結果
| 問題 | No.2602 Real Collider |
| ユーザー |
 tokusakurai
|
| 提出日時 | 2024-01-12 21:57:16 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 40 ms / 2,000 ms |
| コード長 | 18,701 bytes |
| コンパイル時間 | 3,461 ms |
| コンパイル使用メモリ | 224,916 KB |
| 最終ジャッジ日時 | 2025-02-18 18:12:13 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 78 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define per(i, n) for (int i = (n)-1; i >= 0; i--)
#define rep2(i, l, r) for (int i = (l); i < (r); i++)
#define per2(i, l, r) for (int i = (r)-1; i >= (l); i--)
#define each(e, v) for (auto &e : v)
#define MM << " " <<
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using maxheap = priority_queue<T>;
template <typename T>
bool chmax(T &x, const T &y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
bool chmin(T &x, const T &y) {
return (x > y) ? (x = y, true) : false;
}
template <typename T>
int flg(T x, int i) {
return (x >> i) & 1;
}
int pct(int x) { return __builtin_popcount(x); }
int pct(ll x) { return __builtin_popcountll(x); }
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int botbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int botbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
void print(const vector<T> &v, T x = 0) {
int n = v.size();
for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
if (v.empty()) cout << '\n';
}
template <typename T>
void printn(const vector<T> &v, T x = 0) {
int n = v.size();
for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}
template <typename T>
int lb(const vector<T> &v, T x) {
return lower_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, T x) {
return upper_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
void rearrange(vector<T> &v) {
sort(begin(v), end(v));
v.erase(unique(begin(v), end(v)), end(v));
}
template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
int n = v.size();
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
return ret;
}
template <typename T>
void reorder(vector<T> &a, const vector<int> &ord) {
int n = a.size();
vector<T> b(n);
for (int i = 0; i < n; i++) b[i] = a[ord[i]];
swap(a, b);
}
template <typename T>
T floor(T x, T y) {
assert(y != 0);
if (y < 0) x = -x, y = -y;
return (x >= 0 ? x / y : (x - y + 1) / y);
}
template <typename T>
T ceil(T x, T y) {
assert(y != 0);
if (y < 0) x = -x, y = -y;
return (x >= 0 ? (x + y - 1) / y : x / y);
}
template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
return make_pair(p.first + q.first, p.second + q.second);
}
template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
return make_pair(p.first - q.first, p.second - q.second);
}
template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
S a;
T b;
is >> a >> b;
p = make_pair(a, b);
return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
return os << p.first << ' ' << p.second;
}
struct io_setup {
io_setup() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(15);
}
} io_setup;
constexpr int inf = (1 << 30) - 1;
constexpr ll INF = (1LL << 60) - 1;
// constexpr int MOD = 1000000007;
constexpr int MOD = 998244353;
using Real = long double;
using Point = complex<Real>;
const Real EPS = 1e-9; // ここは適宜調節する
const Real pi = acos(-1.0);
int sgn(Real a) { return (a < -EPS) ? -1 : (a > EPS) ? 1 : 0; }
bool eq(Real a, Real b) { return sgn(b - a) == 0; }
Point operator*(const Point &p, const Real &d) { return Point(real(p) * d, imag(p) * d); }
Point operator/(const Point &p, const Real &d) { return p * (1 / d); }
istream &operator>>(istream &is, Point &p) {
ll a, b;
is >> a >> b;
p = Point(a, b);
return is;
}
ostream &operator<<(ostream &os, const Point &p) { return os << real(p) << ' ' << imag(p); }
bool compare_x(const Point &p, const Point &q) {
if (!eq(real(p), real(q))) return real(p) < real(q);
return imag(p) < imag(q);
}
bool compare_y(const Point &p, const Point &q) {
if (!eq(imag(p), imag(q))) return imag(p) < imag(q);
return real(p) < real(q);
}
struct Line {
Point a, b;
Line() {}
Line(Point a, Point b) : a(a), b(b) {}
friend ostream &operator<<(ostream &os, Line &l) { return os << l.a << ' ' << l.b; }
friend istream &operator>>(istream &is, Line &l) { return is >> l.a >> l.b; }
};
struct Segment : Line {
Segment() {}
Segment(Point a, Point b) : Line(a, b) {}
};
struct Circle {
Point p;
Real r;
Circle() {}
Circle(Point p, Real r) : p(p), r(r) {}
};
Point rotate(const Point &p, const Real &t) { return p * Point(cos(t), sin(t)); }
Real dot(const Point &p, const Point &q) { return real(p) * real(q) + imag(p) * imag(q); }
Real det(const Point &p, const Point &q) { return real(p) * imag(q) - imag(p) * real(q); }
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_C&lang=ja
// 線分 ab に対する c の位置関係
int ccw(const Point &a, Point b, Point c) {
b = b - a, c = c - a;
if (sgn(det(b, c)) == 1) return +1; // COUNTER_CLOCKWISE
if (sgn(det(b, c)) == -1) return -1; // CLOCKWISE
if (sgn(dot(b, c)) == -1) return +2; // ONLINE_BACK
if (sgn(norm(c) - norm(b)) == 1) return -2; // ONLINE_FRONT
return 0; // ON_SEGMENT
}
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_A&lang=ja
// 平行判定
bool parallel(const Line &a, const Line &b) { return eq(det(a.b - a.a, b.b - b.a), 0.0); }
// 垂直判定
bool orthogonal(const Line &a, const Line &b) { return eq(dot(a.b - a.a, b.b - b.a), 0.0); }
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_A&lang=ja
// 垂線の足
Point projection(const Line &l, const Point &p) {
Real t = dot(p - l.a, l.b - l.a) / norm(l.b - l.a);
return l.a + (l.b - l.a) * t;
}
Point projection(const Segment &s, const Point &p) {
Real t = dot(p - s.a, s.b - s.a) / norm(s.b - s.a);
return s.a + (s.b - s.a) * t;
}
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_B&lang=ja
// 線対称の位置にある点
Point reflection(const Line &l, const Point &p) { return p + (projection(l, p) - p) * 2.0; }
bool intersect(const Line &l, const Point &p) { return abs(ccw(l.a, l.b, p)) != 1; }
bool intersect(const Segment &s, const Point &p) { return ccw(s.a, s.b, p) == 0; }
bool intersect(const Line &l, const Line &m) {
if (!eq(det(l.b - l.a, m.b - m.a), 0.0)) return true;
return eq(det(l.b - l.a, m.b - l.a), 0.0);
}
bool intersect(const Line &l, const Segment &s) { return sgn(det(l.b - l.a, s.a - l.a) * det(l.b - l.a, s.b - l.a)) <= 0; }
bool intersect(const Segment &s, const Line &l) { return intersect(l, s); }
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_B&lang=ja
bool intersect(const Segment &s, const Segment &t) {
if (ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) > 0) return false;
return ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}
Real distance(const Line &l, const Point &p);
bool intersect(const Circle &c, const Line &l) { return sgn(c.r - distance(l, c.p)) >= 0; }
bool intersect(const Circle &c, const Point &p) { return eq(abs(p - c.p), c.r); }
bool intersect(const Circle &c1, const Circle &c2) {
Real d = abs(c1.p - c2.p);
if (sgn(d - c1.r - c2.r) == 1) return false;
if (sgn(d - abs(c1.r - c2.r)) == -1) return false;
return true;
}
Real distance(const Point &p, const Point &q) { return abs(q - p); }
Real distance2(const Point &p, const Point &q) { return (p.real() - q.real()) * (p.real() - q.real()) + (p.imag() - q.imag()) * (p.imag() - q.imag()); }
Real distance(const Line &l, const Point &p) { return abs(p - Point(projection(l, p))); }
// https://atcoder.jp/contests/arc042/tasks/arc042_b
Real distance(const Segment &s, const Point &p) {
Point h = projection(s, p);
if (intersect(s, h)) return abs(h - p);
return min(abs(s.a - p), abs(s.b - p));
}
Real distance(const Line &l, const Line &m) { return intersect(l, m) ? 0.0 : distance(l, m.a); }
Real distance(const Line &l, const Segment &s) {
if (intersect(l, s)) return 0.0;
return min(distance(l, s.a), distance(l, s.b));
}
Real distance(const Segment &s, const Line &l) { return distance(l, s); }
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_D&lang=ja
Real distance(const Segment &s, const Segment &t) {
if (intersect(s, t)) return 0.0;
return min({distance(s, t.a), distance(s, t.b), distance(t, s.a), distance(t, s.b)});
}
vector<Point> crosspoint(const Line &l, const Line &m) {
if (!intersect(l, m)) return {};
if (parallel(l, m)) return {l.a, l.b};
vector<Point> ret;
Real A = det(l.b - l.a, m.b - m.a);
Real B = det(l.b - l.a, l.b - m.a);
if (eq(A, 0.0) && eq(B, 0.0)) {
ret.push_back(m.a);
} else {
ret.push_back(m.a + (m.b - m.a) * B / A);
}
return ret;
}
// 平行な場合は共通する区間の端点を返す
vector<Point> crosspoint(const Line &l, const Segment &s) {
if (!intersect(l, s)) return {};
if (parallel(l, Line(s))) return {s.a, s.b};
vector<Point> ret, tmp = crosspoint(Line(l), Line(s));
for (auto &p : tmp) {
if (ccw(s.a, s.b, p) == 0) ret.push_back(p);
}
return ret;
}
vector<Point> crosspoint(const Segment &s, const Line &l) { return crosspoint(l, s); }
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_C&lang=ja
vector<Point> crosspoint(const Segment &s, const Segment &t) {
if (!intersect(s, t)) return {};
vector<Point> ret, tmp;
if (parallel(Line(s), Line(t))) {
tmp = {s.a, s.b};
if (sgn(distance(t.a, s.a)) == 1 && sgn(distance(t.a, s.b)) == 1) tmp.push_back(t.a);
if (sgn(distance(t.b, s.a)) == 1 && sgn(distance(t.b, s.b)) == 1) tmp.push_back(t.b);
} else {
tmp = crosspoint(Line(s), Line(t));
}
for (auto &p : tmp) {
if (ccw(s.a, s.b, p) == 0 && ccw(t.a, t.b, p) == 0) ret.push_back(p);
}
return ret;
}
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_D&lang=ja
vector<Point> crosspoint(const Circle &c, const Line &l) {
Point h = projection(l, c.p);
Point e = (l.b - l.a) / abs(l.b - l.a);
vector<Point> ret;
if (!intersect(c, l)) return ret;
if (eq(distance(l, c.p), c.r)) {
ret.push_back(h);
} else {
Real base = sqrt(c.r * c.r - norm(h - c.p));
ret.push_back(h + e * base), ret.push_back(h - e * base);
}
return ret;
}
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_E&lang=ja
vector<Point> crosspoint(const Circle &c1, const Circle &c2) {
Real d = abs(c1.p - c2.p);
Real a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
Real t = atan2(c2.p.imag() - c1.p.imag(), c2.p.real() - c1.p.real());
vector<Point> ret;
if (!intersect(c1, c2)) return ret;
if (eq(a, 0.0)) {
ret.push_back(Point(c1.p + rotate(Point(c1.r, 0.0), t)));
} else {
Point p1 = c1.p + rotate(Point(c1.r, 0.0), t + a);
Point p2 = c1.p + rotate(Point(c1.r, 0.0), t - a);
ret.push_back(p1), ret.push_back(p2);
}
return ret;
}
// 垂直二等分線
Line vertical_bisector(const Point &p, const Point &q) {
Line l;
l.a = (p + q) * 0.5;
l.b = l.a + rotate(q - p, pi * 0.5);
return l;
}
// アポロニウスの円
Circle Apollonius(const Point &p, const Point &q, const Real &a, const Real &b) {
Point p1 = (p * b + q * a) / (a + b), p2 = (-p * b + q * a) / (a - b);
Circle c;
c.p = (p1 + p2) * 0.5;
c.r = abs(p1 - p2) * 0.5;
return c;
}
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_A&lang=ja
Real area(const vector<Point> &p) {
Real ret = 0.0;
int n = p.size();
for (int i = 0; i < n; i++) ret += det(p[i], p[(i + 1) % n]);
return abs(ret * 0.5);
}
// https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_C&lang=ja
// IN:2, ON:1, OUT:0
// 反時計回り、O(n)
int in_polygon(const vector<Point> &p, const Point &q) {
int n = p.size();
int ret = 0;
for (int i = 0; i < n; i++) {
Point a = p[i] - q, b = p[(i + 1) % n] - q;
if (eq(det(a, b), 0.0) && sgn(dot(a, b)) <= 0) return 1;
if (imag(a) > imag(b)) swap(a, b);
if (sgn(imag(a)) <= 0 && sgn(imag(b)) == 1 && sgn(det(a, b)) == 1) ret ^= 2;
}
return ret;
}
// https://atcoder.jp/contests/abc296/tasks/abc296_g
// 反時計回り、凸多角形、O(log(n))
int in_convex_polygon(const vector<Point> &p, const Point &q) {
int n = p.size();
assert(n >= 3);
Real b1 = det(p[1] - p[0], q - p[0]);
Real b2 = det(p[n - 1] - p[0], q - p[0]);
if (sgn(b1) == -1 || sgn(b2) == 1) return 0;
int l = 1, r = n - 1;
while (r - l > 1) {
int m = (l + r) / 2;
(det(p[m] - p[0], q - p[0]) >= 0 ? l : r) = m;
}
Real v = det(p[l] - q, p[r] - q);
return (sgn(v) == 0 ? 1 : sgn(v) == -1 ? 0 : sgn(b1) == 0 || sgn(b2) == 0 ? 1 : 2);
}
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_F&lang=ja
// 点 p を通る円 c の接線と c の接点
vector<Point> tangent(const Circle &c, const Point &p) { return crosspoint(c, Circle(p, sqrt(norm(p - c.p) - c.r * c.r))); }
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_G&lang=ja
// 共通接線
vector<Line> tangent(Circle c1, Circle c2) {
vector<Line> ret;
if (c1.r < c2.r) swap(c1, c2);
Real r = abs(c2.p - c1.p);
if (eq(r, 0.0)) return ret;
Point u = (c2.p - c1.p) / r;
Point v = rotate(u, pi * 0.5);
for (Real s : {1.0, -1.0}) {
Real h = (c1.r + c2.r * s) / r;
if (eq(abs(h), 1.0)) {
ret.emplace_back(c1.p + u * c1.r, c1.p + (u + v) * c1.r);
} else if (abs(h) < 1.0) {
Point uu = u * h, vv = v * sqrt(1.0 - h * h);
ret.emplace_back(c1.p + (uu + vv) * c1.r, c2.p - (uu + vv) * c2.r * s);
ret.emplace_back(c1.p + (uu - vv) * c1.r, c2.p - (uu - vv) * c2.r * s);
}
}
return ret;
}
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_A&lang=ja
// 共通接線の本数
int tangent_num(Circle c1, Circle c2) {
if (c1.r < c2.r) swap(c1, c2);
Real d = abs(c1.p - c2.p);
int a = sgn(d - c1.r - c2.r);
if (a >= 0) return 3 + a;
return 1 + sgn(d - c1.r + c2.r);
}
// 下側凸包
vector<Point> lower_convex_hull(vector<Point> p) {
sort(begin(p), end(p), compare_x);
p.erase(unique(begin(p), end(p)), end(p));
int n = p.size(), k = 0;
if (n == 1) return p;
vector<Point> ch(n);
for (int i = 0; i < n; i++) {
if (k == 1 && eq(real(ch[0]), real(p[i]))) {
if (imag(ch[0]) > imag(p[i])) ch[0] = p[i];
continue;
}
while (k >= 2 && sgn(det(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1])) <= 0) k--;
ch[k++] = p[i];
}
if (k >= 2 && eq(real(ch[k - 1]), real(ch[k - 2]))) k--;
ch.resize(k);
return ch;
}
// 上側凸包
vector<Point> upper_convex_hull(vector<Point> p) {
sort(begin(p), end(p), compare_x);
p.erase(unique(begin(p), end(p)), end(p));
int n = p.size(), k = 0;
if (n == 1) return p;
vector<Point> ch(n);
for (int i = 0; i < n; i++) {
if (k == 1 && eq(real(ch[0]), real(p[i]))) {
if (imag(ch[0]) < imag(p[i])) ch[0] = p[i];
continue;
}
while (k >= 2 && sgn(det(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1])) >= 0) k--;
ch[k++] = p[i];
}
if (k >= 2 && eq(real(ch[k - 1]), real(ch[k - 2]))) k--;
ch.resize(k);
return ch;
}
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_4_A&lang=ja
vector<Point> convex_hull(vector<Point> p) {
sort(begin(p), end(p), compare_x);
p.erase(unique(begin(p), end(p)), end(p));
int n = p.size(), k = 0;
if (n == 1) return p;
vector<Point> ch(2 * n);
for (int i = 0; i < n; ch[k++] = p[i++]) {
while (k >= 2 && sgn(det(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1])) <= 0) k--;
}
for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = p[i--]) {
while (k >= t && sgn(det(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1])) <= 0) k--;
}
ch.resize(k - 1);
return ch;
}
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_5_A&lang=ja
Real closest_pair(vector<Point> p) {
if (p.size() <= 1) return 1e18;
sort(begin(p), end(p), compare_x);
vector<Point> memo(p.size());
function<Real(int, int)> rec = [&](int l, int r) {
if (r - l <= 1) return Real(1e18);
int m = (l + r) >> 1;
Real x = real(p[m]);
Real ret = min(rec(l, m), rec(m, r));
inplace_merge(p.begin() + l, p.begin() + m, p.begin() + r, compare_y);
int cnt = 0;
for (int i = l; i < r; i++) {
if (abs(real(p[i]) - x) >= ret) continue;
for (int j = 0; j < cnt; j++) {
Point d = p[i] - memo[cnt - j - 1];
if (imag(d) >= ret) break;
ret = min(ret, abs(d));
}
memo[cnt++] = p[i];
}
return ret;
};
return rec(0, p.size());
}
void solve() {
int Q;
cin >> Q;
vector<Point> p(3);
rep(i, 3) cin >> p[i];
vector<Real> d(3);
rep(i, 3) d[i] = distance2(p[(i + 1) % 3], p[i]);
int id = -1;
rep(i, 3) {
if (d[i] > d[(i + 1) % 3] + d[(i + 2) % 3]) {
id = i; //
}
}
Point center;
if (id != -1) {
center = (p[id] + p[(id + 1) % 3]) * 0.5;
} else {
Line l1 = vertical_bisector(p[0], p[1]);
Line l2 = vertical_bisector(p[0], p[2]);
center = crosspoint(l1, l2)[0];
}
Real r = 0;
rep(i, 3) chmax(r, distance2(center, p[i]));
// cout << center << endl << r << endl;
while (Q--) {
Point q;
cin >> q;
if (distance2(center, q) <= r + EPS) {
cout << "Yes\n";
} else {
cout << "No\n";
}
}
}
int main() {
int T = 1;
// cin >> T;
while (T--) solve();
}