//#define _CRT_SECURE_NO_WARNINGS
//#include <iostream>
//#include <algorithm>
//#include <cmath>
//#include <cstring>
//#include <cassert>
//#include <vector>
//#include <deque>
//typedef long long ll;
//typedef double ld;
////typedef long double ld;
//const ld INF = 1e17;
//const ld TOL = 1e-15;
//const ld PI = acos(-1);
//const int LEN = 25;
//int N, M, T, Q;
//inline bool zero(const ld& x) { return std::abs(x) <= TOL; }
//inline int sign(const ld& x) { return x < -TOL ? -1 : x > TOL; }
//inline ll sqr(ll x) { return x * x; }
//inline ld norm(ld th) {
// while (th < 0) th += PI * 2;
// while (th > PI * 2 - TOL) th -= PI * 2;
// return th;
//}
//
////#define DEBUG
////#define ASSERT
//struct Pii {
// int x, y;
// Pii(int X = 0, int Y = 0) : x(X), y(Y) {}
// bool operator == (const Pii& p) const { return x == p.x && y == p.y; }
// bool operator != (const Pii& p) const { return x != p.x || y != p.y; }
// bool operator < (const Pii& p) const { return x == p.x ? y < p.y : x < p.x; }
// bool operator <= (const Pii& p) const { return x == p.x ? y <= p.y : x <= p.x; }
// Pii operator + (const Pii& p) const { return { x + p.x, y + p.y }; }
// Pii operator - (const Pii& p) const { return { x - p.x, y - p.y }; }
// Pii operator * (const int& n) const { return { x * n, y * n }; }
// Pii operator / (const int& n) const { return { x / n, y / n }; }
// ll operator * (const Pii& p) const { return { (ll)x * p.x + (ll)y * p.y }; }
// ll operator / (const Pii& p) const { return { (ll)x * p.y - (ll)y * p.x }; }
// Pii& operator += (const Pii& p) { x += p.x; y += p.y; return *this; }
// Pii& operator -= (const Pii& p) { x -= p.x; y -= p.y; return *this; }
// Pii& operator *= (const int& scale) { x *= scale; y *= scale; return *this; }
// Pii& operator /= (const int& scale) { x /= scale; y /= scale; return *this; }
// Pii operator ~ () const { return { -y, x }; }
// Pii operator ! () const { return { -x, -y }; }
// ll xy() const { return (ll)x * y; }
// inline ll Euc() const { return (ll)x * x + (ll)y * y; }
// inline ld rad() const { return atan2(y, x); }
// int Man() const { return std::abs(x) + std::abs(y); }
// ld mag() const { return hypot(x, y); }
// inline friend std::istream& operator >> (std::istream& is, Pii& p) { is >> p.x >> p.y; return is; }
// friend std::ostream& operator << (std::ostream& os, const Pii& p) { os << p.x << " " << p.y; return os; }
//};
//const Pii Oii = { 0, 0 };
//const Pii INF_PT = { (int)INF, (int)INF };
//inline ll cross(const Pii& d1, const Pii& d2, const Pii& d3) { return (d2 - d1) / (d3 - d2); }
//inline ll cross(const Pii& d1, const Pii& d2, const Pii& d3, const Pii& d4) { return (d2 - d1) / (d4 - d3); }
//inline ll dot(const Pii& d1, const Pii& d2, const Pii& d3) { return (d2 - d1) * (d3 - d2); }
//inline ll dot(const Pii& d1, const Pii& d2, const Pii& d3, const Pii& d4) { return (d2 - d1) * (d4 - d3); }
//inline int ccw(const Pii& d1, const Pii& d2, const Pii& d3) {
// ll ret = cross(d1, d2, d3);
// return !ret ? 0 : ret > 0 ? 1 : -1;
//}
//struct Pos {
// ld x, y;
// Pos(ld X = 0, ld Y = 0) : x(X), y(Y) {}
// bool operator == (const Pos& p) const { return zero(x - p.x) && zero(y - p.y); }
// bool operator != (const Pos& p) const { return !zero(x - p.x) || !zero(y - p.y); }
// bool operator < (const Pos& p) const { return zero(x - p.x) ? y < p.y : x < p.x; }
// Pos operator + (const Pos& p) const { return { x + p.x, y + p.y }; }
// Pos operator - (const Pos& p) const { return { x - p.x, y - p.y }; }
// Pos operator * (const ld& scalar) const { return { x * scalar, y * scalar }; }
// Pos operator / (const ld& scalar) const { return { x / scalar, y / scalar }; }
// ld operator * (const Pos& p) const { return x * p.x + y * p.y; }
// ld operator / (const Pos& p) const { return x * p.y - y * p.x; }
// Pos operator ^ (const Pos& p) const { return { x * p.x, y * p.y }; }
// Pos operator - () const { return { -x, -y }; }
// Pos operator ~ () const { return { -y, x }; }
// Pos operator ! () const { return { y, x }; }
// Pos& operator += (const Pos& p) { x += p.x; y += p.y; return *this; }
// Pos& operator -= (const Pos& p) { x -= p.x; y -= p.y; return *this; }
// Pos& operator *= (const ld& scale) { x *= scale; y *= scale; return *this; }
// Pos& operator /= (const ld& scale) { x /= scale; y /= scale; return *this; }
// ld xy() const { return x * y; }
// inline Pos rot(ld the) const { return Pos(x * cos(the) - y * sin(the), x * sin(the) + y * cos(the)); }
// inline ld Euc() const { return x * x + y * y; }
// ld mag() const { return sqrt(Euc()); }
// //ld mag() const { return hypotl(x, y); }
// Pos unit() const { return *this / mag(); }
// inline ld rad() const { return norm(atan2(y, x)); }
// inline friend ld rad(const Pos& p1, const Pos& p2) { return norm(atan2(p1 / p2, p1 * p2)); }
// int quad() const { return sign(y) == 1 || (sign(y) == 0 && sign(x) >= 0); }
// friend bool cmpq(const Pos& a, const Pos& b) { return (a.quad() != b.quad()) ? a.quad() < b.quad() : a / b > 0; }
// bool close(const Pos& p) const { return zero((*this - p).Euc()); }
// friend std::istream& operator >> (std::istream& is, Pos& p) { is >> p.x >> p.y; return is; }
// friend std::ostream& operator << (std::ostream& os, const Pos& p) { os << p.x << " " << p.y; return os; }
//};
//const Pos O = Pos(0, 0);
//typedef std::vector<Pos> Polygon;
//inline ld cross(const Pos& d1, const Pos& d2, const Pos& d3) { return (d2 - d1) / (d3 - d2); }
//inline int ccw(const Pos& d1, const Pos& d2, const Pos& d3) {
// ld ret = cross(d1, d2, d3);
// return zero(ret) ? 0 : ret > 0 ? 1 : -1;
//}
//Pos intersection(const Pos& p1, const Pos& p2, const Pos& q1, const Pos& q2) {
// ld a1 = cross(q1, q2, p1), a2 = -cross(q1, q2, p2);
// return (p1 * a2 + p2 * a1) / (a1 + a2);
//}
//struct Circle {
// Pii c;
// int r;
// Circle(Pii C = Pii(0, 0), int R = 0) : c(C), r(R) {}
// bool operator == (const Circle& C) const { return c == C.c && r == C.r; }
// bool operator != (const Circle& C) const { return !(*this == C); }
// bool operator < (const Circle& q) const {
// ll dist = sqr((ll)r - q.r);
// return r < q.r && dist >= (c - q.c).Euc();
// }
// bool operator > (const Pii& p) const { return r > (c - p).mag(); }
// bool operator >= (const Pii& p) const { return r + TOL > (c - p).mag(); }
// bool operator < (const Pii& p) const { return r < (c - p).mag(); }
// Circle operator + (const Circle& C) const { return { c + C.c, r + C.r }; }
// Circle operator - (const Circle& C) const { return { c - C.c, r - C.r }; }
// ld H(const ld& th) const { return sin(th) * c.x + cos(th) * c.y + r; }//coord trans | check right
// inline ld A() const { return r * r * PI; }
// friend std::istream& operator >> (std::istream& is, Circle& c) { is >> c.c >> c.r; return is; }
// friend std::ostream& operator << (std::ostream& os, const Circle& c) { os << c.c << " " << c.r; return os; }
//};
//inline bool cmpr(const Circle& p, const Circle& q) { return p.r > q.r; }//sort descending order
//typedef std::vector<Circle> Disks;
//struct Arc {
// ld lo, hi;// [lo, hi] - radian range of arc, 0 ~ 2pi
// Arc(ld LO = 0, ld HI = 0) : lo(LO), hi(HI) {}
// bool operator < (const Arc& a) const { return zero(lo - a.lo) ? hi < a.hi : lo < a.lo; }
// inline ld area(const Circle& cen) const { return (hi - lo) * cen.r * cen.r; }
// inline ld green(const Circle& cen) const {
// //Pos LO = -Pos(1, 0).rot(lo) * cen.r / 1;
// //Pos HI = Pos(1, 0).rot(hi) * cen.r / 1;
// //Pos vec = Pos(cen.c.x, cen.c.y);
// //return (area() + vec / (HI + LO)) * .5;
// int x = cen.c.x, y = cen.c.y, r = cen.r;
// ld b = x * r * (sin(hi) - sin(lo));
// ld d = y * r * (cos(lo) - cos(hi));
// return (area(cen) + b + d) * .5;
// }
// friend std::ostream& operator << (std::ostream& os, const Arc& l) { os << l.lo << " " << l.hi; return os; }
//};
//typedef std::vector<Arc> Arcs;
//inline std::vector<Pos> intersection(const Circle& a, const Circle& b) {
// Pii ca = a.c, cb = b.c;
// Pii vec = cb - ca;
// ll ra = a.r, rb = b.r;
// ld distance = vec.mag();
// ld rd = vec.rad();
//
// if (vec.Euc() >= sqr(ra + rb)) return {};
// if (vec.Euc() <= sqr(ra - rb)) return {};
//
// //2nd hyprblc law of cos
// ld X = (ra * ra - rb * rb + vec.Euc()) / (2 * distance * ra);
// //if (X < -1 + TOL || X > 1 - TOL) return {};
// if (X < -1) X = -1;
// if (X > 1) X = 1;
// ld h = acos(X);
// if (zero(h)) return {};
// return { Pos(norm(rd - h), norm(rd + h)) };
//}
//inline ld union_except_x(const int& x, std::vector<Circle>& VC) {
// ld union_area = 0;
// int sz = VC.size();
// std::vector<bool> V(sz, 0);
// for (int i = 0; i < sz; i++) {
// if (i == x || V[i]) continue;
// Circle& disk = VC[i];
// Arcs arcs = {};
// for (int j = 0; j < sz; j++) {
// if (j == x || j == i || V[j]) continue;
// Pii vec = VC[i].c - VC[j].c;
// int ra = VC[i].r, rb = VC[j].r;
// if (vec.Euc() >= sqr(ra + rb)) continue;
// if (vec.Euc() <= sqr(ra - rb) || VC[j] < VC[i] || VC[i] == VC[j]) { V[j] = 1; continue; }
// auto inx = intersection(VC[i], VC[j]);
// if (!inx.size()) continue;
// ld lo = inx[0].x;
// ld hi = inx[0].y;
//
// Arc a1, a2;
// if (lo > hi) {
// a1 = Arc(lo, PI * 2);
// a2 = Arc(0, hi);
// arcs.push_back(a1);
// arcs.push_back(a2);
// }
// else {
// a1 = Arc(lo, hi);
// arcs.push_back(a1);
// }
// }
//
// if (!arcs.size()) {
// union_area += disk.A();
// continue;
// }
//
// std::sort(arcs.begin(), arcs.end());
// arcs.push_back(Arc(2 * PI, 2 * PI));
// ld hi = 0;
// for (const Arc& a : arcs) {
// if (a.lo > hi) union_area += Arc(hi, a.lo).green(disk), hi = a.hi;
// else hi = std::max(hi, a.hi);
// }
// }
// return union_area;
//}
//inline void solve() {
// std::cin.tie(0)->sync_with_stdio(0);
// std::cout.tie(0);
//
// //int ret = 0;
// //std::cin >> N;
// //std::vector<Circle> tmp(N);
// //std::vector<bool> VX(N, 0);
// //for (Circle& c : tmp) std::cin >> c;
// //for (int i = 0; i < N; i++) {//remove
// // if (VX[i]) continue;
// // for (int j = 0; j < N; j++) {
// // //if (i < j && tmp[i] == tmp[j]) V[i] = 1;
// // if (tmp[i] < tmp[j]) VX[i] = 1;
// // if (tmp[j] < tmp[i]) VX[j] = 1;
// // }
// //}
// //Disks VC;
// //for (int i = 0; i < N; i++) {
// // if (!VX[i]) VC.push_back(tmp[i]);
// // if (VX[i]) ret++;
// //}
//
// int ret = 0;
// std::cin >> N;
// Disks VC(N);
// for (Circle& c : VC) std::cin >> c;
// std::sort(VC.begin(), VC.end(), cmpr);
// int sz = VC.size();
// ld U = union_except_x(-1, VC);
// for (int x = 0; x < sz; x++) {
// ld A = union_except_x(x, VC);
// ret += zero(U - A);//no-dabwon
// }
// std::cout << ret << "\n";
//}
//int main() { solve(); return 0; }//boj10900 lonely mdic
//
///*
//
//3
//3 0 4
//-3 0 4
//0 0 2
//
//5
//0 0 1
//1 1 1
//-1 1 1
//-1 -1 1
//1 -1 1
//
//9
//3 0 4
//-3 0 4
//0 0 2
//9 0 4
//6 0 2
//15 0 4
//12 0 2
//21 0 4
//18 0 2
//
//5
//1000 1000 1415
//1000 -1000 1415
//-1000 -1000 1415
//-1000 1000 1415
//0 0 1
//
//5
//1000 1000 1414
//1000 -1000 1414
//-1000 -1000 1414
//-1000 1000 1414
//0 0 1
//
//
//
//*/
#include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>
#include <set>
using namespace std;
typedef long long ll;
typedef double ld;
const ld PI = acos(-1);
const ld TOL = 1e-9;
struct Circle {
int x, y, r;
Circle(int X = 0, int Y = 0, int R = 0) : x(X), y(Y), r(R) {}
};
struct Event {
ld angle;
int type; // -1 for entering, 1 for exiting
int index;
Event(ld a, int t, int i) : angle(a), type(t), index(i) {}
bool operator<(const Event& e) const {
if (abs(angle - e.angle) > TOL)
return angle < e.angle;
return type > e.type; // start events (-1) come before end events (1)
}
};
bool circlesIntersect(const Circle& a, const Circle& b) {
ll dx = a.x - b.x;
ll dy = a.y - b.y;
ll distSq = dx * dx + dy * dy;
ll radSumSq = (ll)(a.r + b.r) * (a.r + b.r);
return distSq < radSumSq;
}
ld calculateUnionArea(const vector<Circle>& circles, int excludeIndex = -1) {
int n = circles.size();
vector<Event> events;
for (int i = 0; i < n; ++i) {
if (i == excludeIndex) continue;
Circle c = circles[i];
events.emplace_back(c.x - c.r, -1, i);
events.emplace_back(c.x + c.r, 1, i);
}
sort(events.begin(), events.end());
set<pair<int, int>> activeCircles;
ld unionArea = 0.0;
ld lastX = 0.0;
for (const auto& event : events) {
ld currentX = event.angle;
if (!activeCircles.empty()) {
ld width = currentX - lastX;
set<pair<int, int>> currentActiveCircles = activeCircles;
vector<pair<int, int>> segments;
for (const auto& circle : currentActiveCircles) {
int i = circle.second;
ld y1 = circles[i].y - sqrt((ld)circles[i].r * circles[i].r - (ld)(currentX - circles[i].x) * (currentX - circles[i].x));
ld y2 = circles[i].y + sqrt((ld)circles[i].r * circles[i].r - (ld)(currentX - circles[i].x) * (currentX - circles[i].x));
segments.emplace_back(y1, y2);
}
sort(segments.begin(), segments.end());
ld currentHeight = 0.0;
ld start = -1e17;
for (const auto& seg : segments) {
if (seg.first > start) {
unionArea += currentHeight * width;
start = seg.first;
currentHeight = seg.second - seg.first;
}
else {
if (seg.second > start) {
currentHeight += seg.second - start;
start = seg.second;
}
}
}
unionArea += currentHeight * width;
}
if (event.type == -1) {
activeCircles.insert({ circles[event.index].y, event.index });
}
else {
activeCircles.erase({ circles[event.index].y, event.index });
}
lastX = currentX;
}
return unionArea;
}
void solve() {
int N;
cin >> N;
vector<Circle> circles(N);
for (int i = 0; i < N; ++i) {
cin >> circles[i].x >> circles[i].y >> circles[i].r;
}
ld totalUnionArea = calculateUnionArea(circles);
int count = 0;
for (int i = 0; i < N; ++i) {
ld unionAreaWithoutCircle = calculateUnionArea(circles, i);
if (abs(totalUnionArea - unionAreaWithoutCircle) < TOL) {
count++;
}
}
cout << count << "\n";
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
solve();
return 0;
}
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Incorrect |
14 ms |
344 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
