {
const point h = projection(s, c.center);
const int c0 = compare(distance(h, c.center), c.radius);
if(c0 == 1) return 0;
if(c0 == 0) return intersect(s, h);
const int c1 = compare(distance(c.center, s.a), c.radius), c2 = compare(distance(c.center, s.b), c.radius);
if(std::min(c1, c2) == -1) return int(std::max(c1, c2) >= 0);
return intersect(s, h) ? 2 : 0;
}
int intersect(const segment &s, const circle &c) { return intersect(c, s); }
int intersect(const circle &c1, const circle &c2) { return 2 - abs(2 - number_of_common_tangents(c1, c2)); }
// distance of two shaps
R distance(const point &a, const point &b) { return fabs(a - b); }
R distance(const line &l, const point &p) { return distance(p, projection(l, p)); }
R distance(const point &p, const line &l) { return distance(l, p); }
R distance(const line &l, const line &m) { return parallel(l, m) ? distance(l, m.a) : 0; }
R distance(const segment &s, const point &p) {
const point r = projection(s, p);
return intersect(s, r) ? distance(r, p) : std::min(distance(s.a, p), distance(s.b, p));
}
R distance(const point &p, const segment &s) { return distance(s, p); }
R distance(const segment &a, const segment &b) {
if(intersect(a, b)) return R(0);
return std::min({distance(a, b.a), distance(a, b.b), distance(b, a.a), distance(b, a.b)});
}
R distance(const line &l, const segment &s) {
if(intersect(l, s)) return 0;
return std::min(distance(l, s.a), distance(l, s.b));
}
R distance(const segment &s, const line &l) { return distance(l, s); }
R distance(const circle &c, const point &p) { return fabsl(distance(c.center, p) - c.radius); }
R distance(const point &p, const circle &c) { return distance(c, p); }
R distance(const circle &c, const line &l) { return std::max(R(0), distance(l, c.center) - c.radius); }
R distance(const line &l, const circle &c) { return distance(c, l); }
R distance(const circle &c1, const circle &c2) {
const R d = distance(c1.center, c2.center);
if(d > c1.radius + c2.radius) return d - c1.radius - c2.radius;
if(d < fabsl(c1.radius - c2.radius)) return fabsl(c1.radius - c2.radius) - d;
return R(0);
}
R distance(const circle &c, const segment &s) {
const point p = projection(s, c.center);
const R dist_min = intersect(s, p) ? distance(c.center, p) : std::min(distance(c.center, s.a), distance(c.center, s.b));
if(dist_min > c.radius) return dist_min - c.radius;
const R dist_max = std::max(distance(c.center, s.a), distance(c.center, s.b));
return dist_max < c.radius ? c.radius - dist_max : R(0);
}
R distance(const segment &s, const circle &c) { return distance(c, s); }
point crosspoint(const line &l, const line &m) {
R A = cross(l.b - l.a, m.b - m.a);
R B = cross(l.b - l.a, l.b - m.a);
if(eq(A, 0.)) return m.a;
return m.a + (m.b - m.a) * B / A;
}
point crosspoint(const segment &s, const segment &t) { return crosspoint(line(s), line(t)); }
point crosspoint(const segment &s, const line &l) { return crosspoint(line(s), l); }
point crosspoint(const line &l, const segment &s) { return crosspoint(l, line(s)); }
points crosspoints(const circle &c, const line &l) {
const point pr = projection(l, c.center);
const R square = c.radius * c.radius - norm(pr - c.center);
switch(sgn(square)) {
case 0 :
return points{pr};
case -1 :
return points(0);
}
const arrow v = (l.b - l.a) / abs(l.b - l.a) * sqrtl(square);
return points{pr - v, pr + v};
}
points crosspoints(const line &l, const circle &c) { return crosspoints(c, l); }
points crosspoints(const circle &c, const segment &s) {
points ret;
for(const auto &pt : crosspoints(c, line(s)))
if(intersect(s, pt)) ret.push_back(pt);
return ret;
}
points crosspoints(const segment &s, const circle &c) { return crosspoints(c, s); }
points crosspoints(const circle &c1, const circle &c2) {
R d = abs(c1.center - c2.center);
if(compare(d, c1.radius + c2.radius) == 1) return points(0);
if(compare(d, fabsl(c1.radius - c2.radius)) == -1) return points(0);
bool one_crosspoint = false;
if(eq(d, c1.radius + c2.radius) || eq(d, fabsl(c1.radius - c2.radius))) one_crosspoint = true;
const R alpha = acosl((c1.radius * c1.radius + d * d - c2.radius * c2.radius) / (2 * c1.radius * d)); // cosine theorem
const R beta = std::arg(c2.center - c1.center);
if(one_crosspoint) return points{c1.center + std::polar(c1.radius, beta + alpha)};
return points{c1.center + std::polar(c1.radius, beta + alpha), c1.center + std::polar(c1.radius, beta - alpha)};
}
points tangent_points(const circle &c, const point &p) {
const R square = norm(c.center - p) - c.radius * c.radius;
switch(sgn(square)) {
case 0 :
return points{p};
case -1 :
return points{};
}
return crosspoints(c, circle(p, sqrtl(square)));
}
// common tangents of two circles
lines tangents(circle c1, circle c2) {
lines ret;
if(c1.radius < c2.radius) std::swap(c1, c2);
const R g = distance(c1.center, c2.center);
if(!sgn(g)) return ret;
const arrow u = (c2.center - c1.center) / g;
const arrow v = rotate(u, PI * 0.5);
for(const int &s : {-1, 1}) {
const R h = (c1.radius + s * c2.radius) / g;
if(eq(1 - h * h, 0)) {
ret.emplace_back(c1.center + u * c1.radius, c1.center + (u + v) * c1.radius);
} else if(1 - h * h > 0) {
const point uu = u * h, vv = v * sqrtl(1 - h * h);
ret.emplace_back(c1.center + (uu + vv) * c1.radius, c2.center - (uu + vv) * c2.radius * R(s));
ret.emplace_back(c1.center + (uu - vv) * c1.radius, c2.center - (uu - vv) * c2.radius * R(s));
}
}
return ret;
}
enum CONTAIN { OUT = 0,
ON = 1,
IN = 2 };
int contains(const polygon &poly, const point &p) {
bool in = false;
for(int i = 0; i < poly.size(); i++) {
point a = poly[i], b = poly[(i + 1) % poly.size()];
if(ccw(a, b, p) == 0) return CONTAIN::ON;
if(a.imag() > b.imag()) swap(a, b);
if(a.imag() <= p.imag() && p.imag() < b.imag() && cross(a - p, b - p) < 0) in = !in;
}
return in ? CONTAIN::IN : CONTAIN::OUT;
}
int contains(const circle &c, const point &p) { return compare(c.radius, distance(c.center, p)) + 1; }
bool is_convex(const polygon &p, bool pi_is_ok = true) {
int n = (int)p.size();
if(pi_is_ok) {
for(int i = 0; i < n; i++)
if(ccw(p[i], p[(i + 1) % n], p[(i + 2) % n]) == -1) return false;
} else {
for(int i = 0; i < n; i++)
if(ccw(p[i], p[(i + 1) % n], p[(i + 2) % n]) != 1) return false;
}
return true;
}
polygon convex_hull(polygon &p, bool vertices_on_edge_remain = true) {
int n = (int)p.size(), k = 0;
if(n <= 2) return p;
sort(p.begin(), p.end());
points ch(2 * n);
if(vertices_on_edge_remain) {
for(int i = 0; i < n; ch[k++] = p[i++])
while(k >= 2 && ccw(ch[k - 2], ch[k - 1], p[i]) == -1) --k;
for(int i = n - 2, t = k + 1; i >= 0; ch[k++] = p[i--])
while(k >= t && ccw(ch[k - 2], ch[k - 1], p[i]) == -1) --k;
} else {
for(int i = 0; i < n; ch[k++] = p[i++])
while(k >= 2 && ccw(ch[k - 2], ch[k - 1], p[i]) != 1) --k;
for(int i = n - 2, t = k + 1; i >= 0; ch[k++] = p[i--])
while(k >= t && ccw(ch[k - 2], ch[k - 1], p[i]) != 1) --k;
}
ch.resize(k - 1);
return ch;
}
// cut the convex polygon 'U' with line 'a'-'b', then return the leftside polygon
// (i.e. forall p \in (returned polygon), ccw(a, b, p) != -1)
// only 0~2 points may be returned
polygon convex_cut(const polygon &U, const point &a, const point &b) {
polygon ret;
const line l(a, b);
for(int i = 0; i < U.size(); i++) {
const point &now = U[i], &nxt = U[(i + 1) % U.size()];
if(ccw(l.a, l.b, now) != -1) ret.push_back(now);
if(ccw(l.a, l.b, now) * ccw(l.a, l.b, nxt) == -1) ret.push_back(crosspoint(line(now, nxt), l));
}
return ret;
}
void main_();
int main() {
int t = 1;
while(t--) main_();
}
void main_() {
INT(n, k);
points rp, bp;
rep(i, n) {
INT(x, y, c);
if(c)
rp.push_back(point{x, y});
else
bp.push_back(point{x, y});
}
if(k >= 4) {
auto rh = convex_hull(rp);
auto bh = convex_hull(bp);
bool res = 0;
foa(v, rh) {
if(contains(bh, v)) res = 1;
}
foa(v, bh) {
if(contains(rh, v)) res = 1;
}
rep(i, SZ(rh)) {
rep(j, SZ(bh)) {
auto l1 = segment(rh[i], rh[(i + 1) % SZ(rh)]);
auto l2 = segment(bh[i], bh[(i + 1) % SZ(bh)]);
if(intersect(l1, l2)) res = 1;
}
}
Yes(res);
} else {
assert(false);
// あとで
}
}