結果
| 問題 | No.5009 Draw A Convex Polygon |
| ユーザー |
 hitonanode
|
| 提出日時 | 2022-12-02 00:24:15 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 856 ms / 2,600 ms |
| コード長 | 13,731 bytes |
| コンパイル時間 | 2,106 ms |
| 実行使用メモリ | 44,388 KB |
| スコア | 1,000,000 |
| 平均クエリ数 | 978883.00 |
| 最終ジャッジ日時 | 2022-12-02 00:24:20 |
| 合計ジャッジ時間 | 4,606 ms |
|
ジャッジサーバーID （参考情報） |
judge13 / judge11 |
| 純コード判定しない問題か言語 |
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ソースコード
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif
template <typename T_P> struct Point2d {
static T_P EPS;
static void set_eps(T_P e) { EPS = e; }
T_P x, y;
Point2d() : x(0), y(0) {}
Point2d(T_P x, T_P y) : x(x), y(y) {}
Point2d(const std::pair<T_P, T_P> &p) : x(p.first), y(p.second) {}
Point2d(const std::complex<T_P> &p) : x(p.real()), y(p.imag()) {}
std::complex<T_P> to_complex() const noexcept { return {x, y}; }
Point2d operator+(const Point2d &p) const noexcept { return Point2d(x + p.x, y + p.y); }
Point2d operator-(const Point2d &p) const noexcept { return Point2d(x - p.x, y - p.y); }
Point2d operator*(const Point2d &p) const noexcept {
static_assert(std::is_floating_point<T_P>::value == true);
return Point2d(x * p.x - y * p.y, x * p.y + y * p.x);
}
Point2d operator*(T_P d) const noexcept { return Point2d(x * d, y * d); }
Point2d operator/(T_P d) const noexcept {
static_assert(std::is_floating_point<T_P>::value == true);
return Point2d(x / d, y / d);
}
Point2d inv() const {
static_assert(std::is_floating_point<T_P>::value == true);
return conj() / norm2();
}
Point2d operator/(const Point2d &p) const { return (*this) * p.inv(); }
bool operator<(const Point2d &r) const noexcept { return x != r.x ? x < r.x : y < r.y; }
bool operator==(const Point2d &r) const noexcept { return x == r.x and y == r.y; }
bool operator!=(const Point2d &r) const noexcept { return !((*this) == r); }
T_P dot(Point2d p) const noexcept { return x * p.x + y * p.y; }
T_P det(Point2d p) const noexcept { return x * p.y - y * p.x; }
T_P absdet(Point2d p) const noexcept { return std::abs(det(p)); }
T_P norm() const noexcept {
static_assert(std::is_floating_point<T_P>::value == true);
return std::sqrt(x * x + y * y);
}
T_P norm2() const noexcept { return x * x + y * y; }
T_P arg() const noexcept { return std::atan2(y, x); }
// rotate point/vector by rad
Point2d rotate(T_P rad) const noexcept {
static_assert(std::is_floating_point<T_P>::value == true);
return Point2d(x * std::cos(rad) - y * std::sin(rad), x * std::sin(rad) + y * std::cos(rad));
}
Point2d normalized() const {
static_assert(std::is_floating_point<T_P>::value == true);
return (*this) / this->norm();
}
Point2d conj() const noexcept { return Point2d(x, -y); }
template <class IStream> friend IStream &operator>>(IStream &is, Point2d &p) {
T_P x, y;
is >> x >> y;
p = Point2d(x, y);
return is;
}
template <class OStream> friend OStream &operator<<(OStream &os, const Point2d &p) {
return os << '(' << p.x << ',' << p.y << ')';
}
};
template <> double Point2d<double>::EPS = 1e-9;
template <> long double Point2d<long double>::EPS = 1e-12;
template <> long long Point2d<long long>::EPS = 0;
template <typename T_P>
int ccw(const Point2d<T_P> &a, const Point2d<T_P> &b, const Point2d<T_P> &c) {
// a->b->cの曲がり方
Point2d<T_P> v1 = b - a;
Point2d<T_P> v2 = c - a;
if (v1.det(v2) > Point2d<T_P>::EPS) return 1; // 左折
if (v1.det(v2) < -Point2d<T_P>::EPS) return -1; // 右折
if (v1.dot(v2) < -Point2d<T_P>::EPS) return 2; // c-a-b
if (v1.norm2() < v2.norm2()) return -2; // a-b-c
return 0; // a-c-b
}
// Convex hull （凸包）
// return: IDs of vertices used for convex hull, counterclockwise
// include_boundary: If true, interior angle pi is allowed
template <typename T_P>
std::vector<int> convex_hull(const std::vector<Point2d<T_P>> &ps, bool include_boundary = false) {
int n = ps.size();
if (n <= 1) return std::vector<int>(n, 0);
std::vector<std::pair<Point2d<T_P>, int>> points(n);
for (size_t i = 0; i < ps.size(); i++) points[i] = std::make_pair(ps[i], i);
std::sort(points.begin(), points.end());
int k = 0;
std::vector<std::pair<Point2d<T_P>, int>> qs(2 * n);
auto ccw_check = [&](int c) { return include_boundary ? (c == -1) : (c <= 0); };
for (int i = 0; i < n; i++) {
while (k > 1 and ccw_check(ccw(qs[k - 2].first, qs[k - 1].first, points[i].first))) k--;
qs[k++] = points[i];
}
for (int i = n - 2, t = k; i >= 0; i--) {
while (k > t and ccw_check(ccw(qs[k - 2].first, qs[k - 1].first, points[i].first))) k--;
qs[k++] = points[i];
}
std::vector<int> ret(k - 1);
for (int i = 0; i < k - 1; i++) ret[i] = qs[i].second;
return ret;
}
// Point on grid, sortable by its argument
struct Point {
constexpr static double eps = 1e-2;
long long X, Y;
double theta;
Point() = default;
Point(long long x, long long y) : X(x), Y(y), theta(std::atan2(y, x)) {}
bool operator<(const Point &r) const {
double b = theta - r.theta;
return std::abs(b) > eps ? (b < 0) : (X * r.Y > r.X * Y);
}
bool operator==(const Point &r) const {
return std::abs(theta - r.theta) < eps and X * r.Y == r.X * Y;
}
void rotate_pi() {
theta += M_PI;
X *= -1;
Y *= -1;
}
};
int main() {
const int N = 1000000;
// const int N = 1000;
cout << N << endl;
const lint R = 1000000000;
lint sum = 0, n = 0;
vector<Point> vs;
for (lint y = 1; n * 4 <= 1000000; ++y) {
FOR(e, 1, y) {
if (std::gcd(e, y - e) == 1) vs.emplace_back(e, y - e), sum += y, ++n;
}
}
dbg(make_tuple(n, sum, vs.size()));
vs.resize(N / 4);
sort(vs.begin(), vs.end());
// dbg(vs.front().X);
// dbg(vs.front().Y);
// dbg(vs.back().X);
// dbg(vs.back().Y);
const double pi = acos(-1);
const double r = pi * 2 / N;
vector<Point2d<long long>> xys;
{
lint x = 0, y = -R;
REP(_, 4) {
for (auto &p : vs) {
xys.emplace_back(x, y);
x += p.X;
y += p.Y;
swap(p.X, p.Y);
p.X *= -1;
// p.rotate_pi();
}
}
}
// REP(t, N) {
// double theta = r * t;
// int x = roundl(cos(theta) * R);
// int y = roundl(sin(theta) * R);
// assert(abs(x) <= R);
// assert(abs(y) <= R);
// cout << x << ' ' << y << '\n';
// xys.emplace_back(x, y);
// }
REP(i, N) {
int j = (i + 1) % N;
int k = (i + 2) % N;
int c = ccw(xys.at(i), xys.at(j), xys.at(k));
if (c != 1) {
dbg(make_tuple(i, c, xys.at(i), xys.at(j), xys.at(k)));
exit(1);
}
}
dbg(xys.size());
dbg(convex_hull(xys, false).size());
for (auto p : xys) {
assert(abs(p.x) <= R);
assert(abs(p.y) <= R);
cout << p.x << ' ' << p.y << '\n';
}
cout.flush();
}