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#include <bits/stdc++.h> using namespace std; long long gcd(long long x, long long y) { return (y ? gcd(y, x % y) : x); } long long lcm(long long x, long long y) { return x * (y / gcd(x, y)); } const long double Pi = 3.14159265358979323846; long double distance(long double x, long double y, long double x1, long double y1, long double x2, long double y2) { long double A = x - x1; long double B = y - y1; long double C = x2 - x1; long double D = y2 - y1; long double dot = A * C + B * D; long double len_sq = C * C + D * D; long double param = -1; long double xx, yy; if (len_sq != 0.0) param = dot / len_sq; if (param < 0.0) { xx = x1; yy = y1; } else if (param > 1.0) { xx = x2; yy = y2; } else { xx = x1 + param * C; yy = y1 + param * D; } long double dx = x - xx; long double dy = y - yy; return dx * dx + dy * dy; } int main() { ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); int n, x, y; cin >> n >> x >> y; long double r1 = 1e15, r2 = -100000000000; vector<pair<long double, long double>> a(n + 1); for (int i = 0; i < n; i++) { long long x1, y1; cin >> x1 >> y1; a[i].first = x1 - x; a[i].second = y1 - y; if (i == 0) { a[n].first = x1 - x; a[n].second = y1 - y; } r2 = max(r2, (a[i].first * a[i].first) + (a[i].second * a[i].second)); } for (int i = 1; i < n + 1; i++) { r1 = min(r1, distance(0, 0, a[i - 1].first, a[i - 1].second, a[i].first, a[i].second)); } long double ans = Pi * ((r2 - r1) * 1.0); cout << setprecision(15) << ans << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; inline void in() { freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout); } inline void out() { fclose(stdin); fclose(stdout); } const int MAXN = 100004; const double eps = 1e-7; int N; double px, py; double x[MAXN], y[MAXN]; double xx, yy; double maxi = 0, mini = 1e18; inline double Calc(double x1, double y1, double x2, double y2) { return (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2); } inline void Solve() { double e; double xl, xr, yl, yr; double x1, y1, x2, y2; double d1 = 1.0 / 3.0, d2 = 2.0 / 3.0; for (register int i = 1; i <= N; i++) scanf("%lf%lf", &x[i], &y[i]); x[0] = x[N], y[0] = y[N]; for (register int i = 1; i <= N; i++) { xl = x[i], yl = y[i], xr = x[i - 1], yr = y[i - 1]; while (fabs(xl - xr) + fabs(yl - yr) > eps) { x1 = xl + (xr - xl) * d1, y1 = yl + (yr - yl) * d1; x2 = xl + (xr - xl) * d2, y2 = yl + (yr - yl) * d2; if (Calc(x1, y1, px, py) < Calc(x2, y2, px, py)) xr = x2, yr = y2; else xl = x1, yl = y1; } e = Calc(xl, yl, px, py); maxi = max(e, maxi), mini = min(e, mini); xl = x[i], yl = y[i], xr = x[i - 1], yr = y[i - 1]; while (fabs(xl - xr) + fabs(yl - yr) > eps) { x1 = xl + (xr - xl) * d1, y1 = yl + (yr - yl) * d1; x2 = xl + (xr - xl) * d2, y2 = yl + (yr - yl) * d2; if (Calc(x1, y1, px, py) < Calc(x2, y2, px, py)) xl = x1, yl = y1; else xr = x2, yr = y2; } e = Calc(xl, yl, px, py); maxi = max(e, maxi), mini = min(e, mini); } printf("%.10lf\n", (maxi - mini) * acos(-1)); } int main() { scanf("%d", &N); scanf("%lf%lf", &px, &py); Solve(); return 0; }
#include <bits/stdc++.h> using namespace std; using ld = long double; ld r = 1e50, R = -1; const ld pi = acos(-1); ld sqr(ld x) { return x * x; } struct point { ld x, y; void read() { cin >> x >> y; } point operator-(point& b) { return {x - b.x, y - b.y}; } ld norm() { return sqrt(x * x + y * y); } } o, p[100003]; inline ld det(const point& a, const point& b) { return a.x * b.y - a.y * b.x; } inline ld dot(const point& a, const point& b) { return a.x * b.x + a.y * b.y; } int main() { ios::sync_with_stdio(false); int n; cin >> n; o.read(); for (int i = 0; i < n; ++i) { p[i].read(); R = max(R, (p[i] - o).norm()); } p[n] = *p; for (int i = 0; i < n; ++i) { if (dot(o - p[i], p[i + 1] - p[i]) < 0) r = min(r, (o - p[i]).norm()); else if (dot(o - p[i + 1], p[i] - p[i + 1]) < 0) r = min(r, (o - p[i + 1]).norm()); else r = min(r, abs(det(p[i] - o, p[i + 1] - o) / (p[i] - p[i + 1]).norm())); } cout << setprecision(30) << (R * R - r * r) * pi; }
#include <bits/stdc++.h> using namespace std; struct Point { double x, y, dis; Point() {} Point(double a, double b) { x = a; y = b; } } C[1000005]; double c_x, c_y; int n; double dis(Point a, Point b) { return (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y); } double dis2(Point a, Point b, Point c) { double k1 = dis(a, b), k2 = dis(a, c), k3 = dis(b, c); if (k1 >= k2 + k3) return k2; if (k2 >= k1 + k3) return k1; double d = fabs((b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x)); return d * d / k3; } int main() { cin >> n >> c_x >> c_y; Point p(c_x, c_y); double MAX = 0; double Min = 1e18; for (int i = 0; i < n; i++) { double a, b; cin >> a >> b; C[i].x = a; C[i].y = b; C[i].dis = dis(p, C[i]); if (MAX < dis(p, C[i])) MAX = dis(p, C[i]); if (Min > dis(p, C[i])) Min = dis(p, C[i]); } for (int i = 0; i < n; i++) { if (Min > dis2(p, C[i], C[(i + 1) % n])) Min = dis2(p, C[i], C[(i + 1) % n]); } printf("%.18lf\n", acos(-1) * (MAX - Min)); }
#include <bits/stdc++.h> using namespace std; struct Point { double x, y; int id; } pot[100000], po; int n; double cross(Point p, Point p1, Point p2) { double x1 = p1.x - p.x, y1 = p1.y - p.y; double x2 = p2.x - p.x, y2 = p2.y - p.y; return x1 * y2 - x2 * y1; } double dis2(Point p1, Point p2) { return sqrt(pow(p1.x - p2.x, 2.0) + pow(p1.y - p2.y, 2.0)); } double disptoseg(Point p, Point p1, Point p2) { if (dis2(p1, p2) == 0) return dis2(p, p1); Point t = po; t.y += p1.x - p2.x; t.x += p2.y - p1.y; if (cross(t, p, p1) * cross(t, p, p2) >= 0) { return min(dis2(p, p1), dis2(p, p2)); } return fabs(cross(p, p1, p2)) / dis2(p1, p2); } int main() { cin >> n >> po.x >> po.y; { for (int i = 0; i < n; ++i) { cin >> pot[i].x >> pot[i].y; } pot[n] = pot[0]; double ans = 1e30; double mmax = 0; double tmp; for (int i = 0; i < n; ++i) { tmp = disptoseg(po, pot[i], pot[i + 1]); if (tmp < ans) ans = tmp; tmp = dis2(po, pot[i]); if (tmp > mmax) mmax = tmp; } printf("%.20f\n", ((mmax * mmax) - (ans * ans)) * 3.141592653589793238462643383279502884); } return 0; }
#include <bits/stdc++.h> const long double pi = acos(-1.0); using namespace std; long double distance(long long x1, long long y1, long long x2, long long y2) { return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)); } long double mina(long double a, long double b) { if (a < b) return a; else return b; } long double maxa(long double a, long double b) { if (a > b) return a; else return b; } int main() { long long n; long double x, y; vector<pair<long double, long double>> a; cin >> n >> x >> y; a.resize(n + 1); for (long long i = 1; i <= n; i++) cin >> a[i].first >> a[i].second; a[0] = a[n]; long double max = -1; long double min = 1E18; for (long long i = 0; i < n; i++) { long double d = distance(x, y, a[i].first, a[i].second); if (d > max) max = d; if (d < min) min = d; } for (long long i = 1; i <= n; i++) { long double a1 = a[i].second - a[i - 1].second; long double b1 = a[i - 1].first - a[i].first; long double c1 = -a[i].first * a1 - a[i].second * b1; long double a2 = b1, b2 = -a1, c2 = -x * a2 - y * b2; long double x1 = -(c1 * b2 - c2 * b1) / (a1 * b2 - a2 * b1); long double y1 = -(a1 * c2 - a2 * c1) / (a1 * b2 - a2 * b1); if (x1 >= mina(a[i].first, a[i - 1].first) && (x1 <= maxa(a[i].first, a[i - 1].first)) && (y1 >= mina(a[i].second, a[i - 1].second)) && (y1 <= maxa(a[i].second, a[i - 1].second))) { long double d = sqrt((x - x1) * (x - x1) + (y - y1) * (y - y1)); if (d < min) min = d; } } cout.precision(12); cout << pi * (max * max - min * min); }
#include <bits/stdc++.h> using namespace std; const double PI = acos(-1.0); const double EPS = 1e-6; int n; pair<int, int> p; pair<int, int> pt[100100]; double dist(double x, double y) { return sqrt(x * x + y * y); } double distTo(pair<int, int> a, pair<int, int> b) { double res = dist(p.first - a.first, p.second - a.second); res = min(res, dist(p.first - b.first, p.second - b.second)); double A1 = a.second - b.second; double B1 = b.first - a.first; double C1 = -A1 * a.first - B1 * a.second; double A2 = B1; double B2 = -A1; double C2 = -A2 * p.first - B2 * p.second; double X = (B1 * C2 - B2 * C1) / (A1 * B2 - A2 * B1); double Y = (C1 * A2 - C2 * A1) / (A1 * B2 - A2 * B1); if (X + EPS > min(a.first, b.first) && X - EPS < max(a.first, b.first) && Y + EPS > min(a.second, b.second) && Y - EPS < max(a.second, b.second)) res = min(res, dist(p.first - X, p.second - Y)); return res; } int main() { scanf("%d%d%d", &n, &p.first, &p.second); for (int i = 0; i < n; ++i) { scanf("%d%d", &pt[i].first, &pt[i].second); } double R = -1, r = 1e9; for (int i = 0; i < n; ++i) { R = max(R, dist(p.first - pt[i].first, p.second - pt[i].second)); r = min(r, distTo(pt[i], pt[(i + 1) % n])); } printf("%.20f\n", PI * (R * R - r * r)); return 0; }
#include <bits/stdc++.h> using namespace std; const double INF = 1e308; const int IT = 50; const int N = 100000; double x[N + 1], y[N + 1]; double dist(double x1, double y1, double x2, double y2) { return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)); } double findMin(double x1, double y1, double x2, double y2, double x3, double y3) { double l = 0, r = 1; for (int it = 0; it < IT; it++) { double m1 = l + (r - l) / 3; double m2 = r - (r - l) / 3; if (dist(x1 + m1 * (x2 - x1), y1 + m1 * (y2 - y1), x3, y3) < dist(x1 + m2 * (x2 - x1), y1 + m2 * (y2 - y1), x3, y3)) r = m2; else l = m1; } return dist(x1 + l * (x2 - x1), y1 + l * (y2 - y1), x3, y3); } int main() { int n; double xp, yp; cin >> n >> xp >> yp; double minR = INF, maxR = -INF; for (int i = 0; i < n; i++) cin >> x[i] >> y[i]; x[n] = x[0]; y[n] = y[0]; for (int i = 0; i < n; i++) { minR = min(minR, findMin(x[i], y[i], x[i + 1], y[i + 1], xp, yp)); maxR = max(maxR, dist(x[i], y[i], xp, yp)); } printf("%.10lf\n", M_PI * (maxR * maxR - minR * minR)); return 0; }
#include <bits/stdc++.h> using namespace std; long double EPS = 1e-9; long double pi = acos(-1.0); long double go_rad(long double theta) { return (theta * pi / (180 + 0.0)); } long double go_degree(long double rad) { return rad * (180.0 / pi); } complex<long double> tovec(complex<long double> p1, complex<long double> p2) { complex<long double> ans = {p2.real() - p1.real(), p2.imag() - p1.imag()}; return ans; } long double dot(complex<long double> a, complex<long double> b) { return (a.real() * b.real() + a.imag() * b.imag()); } long double angle(complex<long double> a, complex<long double> o, complex<long double> b) { complex<long double> oa = tovec(o, a), ob = tovec(o, b); cout.precision(9); long double ans = (dot(oa, ob) / (abs(oa) * abs(ob))); if (abs(ans - 1.0) < 1e-9) { ans = 1; } return acos(ans); } long double cross_product(complex<long double> v1, complex<long double> v2) { return (conj(v1) * v2).imag(); int a; cin >> a; long double c1, c2; cin >> c1 >> c2; complex<long double> p = {c1, c2}; vector<complex<long double> > v; for (long long int i = (long long int)(0); i < (long long int)(a); i++) { complex<long double> asd; cin >> c1 >> c2; asd = {c1, c2}; v.push_back(asd); } } long double point_location(complex<long double> p1, complex<long double> p2, complex<long double> p_test) { return cross_product(p_test - p1, p_test - p2); } long double dist(complex<long double> p1, complex<long double> p2) { return (abs(p2 - p1)); } complex<long double> rotate(complex<long double> p, long double theta) { long double rad = go_rad(theta); return complex<long double>(p.real() * cos(rad) - p.imag() * sin(rad), p.real() * sin(rad) + p.imag() * cos(rad)); } long double dist_point_line(complex<long double> s1, complex<long double> s2, complex<long double> p) { return abs(cross_product(s1 - p, s2 - p) / dist(s2, s1)); } int main() { ios_base::sync_with_stdio(0); cin.tie(0); int a; cin >> a; long double c1, c2; cin >> c1 >> c2; complex<long double> p = {c1, c2}; vector<complex<long double> > v; for (long long int i = (long long int)(0); i < (long long int)(a); i++) { complex<long double> asd; cin >> c1 >> c2; asd = {c1, c2}; v.push_back(asd); } v.push_back(v[0]); long double mini = 1e7 + 9, maxi = 0; for (long long int i = (long long int)(0); i < (long long int)((v).size() - 1); i++) { long double a1 = go_degree(angle(p, v[i], v[i + 1])); long double a2 = go_degree(angle(p, v[i + 1], v[i])); long double d1 = dist(v[i], p); long double d2 = dist(v[i + 1], p); mini = min({mini, d1, d2}); maxi = max({maxi, d1, d2}); if (a1 < 90.0 and a2 < 90.0) { long double D = dist_point_line(v[i], v[i + 1], p); mini = min(mini, D); maxi = max(maxi, D); } } long double area = pi * (maxi * maxi - mini * mini); cout.precision(17); cout << fixed; cout << area << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const double eps = 1e-8; const double pi = acos(-1); int cmp(double x) { if (fabs(x) < eps) return 0; if (x > 0) return 1; return -1; } int cmp(double x, double y) { return cmp(x - y); } inline double sqr(double x) { return x * x; } struct point { double x, y; point() {} point(double a, double b) : x(a), y(b) {} friend point operator+(const point &a, const point &b) { return point(a.x + b.x, a.y + b.y); } friend point operator-(const point &a, const point &b) { return point(a.x - b.x, a.y - b.y); } friend bool operator==(const point &a, const point &b) { return cmp(a.x - b.x) == 0 && cmp(a.y - b.y) == 0; } friend bool operator<(const point &a, const point &b) { if (cmp(a.x - b.x) < 0) return true; if (cmp(a.x - b.x) > 0) return false; return cmp(a.y - b.y) < 0; } friend point operator*(const point &a, const double &b) { return point(a.x * b, a.y * b); } friend point operator*(const double &a, const point &b) { return point(a * b.x, a * b.y); } friend point operator/(const point &a, const double &b) { return point(a.x / b, a.y / b); } friend istream &operator>>(istream &fin, point &a) { fin >> a.x >> a.y; return fin; } double norm() { return sqrt(sqr(x) + sqr(y)); } }; double det(const point &a, const point &b) { return a.x * b.y - a.y * b.x; } double dot(const point &a, const point &b) { return a.x * b.x + a.y * b.y; } double dist(const point &a, const point &b) { return (a - b).norm(); } point rorate_point(const point &p, double A) { double tx = p.x, ty = p.y; return point(tx * cos(A) - ty * sin(A), tx * sin(A) + ty * cos(A)); } struct line { point a, b; line(point x, point y) : a(x), b(y) {} }; double dis_point_segment(const point p, const point s, const point t) { if (cmp(dot(p - s, t - s)) < 0) return (p - s).norm(); if (cmp(dot(p - t, s - t)) < 0) return (p - t).norm(); return fabs(det(s - p, t - p) / dist(s, t)); } void PointProjLine(const point p, const point s, const point t, point &cp) { double r = dot((t - s), (p - s)) / dot(t - s, t - s); cp = s + r * (t - s); } bool PointOnSegment(point p, point s, point t) { return cmp(det(p - s, t - s)) == 0 && cmp(dot(p - s, p - t)) <= 0; } bool parallel(line a, line b) { return !cmp(det(a.a - a.b, b.a - b.b)); } bool line_make_point(line a, line b, point &res) { if (parallel(a, b)) return false; double s1 = det(a.a - b.a, b.b - b.a); double s2 = det(a.b - b.a, b.b - b.a); res = (s1 * a.b - s2 * a.a) / (s1 - s2); return true; } double multiply(point sp, point ep, point op) { return ((sp.x - op.x) * (ep.y - op.y) - (ep.x - op.x) * (sp.y - op.y)); } bool intersect(line u, line v) { return ((max(u.a.x, u.b.x) >= min(v.a.x, v.b.x)) && (max(v.a.x, v.b.x) >= min(u.a.x, u.b.x)) && (max(u.a.y, u.b.y) >= min(v.a.y, v.b.y)) && (max(v.a.y, v.b.y) >= min(u.a.y, u.b.y)) && (multiply(v.a, u.b, u.a) * multiply(u.b, v.b, u.a) >= 0) && (multiply(u.a, v.b, v.a) * multiply(v.b, u.b, v.a) >= 0)); } const int maxn = 10001; struct polygon { int n; point a[maxn]; double perimeter() { double sum = 0; a[n] = a[0]; for (int i = 0; i < n; i++) sum += (a[i + 1] - a[i]).norm(); return sum; } double area() { double sum = 0; a[n] = a[0]; for (int i = 0; i < n; i++) sum += det(a[i + 1], a[i]); return sum / 2.; } int Point_In(point t) { int num = 0, i, d1, d2, k; a[n] = a[0]; for (int i = 0; i < n; i++) { if (PointOnSegment(t, a[i], a[i + 1])) return 2; k = cmp(det(a[i + 1] - a[i], t - a[i])); d1 = cmp(a[i].y - t.y); d2 = cmp(a[i + 1].y - t.y); if (k > 0 && d1 <= 0 && d2 > 0) num++; if (k < 0 && d2 <= 0 && d1 > 0) num++; } return num & 1; } }; struct polygon_convex { vector<point> P; polygon_convex(int Size = 0) { P.resize(Size); } }; bool comp_less(const point &a, const point &b) { return cmp(a.x - b.x) < 0 || cmp(a.x - b.x) == 0 && cmp(a.y - b.y) < 0; } polygon_convex convex_hull(vector<point> a) { polygon_convex res(2 * a.size() + 5); sort(a.begin(), a.end(), comp_less); a.erase(unique(a.begin(), a.end()), a.end()); int m = 0; for (int i = 0; i < a.size(); ++i) { while (m > 1 && cmp(det(res.P[m - 1] - res.P[m - 2], a[i] - res.P[m - 2])) <= 0) --m; res.P[m++] = a[i]; } int k = m; for (int i = int(a.size()) - 2; i >= 0; --i) { while (m > k && cmp(det(res.P[m - 1] - res.P[m - 2], a[i] - res.P[m - 2])) <= 0) --m; res.P[m++] = a[i]; } res.P.resize(m); if (a.size() > 1) res.P.resize(m - 1); return res; } int containOlogn(const polygon_convex &a, const point &b) { int n = a.P.size(); point g = (a.P[0] + a.P[n / 3] + a.P[2 * n / 3]) / 3.0; int l = 0, r = n; while (l + 1 < r) { int mid = (l + r) / 2; if (cmp(det(a.P[l] - g, a.P[mid] - g)) > 0) { if (cmp(det(a.P[l] - g, b - g)) >= 0 && cmp(det(a.P[mid] - g, b - g)) < 0) r = mid; else l = mid; } else { if (cmp(det(a.P[l] - g, b - g)) < 0 && cmp(det(a.P[mid] - g, b - g)) >= 0) l = mid; else r = mid; } } r %= n; int z = cmp(det(a.P[r] - b, a.P[l] - b)) - 1; if (z == -2) return 1; return z; } bool containOn(const polygon_convex &a, const point &b) { int n = a.P.size(); int sign = 0; for (int i = 0; i < n; ++i) { int x = cmp(det(a.P[i] - b, a.P[((i + 1) % n)] - b)); if (x) { if (sign) { if (sign != x) return false; } else sign = x; } } return true; } bool inaline(line a, line b) { if (!parallel(a, b)) return false; if (cmp(det(a.a - a.b, a.a - b.a)) == 0) return true; return false; } const double INF = 10000; double arg(const point &p) { return atan2(p.y, p.x); } inline double satisfy(point a, pair<point, point> p) { return cmp(det(a - p.first, p.second - p.first)) <= 0; } point crosspoint(const pair<point, point> &a, const pair<point, point> &b) { double k = det(b.first - b.second, a.first - b.second); k = k / (k - det(b.first - b.second, a.second - b.second)); return a.first + (a.second - a.first) * k; } bool cmpp(const pair<point, point> &a, const pair<point, point> &b) { int res = cmp(arg(a.second - a.first) - arg(b.second - b.first)); return res == 0 ? satisfy(a.first, b) : res < 0; } vector<point> HalfplaneIntersection(vector<pair<point, point> > v) { sort(v.begin(), v.end(), cmpp); deque<pair<point, point> > q; deque<point> ans; q.push_back(v[0]); for (int i = 1; i < v.size(); ++i) { if (cmp(arg(v[i].second - v[i].first) - arg(v[i - 1].second - v[i - 1].first)) == 0) { continue; } while (ans.size() > 0 && !satisfy(ans.back(), v[i])) { ans.pop_back(); q.pop_back(); } while (ans.size() > 0 && !satisfy(ans.front(), v[i])) { ans.pop_front(); q.pop_front(); } ans.push_back(crosspoint(q.back(), v[i])); q.push_back(v[i]); } while (ans.size() > 0 && !satisfy(ans.back(), q.front())) { ans.pop_back(); q.pop_back(); } while (ans.size() > 0 && !satisfy(ans.front(), q.back())) { ans.pop_front(); q.pop_front(); } ans.push_back(crosspoint(q.back(), q.front())); return vector<point>(ans.begin(), ans.end()); } vector<point> convexIntersection(vector<point> v1, vector<point> v2) { vector<pair<point, point> > h; for (int i = 0; i < v1.size(); ++i) h.push_back(pair<point, point>(v1[i], v1[(i + 1) % v1.size()])); for (int i = 0; i < v2.size(); ++i) h.push_back(pair<point, point>(v2[i], v2[(i + 1) % v2.size()])); return HalfplaneIntersection(h); } int n; point o, x; int main() { double mmax = 0, mmin = 1e9; cin >> n >> o; vector<point> v; for (int i = 0; i < n; ++i) { cin >> x; mmax = max(dist(x, o), mmax); mmin = min(dist(x, o), mmin); v.push_back(x); } v.push_back(*v.begin()); for (int i = 0; i < v.size() - 1; ++i) { point cp; PointProjLine(o, v[i], v[i + 1], cp); if (PointOnSegment(cp, v[i], v[i + 1])) mmin = min(mmin, dis_point_segment(o, v[i], v[i + 1])); } printf("%.10f\n", (sqr(mmax) - sqr(mmin)) * pi); }
#include <bits/stdc++.h> using namespace std; long double INF = 1e18; const int N = 1e5 + 1; long double PI = 2 * acos(0); long double EPS = 1e-7; complex<long double> v[N]; long double dot(complex<long double> u, complex<long double> v) { return u.real() * v.real() + u.imag() * v.imag(); } void get_line(complex<long double> p1, complex<long double> p2, long double &a, long double &b, long double &c) { a = p2.imag() - p1.imag(); b = p1.real() - p2.real(); c = p1.imag() * p2.real() - p2.imag() * p1.real(); } complex<long double> intersect(long double a, long double b, long double c, long double e, long double f, long double g) { return complex<long double>(-(b * g - c * f) / (b * e - a * f), -(a * g - c * e) / (a * f - b * e)); } bool is_inside(complex<long double> p, complex<long double> l1, complex<long double> l2) { long double a, b, c, e, f, g, m; m = (l2.imag() - l1.imag()) / (l2.real() - l1.real()); m = -1 / m; get_line(l1, l2, a, b, c); get_line(p, p + (l2.imag() == l1.imag() ? complex<long double>(0, 1) : (l2.real() == l1.real() ? complex<long double>(1, 0) : complex<long double>(1, m))), e, f, g); complex<long double> p2 = intersect(a, b, c, e, f, g); long double d, d1, d2; d = sqrt(dot(l2 - l1, l2 - l1)); d1 = sqrt(dot(p2 - l1, p2 - l1)); d2 = sqrt(dot(p2 - l2, p2 - l2)); return abs(d1 + d2 - d) < EPS; } long double dist(long double x, long double y, complex<long double> l1, complex<long double> l2) { long double a, b, c; get_line(l1, l2, a, b, c); return abs(a * x + b * y + c) / sqrt(a * a + b * b); } int main() { ios::sync_with_stdio(0); int n; long double px, py; while (cin >> n >> px >> py) { complex<long double> p = complex<long double>(px, py); long double r, rr; r = INF; rr = 0; for (int i = 0; i < n; i++) { long double x, y; cin >> x >> y; v[i] = complex<long double>(x, y); long double d; d = sqrt(dot(p - v[i], p - v[i])); r = min(r, d); rr = max(rr, d); } v[n] = v[0]; for (int i = 0; i < n; i++) { long double d = dist(px, py, v[i], v[i + 1]); if (is_inside(p, v[i], v[i + 1])) r = min(r, d); } cout << setprecision(13) << fixed << PI * (rr * rr - r * r) << "\n\n"; } }
#include <bits/stdc++.h> using namespace std; struct p { double x, y; } a[100005]; double x, y; int main() { int n; while (~scanf("%d%lf%lf", &n, &x, &y)) { double r = 1000000000, R = 0; for (int i = 1; i <= n; i++) { scanf("%lf%lf", &a[i].x, &a[i].y); r = min(r, sqrt((a[i].x - x) * (a[i].x - x) + (a[i].y - y) * (a[i].y - y))); R = max(R, sqrt((a[i].x - x) * (a[i].x - x) + (a[i].y - y) * (a[i].y - y))); } a[0].x = a[n].x, a[0].y = a[n].y; for (int i = 1; i <= n; i++) { if ((a[i - 1].x - a[i].x) * (x - a[i].x) + (a[i - 1].y - a[i].y) * (y - a[i].y) <= 0) continue; if ((a[i].x - a[i - 1].x) * (x - a[i - 1].x) + (a[i].y - a[i - 1].y) * (y - a[i - 1].y) <= 0) continue; double k, k2; k = sqrt((a[i].x - a[i - 1].x) * (a[i].x - a[i - 1].x) + (a[i].y - a[i - 1].y) * (a[i].y - a[i - 1].y)); k2 = (a[i - 1].x - x) * (a[i].y - y) - (a[i - 1].y - y) * (a[i].x - x); k2 = fabs(k2); r = min(r, k2 / k); } printf("%.15lf\n", (R * R - r * r) * acos(-1.0)); } return 0; }
#include <bits/stdc++.h> using namespace std; const long double PI = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481; int n, i; long double CAN, xp, yp, MN, MX, big, small; long double x[1001000], y[1001000]; bool good_triangle(long double x1, long double fdkjfsdkfs, long double x2, long double y2, long double x3, long double y3) { long double A = (x2 - x3) * (x2 - x3) + (y2 - y3) * (y2 - y3); long double B = (x1 - x2) * (x1 - x2) + (fdkjfsdkfs - y2) * (fdkjfsdkfs - y2); long double C = (x1 - x3) * (x1 - x3) + (fdkjfsdkfs - y3) * (fdkjfsdkfs - y3); return (A + B >= C && A + C >= B); } long double prod(long double x1, long double fdkjfsdkfs, long double x2, long double y2) { long double ret = x1 * y2 - fdkjfsdkfs * x2; if (ret < 0) ret = -ret; return ret; } int main() { ios_base::sync_with_stdio(0); cout.precision(10); cin >> n >> xp >> yp; for (int i = 1; i <= n; i++) cin >> x[i] >> y[i]; MX = -9e18; MN = 9e18; for (int i = 1; i <= n; i++) { MX = max(MX, hypot(x[i] - xp, y[i] - yp)); MN = min(MN, hypot(x[i] - xp, y[i] - yp)); } big = PI * MX * MX; x[0] = x[n]; y[0] = y[n]; x[n + 1] = x[1]; y[n + 1] = y[1]; for (int i = 1; i <= n; i++) { if (good_triangle(xp, yp, x[i], y[i], x[i + 1], y[i + 1])) { x[i] -= xp; y[i] -= yp; x[i + 1] -= xp; y[i + 1] -= yp; CAN = prod(x[i], y[i], x[i + 1], y[i + 1]) / hypot(x[i] - x[i + 1], y[i] - y[i + 1]); x[i] += xp; y[i] += yp; x[i + 1] += xp; y[i + 1] += yp; MN = min(MN, CAN); } } small = PI * MN * MN; cout << fixed << big - small << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int MAX = 1e5 + 9; int n; long double x[MAX], y[MAX], ma = 0, mi = 1e17, xx, yy; long double dis(long double x1, long double y1, long double x2 = xx, long double y2 = yy) { return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)); } long double f(long double x1, long double y1, long double x2, long double y2) { for (int i = 0; i < 60; i++) { long double mx1 = (x2 - x1) / 3.0 + x1, mx2 = (x2 - x1) / 3.0 * 2 + x1, my1 = (y2 - y1) / 3.0 + y1, my2 = (y2 - y1) / 3.0 * 2 + y1; if (dis(mx1, my1) < dis(mx2, my2)) x2 = mx2, y2 = my2; else x1 = mx1, y1 = my1; } return dis(x1, y1); } int main() { ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0); cin >> n >> xx >> yy; for (int i = 0; i < n; i++) { cin >> x[i] >> y[i], ma = max(ma, dis(x[i], y[i], xx, yy)); if (i) mi = min(mi, f(x[i], y[i], x[i - 1], y[i - 1])); } mi = min(mi, f(x[n - 1], y[n - 1], x[0], y[0])); cout << fixed << setprecision(9) << (ma * ma - mi * mi) * acos(0) * 2; }
#include <bits/stdc++.h> using namespace std; long double ax[100010], by[100010]; long double x, y; int n; long double calc(long double t, int it) { long double xx = ax[it] * t + ax[it - 1] * (1 - t); long double yy = by[it] * t + by[it - 1] * (1 - t); return xx * xx + yy * yy; } long double dist(int it) { long double cur = ax[it] * ax[it] + by[it] * by[it]; if (it) { it--; cur = min(cur, ax[it] * ax[it] + by[it] * by[it]); ++it; } else return cur; long double l = 0.0, r = 1.0; int IT = 50; while (IT--) { double m1 = l + (r - l) / 3.0; double m2 = l + 2.0 / 3.0 * (r - l); if (calc(m1, it) > calc(m2, it)) { l = m1; } else r = m2; } return min(calc(l, it), cur); } int main() { ios::sync_with_stdio(0); cin.tie(0); cout.setf(ios::fixed); cout.precision(10); cin >> n; cin >> x >> y; long double mind = 1e18, maxd = 0; for (int i = 0; i < n; ++i) { long double a, b; cin >> a >> b; ax[i] = (a -= x); by[i] = (b -= y); mind = min(mind, dist(i)); maxd = max(maxd, a * a + b * b); } ax[n] = ax[0]; by[n] = by[0]; mind = min(mind, dist(n)); cout << 4 * atan(1) * (maxd - mind) << endl; }
#include <bits/stdc++.h> using namespace std; struct node { double x; double y; } arr[1001000]; int n; double MAX = 0, MIN = 100000000; double dis(node a, node b) { double x = a.x - b.x; double y = a.y - b.y; return sqrt(x * x + y * y); } int main() { cin >> n >> arr[0].x >> arr[0].y; for (int i = 1; i <= n; i++) { cin >> arr[i].x >> arr[i].y; } for (int i = 1; i <= n; i++) { MAX = max(MAX, dis(arr[0], arr[i])); } arr[n + 1] = arr[1]; for (int i = 1; i <= n; i++) { double bian1 = dis(arr[i], arr[0]); double bian2 = dis(arr[i + 1], arr[0]); double bian3 = dis(arr[i], arr[i + 1]); if (bian1 * bian1 >= bian2 * bian2 + bian3 * bian3) MIN = min(MIN, bian2); else if (bian2 * bian2 >= bian1 * bian1 + bian3 * bian3) MIN = min(MIN, bian1); else { double p = (bian1 + bian2 + bian3) / 2.0; double s = sqrt(p * (p - bian1) * (p - bian2) * (p - bian3)); double h = 2 * s / bian3; MIN = min(MIN, h); } } double ans = ((MAX * MAX) - (MIN * MIN)) * acos(-1.0); printf("%.7lf", ans); return 0; }
#include <bits/stdc++.h> using namespace std; const double PI = acos(-1.0); long long n, a, b, x[100010], y[100010]; int main() { ios::sync_with_stdio(0); cin >> n >> a >> b; double mn = 1e18, mx = 0; for (int i = 0; i < n; i++) { cin >> x[i] >> y[i]; double dx = x[i] - a; double dy = y[i] - b; double d = dx * dx + dy * dy; mn = min(mn, d); mx = max(mx, d); } x[n] = x[0]; y[n] = y[0]; for (int i = 0; i < n; i++) { if (x[i + 1] == x[i] && y[i + 1] == y[i]) continue; double dx = x[i + 1] - x[i]; double dy = y[i + 1] - y[i]; double da = a - x[i]; double db = b - y[i]; double da2 = a - x[i + 1]; double db2 = b - y[i + 1]; double dot1 = dx * da + dy * db; double dot2 = dx * da2 + dy * db2; if (dot1 < 0 || dot2 > 0) continue; double cross = dx * db - dy * da; double d = abs(cross) / hypot(dx, dy); mn = min(mn, d * d); } cout << fixed << setprecision(15) << (mx - mn) * PI << '\n'; }
#include <bits/stdc++.h> using namespace std; template <class T> int size(const T &x) { return x.size(); } const int INF = 2147483647; const double EPS = 1e-9; const double pi = acos(-1.0); double dot(const complex<double> &a, const complex<double> &b) { return real(conj(a) * b); } double cross(const complex<double> &a, const complex<double> &b) { return imag(conj(a) * b); } complex<double> rotate(const complex<double> &p, double radians = pi / 2, const complex<double> &about = complex<double>(0, 0)) { return (p - about) * exp(complex<double>(0, radians)) + about; } complex<double> reflect(const complex<double> &p, const complex<double> &about1, const complex<double> &about2) { complex<double> z = p - about1, w = about2 - about1; return conj(z / w) * w + about1; } complex<double> proj(const complex<double> &u, const complex<double> &v) { return dot(u, v) / dot(u, u) * u; } complex<double> normalize(const complex<double> &p, double k = 1.0) { return abs(p) == 0 ? complex<double>(0, 0) : p / abs(p) * k; } double ccw(const complex<double> &a, const complex<double> &b, const complex<double> &c) { return cross(b - a, c - b); } bool collinear(const complex<double> &a, const complex<double> &b, const complex<double> &c) { return abs(ccw(a, b, c)) < EPS; } double angle(const complex<double> &a, const complex<double> &b, const complex<double> &c) { return acos(dot(b - a, c - b) / abs(b - a) / abs(c - b)); } double signed_angle(const complex<double> &a, const complex<double> &b, const complex<double> &c) { return asin(cross(b - a, c - b) / abs(b - a) / abs(c - b)); } double angle(const complex<double> &p) { return atan2(imag(p), real(p)); } complex<double> perp(const complex<double> &p) { return complex<double>(-imag(p), real(p)); } double progress(const complex<double> &p, const complex<double> &a, const complex<double> &b) { if (abs(real(a) - real(b)) < EPS) return (imag(p) - imag(a)) / (imag(b) - imag(a)); else return (real(p) - real(a)) / (real(b) - real(a)); } double polygon_area_signed(vector<complex<double> > p) { double area = 0; int cnt = size(p); for (__typeof(1) i = (1); i < (cnt - 1); ++i) area += cross(p[i] - p[0], p[i + 1] - p[0]); return area / 2; } double polygon_area(vector<complex<double> > p) { return abs(polygon_area_signed(p)); } int point_in_polygon(vector<complex<double> > p, complex<double> q) { int n = size(p); bool in = false; double d; for (int i = 0, j = n - 1; i < n; j = i++) if (collinear(p[i], q, p[j]) && 0 <= (d = progress(q, p[i], p[j])) && d <= 1) return 0; for (int i = 0, j = n - 1; i < n; j = i++) if ((real(p[i]) < real(q) && real(q) <= real(p[j]) && ccw(p[i], p[j], q) < 0) || (real(p[j]) < real(q) && real(q) <= real(p[i]) && ccw(p[j], p[i], q) < 0)) in = !in; return in ? -1 : 1; } bool collinear(const complex<double> &a, const complex<double> &b, const complex<double> &p, const complex<double> &q) { return abs(ccw(a, b, p)) < EPS && abs(ccw(a, b, q)) < EPS; } bool parallel(const complex<double> &a, const complex<double> &b, const complex<double> &p, const complex<double> &q) { return abs(cross(b - a, q - p)) < EPS; } complex<double> closest_point(const complex<double> &a, const complex<double> &b, const complex<double> &c, bool segment = false) { if (segment) { if (dot(b - a, c - b) > 0) return b; if (dot(a - b, c - a) > 0) return a; } double t = dot(c - a, b - a) / norm(b - a); return a + t * (b - a); } double line_segment_distance(const complex<double> &a, const complex<double> &b, const complex<double> &c, const complex<double> &d) { double x = INFINITY; if (abs(a - b) < EPS && abs(c - d) < EPS) x = abs(a - c); else if (abs(a - b) < EPS) x = abs(a - closest_point(c, d, a, true)); else if (abs(c - d) < EPS) x = abs(c - closest_point(a, b, c, true)); else if ((ccw(a, b, c) < 0) != (ccw(a, b, d) < 0) && (ccw(c, d, a) < 0) != (ccw(c, d, b) < 0)) x = 0; else { x = min(x, abs(a - closest_point(c, d, a, true))); x = min(x, abs(b - closest_point(c, d, b, true))); x = min(x, abs(c - closest_point(a, b, c, true))); x = min(x, abs(d - closest_point(a, b, d, true))); } return x; } bool intersect(const complex<double> &a, const complex<double> &b, const complex<double> &p, const complex<double> &q, complex<double> &res, bool segment = false) { complex<double> r = b - a, s = q - p; double c = cross(r, s), t = cross(p - a, s) / c, u = cross(p - a, r) / c; if (segment && (t < 0 - EPS || t > 1 + EPS || u < 0 - EPS || u > 1 + EPS)) return false; res = a + t * r; return true; } double area(double r) { return r * r * pi; } int main() { int n; double x, y; scanf("%d %lf %lf\n", &n, &x, &y); complex<double> mid(x, y); vector<complex<double> > P; for (__typeof(0) i = (0); i < (n); ++i) { double a, b; scanf("%lf %lf", &a, &b); P.push_back(complex<double>(a, b)); } double mx = 0, mn = INFINITY; for (__typeof(0) i = (0); i < (n); ++i) { int j = (i + 1) % n; mx = max(mx, abs(P[i] - mid)); complex<double> c = closest_point(P[i], P[j], mid, true); mn = min(mn, abs(c - mid)); } printf("%0.10lf\n", area(mx) - area(mn)); return 0; }
#include <bits/stdc++.h> using namespace std; template <class T> T Bitcnt(T a) { int sum = 0; while (a) { if (a & 1) sum++; a /= 2; } return sum; } template <class T> T Max3(T a, T b, T c) { return max(a, max(b, c)); } template <class T> T Lcm(T a, T b) { T tmp = __gcd(a, b); return (a / tmp) * b; } template <class T> T Pow(T a, T b) { T ans = 1; T base = a; while (b) { if (b & 1) ans = (ans * base); base = (base * base); b /= 2; } return ans; } long long Bigmod(long long a, long long b) { long long res = 1; long long pw = a % 1000000007LL; while (b > 0) { if (b & 1) res = (res * pw) % 1000000007LL; pw = (pw * pw) % 1000000007LL; b /= 2; } return res; } int a_x[] = {1, -1, 0, 0}; int a_y[] = {0, 0, 1, -1}; long long X, Y; void extend_euclid(long long a, long long b) { if (b == 0) { X = a; Y = 0; return; } extend_euclid(b, a % b); long long x, y; x = Y; y = X - (a / b) * Y; X = x; Y = y; } long long inverse_modulo(long long a, long long b) { extend_euclid(a, b); return (X + 1000000007LL) % 1000000007LL; } double dist(double x1, double y1, pair<double, double> tmp) { double t = 1LL * (x1 - tmp.first) * (x1 - tmp.first) + 1LL * (y1 - tmp.second) * (y1 - tmp.second); return (t); } int n; pair<int, int> inp[200005]; double dist1(int indx1, int indx2, int x, int y) { double lx, ly, rx, ry, ltx, lty, rtx, rty; lx = inp[indx1].first; ly = inp[indx1].second; rx = inp[indx2].first; ry = inp[indx2].second; int tot = 100; double ans = (long long)1e18; while (tot--) { ltx = (lx * 2 + rx) / 3.0; lty = (ly * 2 + ry) / 3.0; rtx = (lx + rx * 2) / 3.0; rty = (ly + ry * 2) / 3.0; if (dist(ltx, lty, make_pair(x, y)) - dist(rtx, rty, make_pair(x, y)) < 1e-13) { rx = rtx; ry = rty; ans = min(ans, dist(ltx, lty, make_pair(x * 1.0, y * 1.0))); } else { lx = ltx; ly = lty; ans = min(ans, dist(rtx, rty, make_pair(x * 1.0, y * 1.0))); } } return ans; } double dist2(int indx1, int indx2, int x, int y) { double lx, ly, rx, ry, ltx, lty, rtx, rty; lx = inp[indx1].first; ly = inp[indx1].second; rx = inp[indx2].first; ry = inp[indx2].second; int tot = 100; double ans = 0.0; while (tot--) { ltx = (lx * 2 + rx) / 3.0; lty = (ly * 2 + ry) / 3.0; rtx = (lx + rx * 2) / 3.0; rty = (ly + ry * 2) / 3.0; if (dist(ltx, lty, make_pair(x, y)) - dist(rtx, rty, make_pair(x, y)) > 1e-13) { rx = rtx; ry = rty; ans = max(ans, dist(ltx, lty, make_pair(x * 1.0, y * 1.0))); } else { lx = ltx; ly = lty; ans = max(ans, dist(rtx, rty, make_pair(x * 1.0, y * 1.0))); } } return ans; } int main() { int n; scanf("%d", &n); double mx = 0.0; double mn = (long long)1e18; int x, y; scanf("%d %d", &x, &y); for (int i = 0; i <= n - 1; i++) { int a, b; scanf("%d %d", &a, &b); inp[i] = make_pair(a, b); } for (int i = 0; i <= n - 1; i++) { int f = i; int s = (i + 1) % n; double res = dist1(f, s, x, y); mn = min(res, mn); res = dist2(f, s, x, y); mx = max(res, mx); } double ans; ans = acos(-1.0) * (mx - mn); printf("%.12lf\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; class dot { public: dot() { x = 0; y = 0; } dot(long long x, long long y) { this->x = x; this->y = y; } long long x; long long y; }; long double dist(dot dot1, dot dot2) { return std::sqrt((long double)((dot1.x - dot2.x) * (dot1.x - dot2.x) + (dot1.y - dot2.y) * (dot1.y - dot2.y))); } long double scalar_mul(dot a, dot b, dot p) { return (b.x - a.x) * (p.x - a.x) + (b.y - a.y) * (p.y - a.y); } long double dot_segment_dist(dot p, dot a, dot b) { long long aa = b.y - a.y, bb = a.x - b.x, cc = a.y * b.x - a.x * b.y; if (scalar_mul(a, b, p) > 0 && scalar_mul(b, a, p) > 0) { return std::abs((aa * p.x + bb * p.y + cc)) / std::sqrt(aa * aa + bb * bb); } else { return min(dist(a, p), dist(b, p)); } } int main() { ios_base::sync_with_stdio(false); int n; dot p; cin >> n >> p.x >> p.y; dot fst; cin >> fst.x >> fst.y; long double mmax = dist(fst, p); long double mmin = dist(fst, p); dot prev = fst, tmp; for (int i = 1; i < n; i++) { cin >> tmp.x >> tmp.y; mmax = max(mmax, dist(tmp, p)); mmin = min(mmin, dot_segment_dist(p, prev, tmp)); prev = tmp; } mmin = min(mmin, dot_segment_dist(p, fst, tmp)); long double sq = (3.14159265358979323846) * (mmax * mmax - mmin * mmin); cout << fixed << setprecision(10); cout << sq << endl; return 0; }
#include <bits/stdc++.h> using namespace std; int N, PX, PY, prevX, prevY, X, Y, firstX, firstY; double valMin = 1e20, valMax = -1; double dist(double x1, double y1, double x2, double y2) { return (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2); } double dist2(double x1, double y1, double x2, double y2) { double m, A, B, C; m = (double)(y1 - y2) / (x1 - x2); if (abs(m) == INFINITY) { B = 0; A = 1; C = -x1; } else { B = 1, A = -m, C = -y1 + m * x1; } double interX = (B * (B * PX - A * PY) - A * C) / (A * A + B * B); double interY = (A * (-B * PX + A * PY) - B * C) / (A * A + B * B); if (interX - max(x1, x2) <= 1e-9 && interX - min(x1, x2) >= -1e-9 && interY - max(y1, y2) <= 1e-9 && interY - min(y1, y2) >= -1e-9) { return pow(abs(A * PX + B * PY + C) / sqrt(A * A + B * B), 2); } return 1e20; } int main() { scanf("%d%d%d", &N, &PX, &PY); scanf("%d%d", &firstX, &firstY); prevX = firstX, prevY = firstY; valMin = dist(prevX, prevY, PX, PY); valMax = valMin; N--; while (N--) { scanf("%d%d", &X, &Y); valMax = max(valMax, dist(X, Y, PX, PY)); valMin = min(valMin, dist(X, Y, PX, PY)); valMin = min(valMin, dist2(X, Y, prevX, prevY)); prevX = X, prevY = Y; } valMin = min(valMin, dist2(firstX, firstY, X, Y)); printf("%.8lf\n", 3.141592653589793238446264338327950288419716939937510582 * (valMax - valMin)); return 0; }
#include <bits/stdc++.h> using namespace std; using point = complex<long long>; long long cross(point a, point b) { return a.real() * b.imag() - a.imag() * b.real(); } long long dot(point a, point b) { return a.real() * b.real() + a.imag() * b.imag(); } int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(8); int n, px, py; cin >> n >> px >> py; point p = point(px, py); double maxi = 0.0, mini = HUGE_VAL; vector<point> polygon(n); for (auto &v : polygon) { int x, y; cin >> x >> y; v = point(x, y); maxi = max(maxi, M_PI * norm(v - p)); } for (int i = 0; i < n; ++i) { int j = (i + 1) % n; point a = polygon[i], b = polygon[j]; point v = a - b; if ((dot(v, a) < dot(v, p)) == (dot(v, p) < dot(v, b))) { mini = min(mini, M_PI * cross(v, p - b) * cross(v, p - b) / norm(v)); } else { mini = min(mini, M_PI * min(norm(a - p), norm(b - p))); } } cout << maxi - mini << "\n"; }
#include <bits/stdc++.h> using namespace std; const double eps = 1e-10; const int inf = 0x3f3f3f3f; const double pi = acos(-1); const int mod = 100000000; double max(double a, double b) { return a > b ? a : b; }; double min(double a, double b) { return a < b ? a : b; }; const int max_ = 100000; struct Point { double x, y; Point(double xx, double yy) : x(xx), y(yy) {} Point(){}; } p[max_ + 5]; Point o; Point operator-(Point a, Point c) { return Point(a.x - c.x, a.y - c.y); } int n; double Dot(Point a, Point b) { return a.x * b.x + a.y * b.y; } double dist(Point a, Point b) { return sqrt(Dot(a - b, a - b)); } double Cross(Point a, Point b) { return fabs(a.x * b.y - b.x * a.y); } double Pointtoline(Point o, Point a, Point b) { return Cross(o - a, b - a) / dist(a, b); } double Pointtosegment(Point o, Point a, Point b) { if (Dot(o - a, b - a) < 0) return dist(o, a); else if (Dot(o - b, a - b) < 0) return dist(o, b); else return Pointtoline(o, a, b); } int main() { while (~scanf("%d %lf %lf", &n, &o.x, &o.y)) { double minn = inf, maxn = 0; for (int i = 0; i < n; i++) scanf("%lf %lf", &p[i].x, &p[i].y); p[n] = p[0]; for (int i = 0; i < n; i++) { double temp = Pointtosegment(o, p[i], p[i + 1]); minn = min(minn, temp); maxn = max(maxn, dist(p[i], o)); } printf("%.18f\n", pi * (maxn * maxn - minn * minn)); } return 0; }
#include <bits/stdc++.h> using namespace std; const double pai = 3.14159265; struct node { double x, y; } ver[100010]; double dist(double x1, double y1, double x2, double y2) { return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)); } double PointToSegDist(double x, double y, double x1, double y1, double x2, double y2) { double cross = (x2 - x1) * (x - x1) + (y2 - y1) * (y - y1); if (cross <= 0) return sqrt((x - x1) * (x - x1) + (y - y1) * (y - y1)); double d2 = (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1); if (cross >= d2) return sqrt((x - x2) * (x - x2) + (y - y2) * (y - y2)); double r = cross / d2; double px = x1 + (x2 - x1) * r; double py = y1 + (y2 - y1) * r; return sqrt((x - px) * (x - px) + (y - py) * (y - py)); } int main() { double x, y, maxlen, minlen, area; int n, i; scanf("%d %lf %lf", &n, &x, &y); maxlen = 0; minlen = 999999999; for (i = 0; i < n; i++) { scanf("%lf %lf", &ver[i].x, &ver[i].y); maxlen = max(maxlen, dist(x, y, ver[i].x, ver[i].y)); } minlen = min(minlen, PointToSegDist(x, y, ver[0].x, ver[0].y, ver[n - 1].x, ver[n - 1].y)); for (i = 1; i < n; i++) minlen = min(minlen, PointToSegDist(x, y, ver[i].x, ver[i].y, ver[i - 1].x, ver[i - 1].y)); area = maxlen * maxlen * pai - minlen * minlen * pai; printf("%lf\n", area); }
#include <bits/stdc++.h> using namespace std; struct POINT { double x, y; double dis; } xx[2000001], ind; int n; double x0, y666, x, y, ans, mii = 1e50, maxi; double sqr(double k) { return k * k; } double times(double x1, double y1, double x2, double y2) { return fabs(x2 * y1 - x1 * y2) / 2.0; } int main() { cin >> n; cin >> x0 >> y666; for (int i = 1; i <= n; i++) { scanf("%lf %lf", &x, &y); xx[i].x = x; xx[i].y = y; xx[i].dis = sqrt(sqr(x - x0) + sqr(y - y666)); mii = min(mii, xx[i].dis); maxi = max(maxi, xx[i].dis); } xx[n + 1] = xx[1]; for (int i = 1; i <= n; i++) { double x1 = xx[i].x, x2 = xx[i + 1].x, y1 = xx[i].y, y2 = xx[i + 1].y; double d1 = xx[i].dis, d2 = xx[i + 1].dis; if (d1 < d2) swap(d1, d2); double d = sqrt(sqr(x1 - x2) + sqr(y1 - y2)); if (sqr(d1) > sqr(d2) + sqr(d) + 1e-8) continue; double h = times(x1 - x0, y1 - y666, x2 - x0, y2 - y666) / d * 2.0; mii = min(mii, h); maxi = max(maxi, h); } ans = (acos(-1) * sqr(maxi) - acos(-1) * sqr(mii)); printf("%.12lf", ans); }
#include <bits/stdc++.h> using namespace std; struct Node { Node() {} Node(double a, double b) { x = a; y = b; } double x, y; }; Node node[100005]; double dis(Node a, Node b) { return (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y); } double get_dis(Node &a, Node &b, Node &c) { double k1 = dis(a, b), k2 = dis(a, c), k3 = dis(b, c); if (k1 >= k2 + k3) return k2; if (k2 >= k1 + k3) return k1; double d = fabs((b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x)); return d * d / k3; } int main() { int n; double x, y; double maxs = 0, mins = 1e18; Node o; scanf("%d%lf%lf", &n, &o.x, &o.y); for (int i = 0; i < n; i++) { scanf("%lf%lf", &node[i].x, &node[i].y); maxs = max(maxs, dis(o, node[i])); } for (int i = 0; i < n; i++) { int j = (i + 1) % n; mins = min(mins, get_dis(o, node[i], node[j])); } double ans = (maxs - mins) * acos(-1); printf("%.18lf\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; template <class T> void chmin(T& a, const T& b) { if (a > b) a = b; } template <class T> void chmax(T& a, const T& b) { if (a < b) a = b; } int n; double px, py; double X[100100], Y[100100]; double ABS(double x) { return (x >= 0) ? x : -x; } double Angle(double ax, double ay, double bx, double by) { double dot = ax * bx + ay * by; double sza = sqrt(((ax) * (ax)) + ((ay) * (ay))); double szb = sqrt(((bx) * (bx)) + ((by) * (by))); double c = (dot / sza) / szb; return c; } double len(int j) { int a = j, b = (j + 1) % n; double A = Y[b] - Y[a]; double B = X[a] - X[b]; double C = Y[a] * X[b] - X[a] * Y[b]; double D = ABS(A * px + B * py + C) / sqrt(((A) * (A)) + ((B) * (B))); if (Angle(px - X[a], py - Y[a], X[b] - X[a], Y[b] - Y[a]) < 0) return -1.0; if (Angle(px - X[b], py - Y[b], X[a] - X[b], Y[a] - Y[b]) < 0) return -1.0; return D; } double len2(int j) { return sqrt(((X[j] - px) * (X[j] - px)) + ((Y[j] - py) * (Y[j] - py))); } int main() { scanf("%d %lf %lf", &n, &px, &py); for (int i = 0; i < n; i++) { scanf("%lf %lf", &X[i], &Y[i]); } double r = 100000000000000.0, R = -1.0; for (int i = 0; i < n; i++) { double dist = len(i); if (dist >= 0) { r = min(r, dist); R = max(R, dist); } dist = len2(i); r = min(r, dist); R = max(R, dist); } printf("%.16f\n", (((R) * (R)) - ((r) * (r))) * M_PI); return 0; }
#include <bits/stdc++.h> using namespace std; const int inf = 2e9; const int mod = 1e9 + 7; const int N = 1e5 + 123; const double PI = 3.14159265358979323846264338; const double eps = 1e-9; struct point { double x, y; }; double dist(point a, point b) { return hypot(a.x - b.x, a.y - b.y); } double dot(point a, point b) { return a.x * b.x + a.y * b.y; } int main() { ios::sync_with_stdio(0); int n; cin >> n; point p; vector<point> v(n); cin >> p.x >> p.y; point mx = p, mn = {100000000000000, 1}; for (int i = 0; i < n; i++) { cin >> v[i].x >> v[i].y; } double R = -1e18, r = 1e18; for (int i = 0; i < n; i++) { point q = v[i], w = v[(i + 1) % n]; double a, b, c; a = q.y - w.y; b = w.x - q.x; c = -(a * q.x + b * q.y); double d; d = fabs(a * p.x + b * p.y + c) / hypot(a, b); double M = max(dist(q, p), dist(w, p)); r = min(r, min(dist(q, p), dist(w, p))); R = max(R, M); point v1, v2, v3, v4; v1 = {p.x - q.x, p.y - q.y}; v2 = {w.x - q.x, w.y - q.y}; swap(q, w); v3 = {p.x - q.x, p.y - q.y}; v4 = {w.x - q.x, w.y - q.y}; if (dot(v1, v2) > 0 && dot(v3, v4) > 0) { r = min(r, d); } } double s1, s2; s1 = PI * R * R; s2 = PI * r * r; cout << fixed << setprecision(11); cout << s1 - s2; return 0; }
#include <bits/stdc++.h> using namespace std; struct Vector { double x, y; Vector() {} Vector(double x, double y) : x(x), y(y) {} Vector(Vector const &v) : x(v.x), y(v.y) {} Vector(Vector const &a, Vector const &b) : x(b.x - a.x), y(b.y - a.y) {} double length() const { return sqrt(x * x + y * y); } Vector norm() const { double len = length(); return Vector(x / len, y / len); } Vector operator*(double c) const { return Vector(x * c, y * c); } }; struct Line { double a, b, c; Line(Vector const &x, Vector const &y) { a = y.y - x.y; b = x.x - y.x; c = -(a * x.x + b * x.y); } Vector norm() const { return Vector(a, b); } Vector perp(Vector const &v) { Vector n = norm().norm(); double dist = (a * v.x + b * v.y + c) / sqrt(a * a + b * b); Vector to = n * dist; return Vector(v.x - to.x, v.y - to.y); } }; bool on(Vector const &a, Vector const &b, Vector const &p) { return ((a.x <= p.x && b.x >= p.x) || (a.x >= p.x && b.x <= p.x)) && ((a.y <= p.y && b.y >= p.y) || (a.y >= p.y && b.y <= p.y)); } int main() { int n; Vector c; cin >> n >> c.x >> c.y; vector<Vector> v(n); double min_dist = 1e20, max_dist = 0; for (int i = 0; i != n; ++i) { cin >> v[i].x >> v[i].y; double dist = Vector(v[i], c).length(); min_dist = min(min_dist, dist); max_dist = max(max_dist, dist); } for (int i = 0; i != n; ++i) { int next = (i + 1) % n; Line l(v[i], v[next]); Vector p = l.perp(c); if (!on(v[i], v[next], p)) continue; double dist = Vector(p, c).length(); min_dist = min(min_dist, dist); max_dist = max(max_dist, dist); } cout.precision(30); cout << fixed << 3.14159265358979323846L * (max_dist * max_dist - min_dist * min_dist) << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; inline void scanint(int &x) { register int c = 0; x = 0; int flag = 0; for (; ((c != 45) && (c < 48 || c > 57)); c = getchar()) ; for (; ((c == 45) || (c > 47 && c < 58)); c = getchar()) { if (c == 45) flag = 1; else x = (x << 1) + (x << 3) + c - 48; } if (flag) x = -x; } double dist(double x1, double x2, double y1, double y2) { return ((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1)); } struct point { double x, y; } p[100005]; double xx, yy; double fun(point p1, point p2) { double t1 = abs((p2.y - p1.y) * xx - (p2.x - p1.x) * yy + p2.x * p1.y - p2.y * p1.x); double t2 = ((p2.y - p1.y) * (p2.y - p1.y) + (p2.x - p1.x) * (p2.x - p1.x)); return (t1 * t1) / t2; } bool angle(point p1, point p2) { double a = dist(p2.x, p1.x, p2.y, p1.y); double b = dist(p2.x, xx, p2.y, yy); double c = dist(xx, p1.x, yy, p1.y); return (b * b < a * a + c * c); } int main() { int n, j, i; scanf("%d", &n); cin >> xx >> yy; double minn = 999999999999999999.0; double maxx = 0; for (i = 0; i < n; i++) { cin >> p[i].x; cin >> p[i].y; minn = min(minn, dist(xx, p[i].x, yy, p[i].y)); maxx = max(maxx, dist(xx, p[i].x, yy, p[i].y)); } for (i = 0; i < n; i++) { j = (i + 1) % n; if (angle(p[i], p[j]) && angle(p[j], p[i])) { minn = min(minn, fun(p[i], p[j])); } } double an = (acos(-1) * maxx) - (acos(-1) * minn); printf("%0.10lf\n", an); return 0; }
#include <bits/stdc++.h> using namespace std; const long long oo = 10000000000000000ll; const int N = 1000009; int n; pair<long long, long long> P, a[N]; long long vmax, vmin; bool check(pair<long long, long long> i, pair<long long, long long> j, pair<long long, long long> P) { long long a, b, c; a = j.first - i.first; b = j.second - i.second; c = -a * P.first - b * P.second; long long k1 = (a * i.first + b * i.second + c); long long k2 = (a * j.first + b * j.second + c); if ((k1 > 0 && k2 < 0) || (k1 < 0 && k2 > 0)) return 1; else return 0; } long long dis_sq(pair<long long, long long> i, pair<long long, long long> j) { return ((i.first - j.first) * (i.first - j.first) + (i.second - j.second) * (i.second - j.second)); } double dis_line(pair<long long, long long> i, pair<long long, long long> j, pair<long long, long long> P) { double a, b, c; a = j.second - i.second; b = i.first - j.first; c = -a * i.first - b * i.second; return ((double)((a * (double)P.first + b * (double)P.second + c) / (a * a + b * b))) * (a * (double)P.first + b * (double)P.second + c); } double PI = 3.1415926535897932384626433832795; int main() { vmax = 0; vmin = oo; cin >> n >> P.first >> P.second; for (int i = 1; i <= n; i++) { cin >> a[i].first >> a[i].second; long long kk = dis_sq(P, a[i]); vmax = max(vmax, kk); vmin = min(vmin, kk); } a[n + 1] = a[1]; double vm = vmax, vn = vmin; for (int i = 1; i <= n; i++) if (check(a[i], a[i + 1], P)) { double kk = dis_line(a[i], a[i + 1], P); vm = max(vm, kk); vn = min(vn, kk); } double ans = vm - vn; printf("%0.15f", ans * PI); }
#include <bits/stdc++.h> using namespace std; struct node { double x; double y; } arr[1001000]; int n; double MAX = 0, MIN = 100000000; double dis(node a, node b) { double x = a.x - b.x; double y = a.y - b.y; return sqrt(x * x + y * y); } int main() { cin >> n >> arr[0].x >> arr[0].y; for (int i = 1; i <= n; i++) { cin >> arr[i].x >> arr[i].y; } for (int i = 1; i <= n; i++) { MAX = max(MAX, dis(arr[0], arr[i])); } arr[n + 1] = arr[1]; for (int i = 1; i <= n; i++) { double bian1 = dis(arr[i], arr[0]); double bian2 = dis(arr[i + 1], arr[0]); double bian3 = dis(arr[i], arr[i + 1]); if (bian1 * bian1 >= bian2 * bian2 + bian3 * bian3) MIN = min(MIN, bian2); else if (bian2 * bian2 >= bian1 * bian1 + bian3 * bian3) MIN = min(MIN, bian1); else { double p = (bian1 + bian2 + bian3) / 2.0; double s = sqrt(p * (p - bian1) * (p - bian2) * (p - bian3)); double h = 2 * s / bian3; MIN = min(MIN, h); } } double ans = ((MAX * MAX) - (MIN * MIN)) * acos(-1.0); printf("%.7lf", ans); return 0; }
#include <bits/stdc++.h> using namespace std; inline double dist(double a, double b, double c, double d) { return (a - c) * (a - c) + (b - d) * (b - d); } inline double j(double k1, double b1, double k2, double b2) { return (double)(b2 - b1) / (k1 - k2); } double dist2(double a, double b, double c1, double d1, double c, double d) { if (c == c1) { if (b <= d1 && b >= d) { return (c - a) * (c - a); } else if (b <= d && b >= d1) { return (c - a) * (c - a); } else { return min(dist(a, b, c, d), dist(a, b, c1, d1)); } } if (d == d1) { if (a <= c1 && a >= c) { return (d - b) * (d - b); } else if (a <= c && a >= c1) { return (d - b) * (d - b); } else { return min(dist(a, b, c, d), dist(a, b, c1, d1)); } } double k1 = ((double)d - d1) / ((double)c - c1); double k2 = -1 / k1; double b1 = (double)d - (c * k1); double b2 = (double)b - (a * k2); double x = j(k1, b1, k2, b2); if (x > c1 && x > c) { return min(dist(a, b, c, d), dist(a, b, c1, d1)); } if (x < c1 && x < c) { return min(dist(a, b, c, d), dist(a, b, c1, d1)); } return dist(a, b, x, k1 * x + b1); } int main() { int n; double a, b, c, d, c1, d1, c2, d2, min1, max1; cin >> n >> a >> b; cin >> c >> d; c2 = c; d2 = d; min1 = max1 = (dist(a, b, c, d)); for (int i = 2; i <= n; i++) { c1 = c; d1 = d; cin >> c >> d; double dis = dist2(a, b, c1, d1, c, d); if (min1 > dis) min1 = dis; dis = dist(a, b, c, d); if (max1 < dis) max1 = dis; } double dis = dist2(a, b, c2, d2, c, d); if (min1 > dis) min1 = dis; dis = dist(a, b, c, d); if (max1 < dis) max1 = dis; cout << setprecision(12) << 3.141592653589793 * (max1 - min1); }
#include <bits/stdc++.h> using namespace std; int n; pair<long long, long long> P, d[100000]; double rm, rM; int main() { scanf("%d%I64d%I64d", &n, &P.first, &P.second); for (int i = 0; i < n; i++) { pair<long long, long long> Q; scanf("%I64d%I64d", &Q.first, &Q.second); double t = (P.first - Q.first) * (P.first - Q.first) + (P.second - Q.second) * (P.second - Q.second); if (i == 0) rm = rM = t; else { if (rm > t) rm = t; if (rM < t) rM = t; } d[i] = Q; } for (int i = 0; i < n; i++) { int j = (i + 1) % n; pair<long long, long long> Q = make_pair(d[j].first - d[i].first, d[j].second - d[i].second); double t = Q.first * (P.first - d[i].first) + Q.second * (P.second - d[i].second); t /= (Q.first * Q.first + Q.second * Q.second); if (0 <= t && t <= 1) { long long a = d[j].second - d[i].second; long long b = -(d[j].first - d[i].first); long long c = -(a * d[i].first + b * d[i].second); double t = (a * P.first + b * P.second + c); t = t * t / (a * a + b * b); if (t < rm) rm = t; } } double r = rM - rm; printf("%.9f\n", r * 3.1415926535897932384626433832795); return 0; }
#include <bits/stdc++.h> using namespace std; struct p { double x, y; } a[100005]; double x, y; double juli(double xx1, double yy1, double xx2, double yy2) { double xx0 = x, yy0 = y; double temp, temp2; temp = sqrt((xx2 - xx1) * (xx2 - xx1) + (yy2 - yy1) * (yy2 - yy1)); temp2 = (xx1 - xx0) * (yy2 - yy0) - (yy1 - yy0) * (xx2 - xx0); temp2 = fabs(temp2); return (temp2 / temp); } int main() { int n; while (~scanf("%d%lf%lf", &n, &x, &y)) { double r = 1000000000, R = 0; for (int i = 1; i <= n; i++) { scanf("%lf%lf", &a[i].x, &a[i].y); r = min(r, sqrt((a[i].x - x) * (a[i].x - x) + (a[i].y - y) * (a[i].y - y))); R = max(R, sqrt((a[i].x - x) * (a[i].x - x) + (a[i].y - y) * (a[i].y - y))); } a[0].x = a[n].x, a[0].y = a[n].y; for (int i = 1; i <= n; i++) { if ((a[i - 1].x - a[i].x) * (x - a[i].x) + (a[i - 1].y - a[i].y) * (y - a[i].y) <= 0) continue; if ((a[i].x - a[i - 1].x) * (x - a[i - 1].x) + (a[i].y - a[i - 1].y) * (y - a[i - 1].y) <= 0) continue; r = min(r, juli(a[i].x, a[i].y, a[i - 1].x, a[i - 1].y)); } printf("%.15lf\n", (R * R - r * r) * acos(-1.0)); } return 0; }
#include <bits/stdc++.h> using namespace std; long long MOD = 1e9 + 7; int main() { ios_base::sync_with_stdio(0); double pi = 3.141592653589793238462643383279; int n; double a, b; cin >> n >> a >> b; double x[n], y[n]; double u = 0, v = 1000000000000; for (int i = 0; i < n; ++i) { cin >> x[i] >> y[i]; } double m, f; for (int i = 0; i < n; ++i) { if ((x[i] - a) * (x[i] - a) + (y[i] - b) * (y[i] - b) > u) u = (x[i] - a) * (x[i] - a) + (y[i] - b) * (y[i] - b); int l = i, r = (i + 1) % n; if (x[l] != x[r]) { m = (y[r] - y[l]) / (x[r] - x[l]); f = ((m * (a - x[l]) + y[l] - b) * (m * (a - x[l]) + y[l] - b)) / (m * m + 1); if ((m * (y[r] - b) + (x[r] - a)) * (m * (y[l] - b) + (x[l] - a)) < 0) v = min(v, f); else v = min(v, min(((x[i] - a) * (x[i] - a) + (y[i] - b) * (y[i] - b)), ((x[r] - a) * (x[r] - a) + (y[r] - b) * (y[r] - b)))); } else { f = (x[l] - a) * (x[l] - a); v = min(v, f); } } u = pi * (u - v); printf("%0.8f\n", u); return 0; }
#include <bits/stdc++.h> using namespace std; long long cross(long long x1, long long y1, long long x2, long long y2) { return x1 * y2 - x2 * y1; } long long sq(long long x) { return x * x; } long double sq(long double x) { return x * x; } long double dist(long long x, long long y, long long x1, long long y1) { return sqrt(sq(x - x1) + sq(y - y1)); } long double dist(long long x, long long y, long long x1, long long y1, long long x2, long long y2) { long long a = y2 - y1; long long b = x1 - x2; long long c = y1 * (x2 - x1) - x1 * (y2 - y1); if ((x - x1) * (x2 - x1) + (y - y1) * (y2 - y1) < 0) return sqrt(sq(x - x1) + sq(y - y1)); else if ((x - x2) * (x1 - x2) + (y - y2) * (y1 - y2) < 0) return sqrt(sq(x - x2) + sq(y - y2)); else return abs(a * x + b * y + c) / sqrt(a * a + b * b); } int main() { int n, px, py; cin >> n >> px >> py; int x[n + 1], y[n + 1]; for (int k = 0; k < n; k++) cin >> x[k] >> y[k]; x[n] = x[0]; y[n] = y[0]; long double max_dist = -1, min_dist = 2e18; for (int k = 0; k < n; k++) { max_dist = max(max_dist, dist(px, py, x[k], y[k])); min_dist = min(min_dist, dist(px, py, x[k], y[k], x[k + 1], y[k + 1])); } cout << fixed << setprecision(10); cout << acos(-1.0) * (sq(max_dist) - sq(min_dist)) << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1000004; double x[N], y[N]; int main() { double pi = 3.141592653589793238462643383279; int n; double a, b; scanf("%d %lf %lf", &n, &a, &b); double u = 0.0, v = 1000000000000.0; for (int i = 0; i < n; ++i) scanf("%lf %lf", &x[i], &y[i]); double m, f; for (int i = 0; i < n; ++i) { if ((x[i] - a) * (x[i] - a) + (y[i] - b) * (y[i] - b) > u) u = (x[i] - a) * (x[i] - a) + (y[i] - b) * (y[i] - b); int l = i, r = (i + 1) % n; if (x[l] != x[r]) { m = (y[r] - y[l]) / (x[r] - x[l]); f = ((m * (a - x[l]) + y[l] - b) * (m * (a - x[l]) + y[l] - b)) / (m * m + 1); if ((m * (y[r] - b) + (x[r] - a)) * (m * (y[l] - b) + (x[l] - a)) < 0) v = min(v, f); else v = min(v, min(((x[i] - a) * (x[i] - a) + (y[i] - b) * (y[i] - b)), ((x[r] - a) * (x[r] - a) + (y[r] - b) * (y[r] - b)))); } else { f = (x[l] - a) * (x[l] - a); v = min(v, f); } } u = pi * (u - v); printf("%0.12f\n", u); return 0; }
#include <bits/stdc++.h> using namespace std; const double phi = acos(-1.00); const double eps = 1e-19; struct node { double x, y; } p, poin[100005]; double dist(node a) { return ((p.x - a.x) * (p.x - a.x) + (p.y - a.y) * (p.y - a.y)); } int main() { int n; double lingkaranbesar = 0, lingkarankecil = (1 << 30); scanf("%d%lf%lf", &n, &p.x, &p.y); for (int i = 0; i < n; i++) { scanf("%lf%lf", &poin[i].x, &poin[i].y); lingkaranbesar = max(lingkaranbesar, sqrt(dist(poin[i]))); } for (int i = 0; i < n; i++) { double lx = poin[i].x; double ly = poin[i].y; double rx = poin[(i + 1) % n].x; double ry = poin[(i + 1) % n].y; double m1, m2; node mid1, mid2; for (int i = 0; i < 100; i++) { mid1.x = (2.0 * lx + rx) / 3.0; mid1.y = (2.0 * ly + ry) / 3.0; mid2.x = (lx + 2.0 * rx) / 3.0; mid2.y = (ly + 2.0 * ry) / 3.0; m1 = sqrt(dist(mid1)); m2 = sqrt(dist(mid2)); if (m1 - m2 < eps) { rx = mid2.x; ry = mid2.y; } else { lx = mid1.x; ly = mid1.y; } } if (lingkarankecil - m1 > -eps) { lingkarankecil = m1; } } printf("%.7lf", (phi * (lingkaranbesar * lingkaranbesar - lingkarankecil * lingkarankecil))); }
#include <bits/stdc++.h> using namespace std; using namespace std; struct Point { double x, y; Point(double _x, double _y) { x = _x; y = _y; } Point() {} double mod() { return sqrt(x * x + y * y); } double mod2() { return x * x + y * y; } double arg() { return atan2(y, x); } Point ort() { return Point(-y, x); } Point rev() { return Point(y, x); } Point unit() { double k = mod(); return Point(x / k, y / k); } void print() { printf("%lf %lf\n", x, y); } void read() { scanf("%lf%lf", &x, &y); } }; bool operator<(const Point &P1, const Point &P2) { return (P1.x != P2.x) ? (P1.x < P2.x) : (P1.y < P2.y); } bool operator==(const Point &P1, const Point &P2) { return fabs(P1.x - P2.x) < 1e-6 && fabs(P1.y - P2.y) < 1e-6; } bool operator>(const Point &P1, const Point &P2) { return !(P1 == P2) && !(P1 < P2); } bool operator!=(const Point &P1, const Point &P2) { return !(P1 == P2); } Point operator-(const Point &p1, const Point &p2) { return Point(p1.x - p2.x, p1.y - p2.y); } Point operator+(const Point &p1, const Point &p2) { return Point(p1.x + p2.x, p1.y + p2.y); } Point operator*(const Point &p, double k) { return Point(p.x * k, p.y * k); } Point operator/(const Point &p, double k) { return Point(p.x / k, p.y / k); } double dot(const Point &v1, const Point &v2) { return v1.x * v2.x + v1.y * v2.y; } double cross(const Point &v1, const Point &v2) { return v1.x * v2.y - v1.y * v2.x; } double dis(const Point &P1, const Point &P2) { return (P1 - P2).mod(); } double area(const Point &A, const Point &B, const Point &C) { return cross(B - A, C - A); } double areaHeron(double a, double b, double c) { double s = (a + b + c) / 2; return sqrt(s * (s - a) * (s - b) * (s - c)); } double areaHeron(double a, double b, double c, double d) { double s = (a + b + c + d) / 2; return sqrt((s - a) * (s - b) * (s - c) * (s - d)); } double circumradius(double a, double b, double c) { return a * b * c / (4 * areaHeron(a, b, c)); } Point rotate(Point A, Point C, double teta) { Point T = Point(A.x - C.x, A.y - C.y); return C + Point(T.x * cos(teta) - T.y * sin(teta), T.y * cos(teta) + T.x * sin(teta)); } struct line { Point p1, p2; line(Point _p1, Point _p2) { p1 = _p1; p2 = _p2; } line() {} Point dir() { return p2 - p1; } double mod() { return (p2 - p1).mod(); } }; bool isAntihorario(Point *poli, int n) { int top = 0; for (int i = 0; i < n; i++) if (poli[top].y < poli[i].y) top = i; return poli[(top - 1 + n) % n].x > poli[(top + 1 + n) % n].x; } double disPointToLine(Point P, line L) { Point v = P - L.p1; return fabs(cross(v, L.dir())) / L.mod(); } double disLineToPoint(Point P, line L) { Point v = L.p2 - L.p1; Point v1 = P - L.p1; Point v2 = P - L.p2; if (dot(v, v1) <= 0) return v1.mod(); if (dot(v, v2) >= 0) return v2.mod(); return fabs(cross(v1, v)) / v.mod(); } bool between(const Point &A, const Point &B, const Point &P) { return P.x + 1e-6 >= min(A.x, B.x) && P.x <= max(A.x, B.x) + 1e-6 && P.y + 1e-6 >= min(A.y, B.y) && P.y <= max(A.y, B.y) + 1e-6; } bool onSegment(Point P, line L) { return fabs(cross(L.dir(), P - L.p1)) < 1e-6 && dot(P - L.p1, P - L.p2) < 1e-6; } bool intersects(line L1, line L2) { if (onSegment(L1.p1, L2)) return true; if (onSegment(L1.p2, L2)) return true; if (onSegment(L2.p1, L1)) return true; if (onSegment(L2.p2, L1)) return true; double A11 = cross(L1.dir(), L2.p1 - L1.p1); double A12 = cross(L1.dir(), L2.p2 - L1.p1); double A21 = cross(L2.dir(), L1.p1 - L2.p1); double A22 = cross(L2.dir(), L1.p2 - L2.p1); if (A11 > 1e-6) swap(A11, A12); if (A21 > 1e-6) swap(A21, A22); return (A11 < 0 && A12 > 1e-6) && (A21 < 0 && A22 > 1e-6); } Point lineIntersection(line S1, line S2) { return S1.p1 + S1.dir() * (cross(S2.p1 - S1.p1, S2.dir()) / cross(S1.dir(), S2.dir())); } Point circumcenter(const Point &A, const Point &B, const Point &C) { return (A + B + (A - B).ort() * dot(C - B, A - C) / cross(A - B, A - C)) / 2; } double distSeg(line s1, line s2) { double ans = (1 << 30); ans = min(ans, disLineToPoint(s1.p1, s2)); ans = min(ans, disLineToPoint(s1.p2, s2)); ans = min(ans, disLineToPoint(s2.p1, s1)); ans = min(ans, disLineToPoint(s2.p2, s1)); return ans; } double area(vector<Point> &P) { double ans = 0; int n = P.size(); for (int i = 0; i < n; i++) ans += cross(P[i], P[(i + 1) % n]); return fabs(ans) / 2.0; } Point P[1000005], C; pair<double, double> getInterval(int p1, int p2) { double d1 = (P[p1] - C).mod2(); double d2 = (P[p2] - C).mod2(); double maxi = max(d1, d2); Point dir = P[p1] - P[p2]; Point v1 = C - dir.ort() * sqrt(maxi), v2 = C + dir.ort() * sqrt(maxi); line S1 = line(P[p1], P[p2]); line S2 = line(v1, v2); if (!intersects(S1, S2)) return make_pair(min(d1, d2), maxi); Point I = lineIntersection(S1, S2); double mini = (C - I).mod2(); return make_pair(mini, maxi); } int main() { int n; while (cin >> n) { C.read(); for (int i = 0; i < n; i++) P[i].read(); vector<pair<double, double> > v; for (int i = 0; i < n; i++) { v.push_back(getInterval(i, (i + 1) % n)); } sort(v.begin(), v.end()); double ans = 0, last = -1; if (v.size() > 0) ans += v[0].second - v[0].first, last = v[0].second; for (int i = 1; i < v.size(); i++) { if (v[i].first > last) { ans += v[i].second - v[i].first; } else if (v[i].second > last) ans += v[i].second - last; last = max(last, v[i].second); } ans = ans * (atan2(0, -1)); printf("%.10lf\n", ans); } }
#include <bits/stdc++.h> #pragma comment(linker, "/STACK:256000000") using namespace std; struct pt { long long x, y; pt() : x(0), y(0) {} pt(long long x, long long y) : x(x), y(y) {} }; bool cmp(pt a, pt b) { return a.x < b.x || a.x == b.x && a.y < b.y; } bool cw(pt a, pt b, pt c) { return a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y) < 0; } bool ccw(pt a, pt b, pt c) { return a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y) > 0; } inline long long area(pt a, pt b, pt c) { long long res = (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x); return (res > 0 ? 1 : (res < 0 ? -1 : 0)); } inline bool intersect_1(long long a, long long b, long long c, long long d) { if (a > b) swap(a, b); if (c > d) swap(c, d); return max(a, c) <= min(b, d); } bool intersect(pt a, pt b, pt c, pt d) { return intersect_1(a.x, b.x, c.x, d.x) && intersect_1(a.y, b.y, c.y, d.y) && area(a, b, c) * area(a, b, d) <= 0 && area(c, d, a) * area(c, d, b) <= 0; } const double pi = 2.0 * acos(0.0); double getDist(pt p, pt a, pt b) { double A = a.y - b.y; double B = b.x - a.x; double C = a.x * b.y - a.y * b.x; double d = hypot((double)(A), (double)(B)); double len = (A * p.x + B * p.y + C) / d; double dx = A / d; double dy = B / d; double x = (double)(p.x) - len * dx; double y = (double)(p.y) - len * dy; double u = hypot((double)(a.x - b.x), (double)(a.y - b.y)); double v = hypot((double)(a.x) - x, (double)(a.y) - y); double w = hypot((double)(b.x) - x, (double)(b.y) - y); if (fabs(u - v - w) < 1e-9) { return fabs(len); } return hypot((double)(p.x - a.x), (double)(p.y - a.y)); } int main() { int n; scanf("%d", &n); pt p; scanf("%I64d%I64d", &p.x, &p.y); vector<pt> a(n); for (int i = 0; i < n; ++i) { scanf("%I64d%I64d", &a[i].x, &a[i].y); } double l = 1e10, r = 0.0; for (int i = 0; i < a.size(); ++i) { double d = hypot((double)(p.x - a[i].x), (double)(p.y - a[i].y)); l = min(l, d); r = max(r, d); d = getDist(p, a[i], a[(i + 1) % a.size()]); l = min(l, d); r = max(r, d); } int cnt = 0; for (int i = 0; i < a.size(); ++i) { if (intersect(a[i], a[(i + 1) % a.size()], p, pt(p.x + 1000000000, p.y + 1000000001))) { ++cnt; } } if (cnt % 2 == 1) { printf("%.10lf\n", pi * r * r); } else { printf("%.10lf\n", pi * (r * r - l * l)); } return 0; }
#include <bits/stdc++.h> using namespace std; int read() { int x = 0, f = 1; char ch = getchar(); while (!isdigit(ch)) { if (ch == '-') f = -1; ch = getchar(); } while (isdigit(ch)) { x = x * 10 + ch - '0'; ch = getchar(); } return x * f; } struct Point { double x, y; Point() { x = y = 0; } Point(double a, double b) { x = a; y = b; } }; struct vec { double x, y; }; struct Line { double a, b, c; }; double dis(Point a, Point b) { return sqrt(pow(a.x - b.x, 2) + pow(a.y - b.y, 2)); } bool issame(Point A, Point B) { double a = A.x - B.x; double b = A.y - B.y; if (abs(a) < 1e-7 && abs(b) < 1e-7) return 1; return 0; } vec Vector(Point a, Point b) { vec p; p.x = b.x - a.x; p.y = b.y - a.y; return p; } double dot(vec a, vec b) { return a.x * b.x + a.y * b.y; } double cross(vec a, vec b) { return a.x * b.y - a.y * b.x; } double length(vec a) { return sqrt(pow(a.x, 2) + pow(a.y, 2)); } double dist(Point a, Point b, Point c) { vec AB = Vector(a, b), AC = Vector(a, c), BC = Vector(b, c), BA = Vector(b, a); if (dot(AB, BC) > 0) return dis(c, b); if (dot(BA, AC) > 0) return dis(a, c); return abs(cross(AB, AC) / (length(AB))); } Point A[1000010]; int main() { int n = read(), a = read(), b = read(); double mini = 10000000000000000; double maxi = -1; for (int i = 0; i < n; ++i) { int c = read(), d = read(); A[i] = Point(c, d); maxi = max(maxi, dis(A[i], Point(a, b))); } for (int i = 0; i < n; ++i) { mini = min(mini, dist(A[i], A[(i + 1) % n], Point(a, b))); } double ans = acos(-1) * (maxi * maxi - mini * mini); printf("%.17lf", ans); }
#include <bits/stdc++.h> using namespace std; const int nax = 1e5 + 5; const double eps = 1e-9; int n; pair<double, double> orig; double dist(pair<double, double> p1, pair<double, double> p2) { return (p1.first - p2.first) * (p1.first - p2.first) + (p1.second - p2.second) * (p1.second - p2.second); } struct Line { pair<double, double> pi, pf; double a, b, c; void init(pair<double, double> p1, pair<double, double> p2) { pi = p1, pf = p2; a = p2.second - p1.second; b = p1.first - p2.first; c = a * p1.first + b * p1.second; } bool inside(pair<double, double> p) { return sqrt(dist(p, pi)) + sqrt(dist(p, pf)) <= sqrt(dist(pi, pf)) + eps; } double shortestDist() { if (b == 0) { if (inside({c / a, orig.second})) { return (c / a - orig.first) * (c / a - orig.first); } else { return min(dist(orig, pi), dist(orig, pf)); } } else { pair<double, double> pt; double top = a * c / b + b * orig.first - a * orig.second, bot = b + a * a / b; pt.first = top / bot, pt.second = (c - a * pt.first) / b; return inside(pt) ? dist(orig, pt) : min(dist(orig, pi), dist(orig, pf)); } } double longestDist() { return max(dist(orig, pi), dist(orig, pf)); } void print() { printf("%lf %lf %lf\n", a, b, c); } }; Line L[nax]; pair<double, double> P[nax]; int main() { scanf("%d", &n); scanf("%lf %lf", &orig.first, &orig.second); for (int i = 0; i < n; ++i) scanf("%lf %lf", &P[i].first, &P[i].second); for (int i = 0; i < n; ++i) L[i].init(P[i], P[(i + 1) % n]); double r1 = 1e13, r2 = 0; for (int i = 0; i < n; ++i) { r1 = min(r1, L[i].shortestDist()); r2 = max(r2, L[i].longestDist()); } cout << fixed << setprecision(12) << 3.14159265358979323846 * (r2 - r1) << endl; return 0; }
#include <bits/stdc++.h> using namespace std; vector<pair<double, double> > v; double dist(double x0, double y0, double x, double y) { return ((x0 - x) * (x0 - x)) + ((y0 - y) * (y0 - y)); } int main() { int n, i, j; double x0, y0, x, y, mn, mx, t1, t2, t3; scanf("%d", &n); scanf("%lf %lf", &x0, &y0); for (i = 0; i < n; i++) { scanf("%lf %lf", &x, &y); v.push_back(make_pair(x, y)); } mn = (double)LONG_LONG_MAX, mx = 0.0; for (i = 0; i < n; i++) { t1 = dist(x0, y0, v[i].first, v[i].second); mn = min(mn, t1); mx = max(mx, t1); } for (i = 0; i < n; i++) { j = (i + 1) % n; t1 = dist(v[i].first, v[i].second, v[j].first, v[j].second); t2 = dist(v[i].first, v[i].second, x0, y0); t3 = dist(v[j].first, v[j].second, x0, y0); if (t2 < t1 + t3 && t3 < t1 + t2) { t2 = ((v[i].second - v[j].second) * x0) - ((v[i].first - v[j].first) * y0) + (v[i].first * v[j].second) - (v[i].second * v[j].first); t2 = (t2 * t2); t3 = t2 / t1; mn = min(mn, t3); mx = max(mx, t3); } } t1 = (double)3.14159265359 * (mx - mn); printf("%0.6lf\n", t1); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 100000 + 10; const double pi = acos(-1); struct point { double x, y; }; int n; double minR, maxR; point p, v[N]; double dist(point A, point B) { return sqrt(((A.x - B.x) * (A.x - B.x)) + ((A.y - B.y) * (A.y - B.y))); } double dist_to_seg(point A, point B, point C) { if (B.x == C.x) { if (A.y >= min(B.y, C.y) && A.y <= max(B.y, C.y)) return (((A.x - B.x) > 0) ? (A.x - B.x) : (-(A.x - B.x))); return min(dist(A, B), dist(A, C)); } if (B.y == C.y) { if (A.x >= min(B.x, C.x) && A.x <= max(B.x, C.x)) return (((A.y - B.y) > 0) ? (A.y - B.y) : (-(A.y - B.y))); return min(dist(A, B), dist(A, C)); } double k = (B.y - C.y) / (B.x - C.x); double crx = (k * B.x - B.y + A.x / k + A.y) / (k + 1 / k); if (crx >= min(B.x, C.x) && crx <= max(B.x, C.x)) { double cry = k * (crx - B.x) + B.y; return (((k * A.x - A.y + B.y - k * B.x) > 0) ? (k * A.x - A.y + B.y - k * B.x) : (-(k * A.x - A.y + B.y - k * B.x))) / sqrt(k * k + 1); } return min(dist(A, B), dist(A, C)); } int main() { scanf("%d%lf%lf", &n, &p.x, &p.y); for (int i = 1; i <= (n); i++) { scanf("%lf%lf", &v[i].x, &v[i].y); maxR = max(maxR, ((dist(p, v[i])) * (dist(p, v[i])))); } minR = ((dist_to_seg(p, v[1], v[n])) * (dist_to_seg(p, v[1], v[n]))); for (int i = 1; i <= (n - 1); i++) minR = min(minR, ((dist_to_seg(p, v[i], v[i + 1])) * (dist_to_seg(p, v[i], v[i + 1])))); printf("%.11lf\n", pi * (maxR - minR)); return 0; }
#include <bits/stdc++.h> using namespace std; const double PI = acos(-1); struct point { point() {} point(double x, double y) : x(x), y(y) {} double x, y; }; struct segment { segment() {} segment(point a, point b) : a(a), b(b) {} point a, b; }; template <class T> T sqr(T a) { return a * a; } double dist(point a, point b) { return sqrt(sqr(a.x - b.x) + sqr(a.y - b.y)); } double crossProduct(point a1, point a2, point b1, point b2) { return ((a2.x - a1.x) * (b2.y - b1.y) - (a2.y - a1.y) * (b2.x - b1.x)); } double dotProduct(point a1, point a2, point b1, point b2) { return ((a2.x - a1.x) * (b2.x - b1.x) + (a2.y - a1.y) * (b2.y - b1.y)); } double dist(point c, segment seg) { if (dotProduct(seg.a, seg.b, seg.a, c) <= 0 || dotProduct(seg.b, seg.a, seg.b, c) <= 0) return min(dist(c, seg.a), dist(c, seg.b)); return abs(crossProduct(seg.a, seg.b, seg.a, c) / dist(seg.a, seg.b)); } int main() { int n; point a; cin >> n; cin >> a.x >> a.y; double dmax = 0, dmin = 1e18; vector<point> b(n); for (int i = 0; i < n; i++) cin >> b[i].x >> b[i].y; for (int i = 0; i < n; i++) { dmax = max(dmax, dist(a, b[i])); dmin = min(dmin, dist(a, b[i])); dmin = min(dmin, dist(a, segment(b[i], b[(i + 1) % n]))); } double ans = PI * (dmax * dmax - dmin * dmin); printf("%.12lf", ans); return 0; }
#include <bits/stdc++.h> using namespace std; const double pi = acos(-1.0); double sx, sy, Min = 1.0e9, Max = 0, M1 = 1.0e9, M2 = 1.0e9, U1 = -1.0e9, U2 = -1.0e9; double x[100002], y[100002]; int main() { int n; scanf("%d", &n); cin >> sx >> sy; bool flag1 = 0, flag2 = 0, flag3 = 0, flag4 = 0; for (int i = 1; i <= n; i++) { scanf("%lf %lf", &x[i], &y[i]); } int sum = 0; for (int i = 1; i <= n; i++) { double d1 = x[i] - sx; double d2 = y[i] - sy; double d = sqrt(d1 * d1 + d2 * d2); Min = min(Min, d); Max = max(Max, d); int to; if (i == 1) to = n; else to = i - 1; if (x[i] - x[to] == 0) { if (sy >= min(y[i], y[to]) && sy <= max(y[i], y[to])) { Min = min(Min, abs(x[i] - sx)); } continue; } double k = (y[i] - y[to]) / (x[i] - x[to]); double b = y[i] - k * x[i]; double k2 = -1.0 / k; double b2 = sy - sx * k2; double x2 = (b - b2) / (k2 - k); double y2 = x2 * k2 + b2; if (k == 0) x2 = sx, y2 = b; if (min(x[i], x[to]) <= x2 && x2 <= max(x[i], x[to])) { d1 = y2 - sy; d2 = x2 - sx; d = sqrt(d1 * d1 + d2 * d2); Min = min(Min, d); } } printf("%0.7lf", pi * Max * Max - pi * Min * Min); }
#include <bits/stdc++.h> using namespace std; double x[100005], y[100005]; int main() { int n; double x1, y1; cin >> n >> x1 >> y1; double ma = 0, mi = 1000000000000000000000.0; for (int i = 1; i <= n; i++) cin >> x[i] >> y[i]; x[0] = x[n]; y[0] = y[n]; for (int i = 1; i <= n; i++) { double dist = (x[i] - x1) * (x[i] - x1) + (y[i] - y1) * (y[i] - y1); mi = min(mi, dist); ma = max(ma, dist); if (x[i] == x[i - 1]) { if (y1 >= y[i] && y1 <= y[i - 1]) { dist = abs(x1 - x[i - 1]); dist = dist * dist; } else { if (y1 >= y[i - 1] && y1 <= y[i]) { dist = abs(x1 - x[i - 1]); dist = dist * dist; } else continue; } } else { double m = (y[i - 1] - y[i]) / (double)(x[i - 1] - x[i]); double c = y[i - 1] - m * x[i - 1]; if (y[i] == y[i - 1]) { if (x1 >= x[i - 1] && x1 <= x[i]) { dist = abs(y[i] - y1); dist = dist * dist; } else { if (x1 >= x[i] && x1 <= x[i - 1]) { dist = abs(y[i] - y1); dist = dist * dist; } else continue; } } else { double m1 = -1 / (double)m; double c1 = y1 - m1 * x1; if (m == m1) continue; double x2 = (c1 - c) / (double)(m - m1); double y2 = m1 * x2 + c1; if (x2 >= x[i] && x2 <= x[i - 1]) { dist = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2); } else { if (x2 >= x[i - 1] && x2 <= x[i]) { dist = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2); } else continue; } } } mi = min(mi, dist); } ma = 3.14159265358979323846264338327950288419 * (ma - mi); printf("%.9lf\n", (ma)); }
#include <bits/stdc++.h> using namespace std; namespace std { bool operator<(const complex<double>& a, const complex<double>& b) { return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b); } } // namespace std double cross(const complex<double>& a, const complex<double>& b) { return imag(conj(a) * b); } double dot(const complex<double>& a, const complex<double>& b) { return real(conj(a) * b); } struct L : public vector<complex<double> > { L(const complex<double>& a, const complex<double>& b) { push_back(a); push_back(b); } }; struct C { complex<double> p; double r; C(const complex<double>& p, double r) : p(p), r(r) {} }; complex<double> proj(complex<double> a1, complex<double> a2, complex<double> p) { return a1 + dot(a2 - a1, p - a1) / norm(a2 - a1) * (a2 - a1); } double distLP(complex<double> a1, complex<double> a2, complex<double> p) { return abs(proj(a1, a2, p) - p); } const double EPS = 1e-9; int ccw(complex<double> a, complex<double> b, complex<double> c) { b -= a; c -= a; if (cross(b, c) > EPS) return +1; if (cross(b, c) < -EPS) return -1; if (dot(b, c) < -EPS) return +2; if (norm(b) < norm(c)) return -2; return 0; } bool isecSP(complex<double> a1, complex<double> a2, complex<double> b) { return !ccw(a1, a2, b); } double distSP(complex<double> a1, complex<double> a2, complex<double> p) { complex<double> r = proj(a1, a2, p); if (isecSP(a1, a2, r)) return abs(r - p); return min(abs(a1 - p), abs(a2 - p)); } template <class T = int, T divided_by = 10> constexpr T PINF() { return std::numeric_limits<T>::max() / divided_by; } template <class T = int, T divided_by = 10> constexpr T MINF() { return std::numeric_limits<T>::lowest() / divided_by; } double My_PI = 2 * acos(0.0); int main() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); long long n, x, y; cin >> n >> x >> y; double dbx = x, dby = y; complex<double> pos = {dbx, dby}; vector<complex<double> > plist; double mind = numeric_limits<double>::max(); double maxd = numeric_limits<double>::lowest(); double px, py; for (int i = 0; i < n; ++i) { cin >> px >> py; plist.push_back({px, py}); complex<double> dxy = pos - plist[i]; double dist = sqrt(norm(dxy)); maxd = max(maxd, dist); mind = min(mind, dist); } if (true) { for (int i = 0; i < n; ++i) { int ni = (i + 1) % n; mind = min(mind, distSP(plist[i], plist[ni], pos)); } } double ret = maxd * maxd * My_PI - mind * mind * My_PI; cout << ret << endl; return 0; }
#include <bits/stdc++.h> double Px, Py, Hx, Hy, Dx, Dy; double D() { double X = (Px > Dx ? Px - Dx : Dx - Px), Y = (Py > Dy ? Py - Dy : Dy - Py); return X * X + Y * Y; } double H() { double X, Y, PX = Dy - Hy, PY = Hx - Dx, HX = Dx - Hx, HY = Dy - Hy, i, j, L, A, B, mHX, mHY, r = 1e18; A = Hx - Px; B = Hy - Py; mHX = -HX; mHY = -HY; L = (PX * mHY - mHX * PY); i = (A * mHY - mHX * B); j = (PX * B - A * PY); i /= L; j /= L; X = Px + i * PX; Y = Py + i * PY; if (((Hx > Dx ? Hx - Dx : Dx - Hx) > 1e-6 && ((X > Hx + 1e-6 && X < Dx - 1e-6) || (X < Hx - 1e-6 && X > Dx + 1e-6))) || ((Hy > Dy ? Hy - Dy : Dy - Hy) > 1e-6 && ((Y > Hy + 1e-6 && Y < Dy - 1e-6) || (Y < Hy - 1e-6 && Y > Dy + 1e-6)))) { HX = Dx; HY = Dy; Dx = X; Dy = Y; r = D(); Dx = HX; Dy = HY; } return r; } int main() { unsigned q; double lo, hi, mi, Fx, Fy; scanf("%u%lf%lf%lf%lf", &q, &Px, &Py, &Dx, &Dy); Fx = Dx; Fy = Dy; for (lo = hi = D(); --q;) { Hx = Dx; Hy = Dy; scanf("%lf%lf", &Dx, &Dy); mi = D(); if (mi < lo) lo = mi; if (mi > hi) hi = mi; mi = H(); if (mi < lo) lo = mi; } Hx = Fx; Hy = Fy; mi = H(); if (mi < lo) lo = mi; printf("%.18lf\n", (hi - lo) * 3.1415926535897932384626433832795); return 0; }
#include <bits/stdc++.h> using namespace std; int n, xs[233333], ys[233333], px, py; int main() { scanf("%d%d%d", &n, &px, &py); for (int i = 0; i < n; i++) { scanf("%d%d", xs + i, ys + i); } double maxd = 0, mind = 20000000000000LL; for (int i = 0; i < n; i++) { maxd = max(maxd, sqrt(double(xs[i] - px) * (xs[i] - px) + double(ys[i] - py) * (ys[i] - py))); } for (int i = 0; i < n; i++) { double x1 = xs[i], y1 = ys[i], x2 = xs[(i + 1) % n], y2 = ys[(i + 1) % n]; double A = y1 - y2, B = x2 - x1, C = x1 * y2 - x2 * y1; double x0 = px, y0 = py; double qx = (B * B * x0 - A * B * y0 - A * C) / (A * A + B * B), qy = (A * A * y0 - A * B * x0 - B * C) / (A * A + B * B); double cd = 20000000000000LL; cd = min(cd, sqrt(double(x1 - px) * (x1 - px) + double(y1 - py) * (y1 - py))); cd = min(cd, sqrt(double(x2 - px) * (x2 - px) + double(y2 - py) * (y2 - py))); if (qx < min(x1, x2) || qx > max(x1, x2)) ; else { cd = min(cd, fabs(A * x0 + B * y0 + C) / sqrt(A * A + B * B)); } mind = min(mind, cd); } printf("%.23lf\n", asin(1) * 2 * (maxd * maxd - mind * mind)); }
#include <bits/stdc++.h> using namespace std; const int N = int(1e5) + 3; int cmpfunc(const void *a, const void *b) { return *(int *)a - *(int *)b; } vector<pair<long long int, long long int> > a[N]; double ax[N]; double ay[N]; double FindDistanceToSegment(double x1, double y1, double x2, double y2, double pointX, double pointY) { double diffX = x2 - x1; double diffY = y2 - y1; if ((diffX == 0) && (diffY == 0)) { diffX = pointX - x1; diffY = pointY - y1; return sqrt(diffX * diffX + diffY * diffY); } double t = ((pointX - x1) * diffX + (pointY - y1) * diffY) / (diffX * diffX + diffY * diffY); if (t < 0) { diffX = pointX - x1; diffY = pointY - y1; } else if (t > 1) { diffX = pointX - x2; diffY = pointY - y2; } else { diffX = pointX - (x1 + t * diffX); diffY = pointY - (y1 + t * diffY); } return diffX * diffX + diffY * diffY; } int main() { double n, x, y; cin >> n >> x >> y; for (int i = 0; i < n; i++) { long long int t1, t2; cin >> t1 >> t2; ax[i] = (double)t1; ay[i] = (double)t2; } double maxi = 0; double mini = DBL_MAX; for (int i = 0; i < n; i++) { maxi = max(maxi, (x - ax[i]) * (x - ax[i]) + (y - ay[i]) * (y - ay[i])); mini = min(mini, (x - ax[i]) * (x - ax[i]) + (y - ay[i]) * (y - ay[i])); } for (int i = 0; i < n - 1; i++) { mini = min(mini, FindDistanceToSegment(ax[i], ay[i], ax[i + 1], ay[i + 1], x, y)); } mini = min(mini, FindDistanceToSegment(ax[0], ay[0], ax[int(n) - 1], ay[int(n) - 1], x, y)); printf("%.8lf\n", double(3.141592653) * (maxi - mini)); return 0; }
#include <bits/stdc++.h> using namespace std; long long x[100010], y[100010]; double d[100010], dd[100010]; int main() { long long n, x0, y0; while (cin >> n >> x0 >> y0) { double minr = 10000000; double maxr = 0.0; for (int i = 0; i < n; i++) { cin >> x[i] >> y[i]; long long rr = (x[i] - x0) * (x[i] - x0) + (y[i] - y0) * (y[i] - y0); d[i] = sqrt((double)rr); minr = min(minr, d[i]); maxr = max(maxr, d[i]); } for (int i = 0; i < n; i++) { int j = (i + 1) % n; long long rr = (x[i] - x[j]) * (x[i] - x[j]) + (y[i] - y[j]) * (y[i] - y[j]); dd[i] = sqrt((double)rr); if (d[i] * d[i] + rr < d[j] * d[j] || d[j] * d[j] + rr < d[i] * d[i]) continue; double a = acos((d[i] * d[i] + d[j] * d[j] - rr) / d[i] / d[j] / 2); double h = d[i] * d[j] * sin(a) / dd[i]; minr = min(minr, h); } double PI = 2.0 * acos((double)0.0); double ans = PI * (maxr * maxr - minr * minr); printf("%.10lf\n", ans); } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 5; long double dy(long double x1, long double y1, long double x2, long double y2) { return sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1)); } long double di(long double x, long double y, long double x1, long double y1, long double x2, long double y2) { long double A = y1 - y2; long double B = x2 - x1; long double C = -x1 * A - y1 * B; long double a = dy(x, y, x1, y1); a = a * a; long double b = dy(x, y, x2, y2); b = b * b; long double c = dy(x1, y1, x2, y2); c = c * c; if (a > b + c) return sqrt(b + 0.0); if (b > a + c) return sqrt(a + 0.0); long double dis = abs(A * x + B * y + C) / sqrt(0.0 + A * A + B * B); return dis; } pair<int, int> a[N]; const long double EPS = 1e-6; int main() { int n, x, y; long double minR = 1e18; long double maxR = -1e18; scanf("%d %d %d", &n, &x, &y); int lastx, lasty; for (int i = 0; i < n; i++) { int xx, yy; scanf("%d %d", &xx, &yy); a[i] = make_pair(xx, yy); minR = min(minR, dy(x, y, xx, yy)); maxR = max(maxR, dy(x, y, xx, yy)); } for (int i = 0; i < n; i++) { int j = (i + 1) % n; long double dim = di(x, y, a[i].first, a[i].second, a[j].first, a[j].second); minR = min(minR, dim); maxR = max(maxR, dim); } long double PI = 3.1415926535897932384626433832795; long double ans = PI * (maxR * maxR - minR * minR); cout.precision(6); cout << fixed << ans << endl; }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 7; const int mod = 1e9 + 7; const double pi = acos(-1.0); struct pt { double x, y; pt() {} pt(int a, int b) : x(a), y(b) {} }; vector<pt> a; bool cmp(pt a, pt b) { return a.x < b.x || a.x == b.x && a.y < b.y; } bool cw(pt a, pt b, pt c) { return a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y) < 0; } bool ccw(pt a, pt b, pt c) { return a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y) > 0; } void convex_hull(vector<pt>& a) { if (a.size() == 1) return; sort(a.begin(), a.end(), &cmp); pt p1 = a[0], p2 = a.back(); vector<pt> up, down; up.push_back(p1); down.push_back(p1); for (int i = 1; i < a.size(); ++i) { if (i == a.size() - 1 || cw(p1, a[i], p2)) { while (up.size() >= 2 && !cw(up[up.size() - 2], up[up.size() - 1], a[i])) up.pop_back(); up.push_back(a[i]); } if (i == a.size() - 1 || ccw(p1, a[i], p2)) { while (down.size() >= 2 && !ccw(down[down.size() - 2], down[down.size() - 1], a[i])) down.pop_back(); down.push_back(a[i]); } } a.clear(); for (int i = 0; i < up.size(); ++i) a.push_back(up[i]); for (int i = down.size() - 2; i > 0; --i) a.push_back(down[i]); } double range(double xa, double ya, double xb, double yb) { xa -= xb, ya -= yb; return sqrt(xa * xa + ya * ya + .0); } inline double dist(double xa, double ya, double xb, double yb, double x, double y) { double vx = xb - xa; double vy = yb - ya; double d = sqrt(vx * vx + vy * vy); vx /= d; vy /= d; double l = 0, r = range(xa, ya, xb, yb), m1, m2, c1, c2; for (int i = 0; i <= 100; ++i) { m1 = l + (r - l) / 3; m2 = r - (r - l) / 3; c1 = range(xa + m1 * vx, ya + m1 * vy, x, y); c2 = range(xa + m2 * vx, ya + m2 * vy, x, y); if (c1 > c2) l = m1; else r = m2; } return range(xa + r * vx, ya + r * vy, x, y); } int n, cx, cy; double d, dd, mn = INT_MAX, mx = INT_MIN; int main() { ios_base::sync_with_stdio(0), cin.tie(0); cin >> n >> cx >> cy; for (int i = 1; i <= n; ++i) { int x, y; cin >> x >> y; a.push_back(pt(x, y)); } for (int i = 0; i < a.size(); ++i) { d = range(a[i].x, a[i].y, cx, cy); if (d < mn) mn = d; if (d > mx) mx = d; if (i > 0) { dd = dist(a[i - 1].x, a[i - 1].y, a[i].x, a[i].y, cx, cy); if (dd < mn) mn = dd; if (dd > mx) mx = dd; } if (i == a.size() - 1) { dd = dist(a[0].x, a[0].y, a[i].x, a[i].y, cx, cy); if (dd < mn) mn = dd; if (dd > mx) mx = dd; } } double ans = pi * (mx * mx - mn * mn); printf("%.7f\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 1e6 + 5; struct point_t { double x, y; }; double cross(point_t const &O, point_t const &A, point_t const &B) { double xOA = A.x - O.x; double yOA = A.y - O.y; double xOB = B.x - O.x; double yOB = B.y - O.y; return xOA * yOB - xOB * yOA; } double PointTOline(point_t const &a, point_t const &b, point_t const &p) { double ap_ab = (b.x - a.x) * (p.x - a.x) + (b.y - a.y) * (p.y - a.y); if (ap_ab <= 0) return sqrt((p.x - a.x) * (p.x - a.x) + (p.y - a.y) * (p.y - a.y)); double d2 = (b.x - a.x) * (b.x - a.x) + (b.y - a.y) * (b.y - a.y); if (ap_ab >= d2) return sqrt((p.x - b.x) * (p.x - b.x) + (p.y - b.y) * (p.y - b.y)); double r = ap_ab / d2; double px = a.x + (b.x - a.x) * r; double py = a.y + (b.y - a.y) * r; return sqrt((p.x - px) * (p.x - px) + (p.y - py) * (p.y - py)); } bool isOnline(point_t const &a, point_t const &b, point_t const &po) { return po.x >= min(a.x, b.x) && po.x <= max(a.x, b.x) && po.y >= min(a.y, b.y) && po.y <= max(a.y, b.y) && (po.x - a.x) * (b.y - a.y) == (po.y - a.y) * (b.x - a.x); } point_t p[MAXN]; int main() { int n; double x, y, a, b; while (~scanf("%d%lf%lf", &n, &x, &y)) { point_t po; po.x = x, po.y = y; double maxx = 0; for (int i = 0; i <= n - 1; i++) { scanf("%lf%lf", &a, &b); double temp = sqrt((a - x) * (a - x) + (b - y) * (b - y)); p[i].x = a, p[i].y = b; if (temp > maxx) maxx = temp; } double minn = PointTOline(p[0], p[1], po); p[n] = p[0]; for (int i = 1; i < n; ++i) minn = min(minn, PointTOline(p[i], p[i + 1], po)); printf("%lf\n", acos(-1) * (maxx * maxx - minn * minn)); } return 0; }
#include <bits/stdc++.h> using namespace std; const double pi = acos(-1.00); const long long inf = 1000000000000000000; double EPS = 1e-12; struct PT { double x, y; PT() {} PT(double x, double y) : x(x), y(y) {} PT(const PT &p) : x(p.x), y(p.y) {} PT operator+(const PT &p) const { return PT(x + p.x, y + p.y); } PT operator-(const PT &p) const { return PT(x - p.x, y - p.y); } PT operator*(double c) const { return PT(x * c, y * c); } PT operator/(double c) const { return PT(x / c, y / c); } }; double dot(PT p, PT q) { return p.x * q.x + p.y * q.y; } double dist2(PT p, PT q) { return dot(p - q, p - q); } double cross(PT p, PT q) { return p.x * q.y - p.y * q.x; } PT RotateCCW90(PT p) { return PT(-p.y, p.x); } PT RotateCW90(PT p) { return PT(p.y, -p.x); } PT RotateCCW(PT p, double t) { return PT(p.x * cos(t) - p.y * sin(t), p.x * sin(t) + p.y * cos(t)); } PT ProjectPointLine(PT a, PT b, PT c) { return a + (b - a) * dot(c - a, b - a) / dot(b - a, b - a); } PT ProjectPointSegment(PT a, PT b, PT c) { double r = dot(b - a, b - a); if (fabs(r) < EPS) return a; r = dot(c - a, b - a) / r; if (r < 0.00) return a; if (r > 1.00) return b; return a + (b - a) * r; } double DistancePointSegment(PT a, PT b, PT c) { return sqrt(dist2(c, ProjectPointSegment(a, b, c))); } vector<PT> v; int main() { int n; cin >> n; PT base; cin >> base.x >> base.y; double near = 1e20; double far = 0.00; for (int i = 1; i <= n; i++) { PT p; cin >> p.x >> p.y; v.push_back(p); far = max(far, sqrt(dist2(p, base))); } for (int i = 0; i < (n - 1); i++) { double dd = DistancePointSegment(v.at(i), v.at(i + 1), base); near = min(near, dd); far = max(far, dd); } double dd = DistancePointSegment(v.at(0), v.at(n - 1), base); near = min(near, dd); far = max(far, dd); double r = near; double R = far; double ans = pi * ((R * R) - (r * r)); cout.precision(20); cout << fixed << ans << endl; return 0; }
#include <bits/stdc++.h> double distance(long long x0, long long y0, double x1, double y1) { return std::sqrt((x0 - x1) * (x0 - x1) + (y0 - y1) * (y0 - y1)); } double line_segment_point_closest_distance(long long px, long long py, long long x1, long long y1, long long x2, long long y2) { long long minx = std::min(x1, x2); long long maxx = std::max(x1, x2); long long miny = std::min(y1, y2); long long maxy = std::max(y1, y2); double xint, yint; if (x1 - x2 == 0) { xint = x2; yint = py; } else if (y1 - y2 == 0) { xint = px; yint = y2; } else { double m1 = (y1 - y2) / static_cast<double>(x1 - x2); double m2 = -1 / m1; xint = (-m2 * px + m1 * x1 + py - y1) / (m1 - m2); yint = m1 * (xint - x1) + y1; } if (xint <= maxx and xint >= minx and yint <= maxy and yint >= miny) { return distance(px, py, xint, yint); } else if (distance(x1, y1, xint, yint) >= distance(x2, y2, xint, yint)) { return distance(px, py, x2, y2); } else { return distance(px, py, x1, y1); } } int main() { long long n, px, py; std::cin >> n >> px >> py; long long fx, fy, lx, ly; std::cin >> fx >> fy; lx = fx; ly = fy; double min = distance(px, py, fx, fy); double max = min; for (long i = 1; i < n; i++) { long long ix, iy; std::cin >> ix >> iy; double dist = distance(px, py, ix, iy); max = std::max(max, dist); dist = line_segment_point_closest_distance(px, py, lx, ly, ix, iy); min = std::min(min, dist); lx = ix; ly = iy; } double dist = line_segment_point_closest_distance(px, py, lx, ly, fx, fy); min = std::min(min, dist); double pi = 3.141592653589793238462643383279502884; std::cout.precision(10); std::cout << pi * (max * max - min * min) << "\n"; return 0; }
#include <bits/stdc++.h> using namespace std; const int M = 1000000007, BIG = 0x3f3f3f3f; const double PI = 3.14159265358979323846, EPS = 0.0000000001; struct Point { double x, y; Point() {} Point(double x, double y) : x(x), y(y) {} Point Rotate(double theta) { double rad = theta * PI / 180.; return {x * cos(rad) - y * sin(rad), x * sin(rad) + y * cos(rad)}; } Point Rotate_Around(double theta, const Point& axis) { double rad = theta * PI / 180.; return {(x - axis.x) * cos(rad) - (y - axis.y) * sin(rad) + axis.x, (x - axis.x) * sin(rad) + (y - axis.y) * cos(rad) + axis.y}; } }; bool operator==(const Point& p1, const Point& p2) { return (fabs(p1.x - p2.x) < EPS) && (fabs(p1.y - p2.y) < EPS); } istream& operator>>(istream& is, Point& _a) { is >> _a.x >> _a.y; return is; } ostream& operator<<(ostream& os, Point& _a) { os << _a.x << " " << _a.y; return os; } double Euclidean_Distance(const Point& _a, const Point& _b) { return hypot(_a.x - _b.x, _a.y - _b.y); } struct Line { double a, b, c; Line() {} Line(double a, double b, double c) : a(a), b(b), c(c) {} Line(const Point& _a, const Point& _b) { if (fabs(_a.x - _b.x) < EPS) { a = 1; b = 0; c = -_a.x; } else { a = -(_a.y - _b.y) / (_a.x - _b.x); b = 1.; c = -(a * _a.x) - _a.y; } } }; Line Perpendicular_Line(const Line& _a, const Point& _p) { double sl = 1. / (_a.a / _a.b); double cc = _p.y - sl * _p.x; return Line(-sl, 1, -cc); } bool Parallel_Lines(const Line& _a, const Line& _b) { return (fabs(_a.a - _b.a) < EPS) && (fabs(_a.b - _b.b) < EPS); } bool operator==(const Line& _a, const Line& _b) { return Parallel_Lines(_a, _b) && (fabs(_a.c - _b.c) < EPS); } Point Intersection(const Line& _a, const Line& _b) { double w = _a.a * _b.b - _b.a * _a.b; if (fabs(w) < EPS) { cout << "Division by zero\n"; exit(0); } return {(_a.b * _b.c - _b.b * _a.c) / w, (_b.a * _a.c - _a.a * _b.c) / w}; } struct Vec { double x, y; Vec() {} Vec(double x, double y) : x(x), y(y) {} Vec(const Point& _a, const Point& _b) : x(_b.x - _a.x), y(_b.y - _a.y) {} Vec Scale(double _s) const { return {x * _s, y * _s}; } double Squared_Norm() { return x * x + y * y; } }; double operator*(const Vec& _a, const Vec& _b) { return _a.x * _b.x + _a.y * _b.y; } double Cross_Product(const Vec& _a, const Vec& _b) { return _a.x * _b.y - _a.y * _b.x; } double Cross_Product(const Point& _a, const Point& _b) { return _a.x * _b.y - _a.y * _b.x; } Point Translate(const Point& _p, const Vec& _v) { return {_p.x + _v.x, _p.y + _v.y}; } Point Closest_Point_In_Line(const Point& _p, const Point& _a, const Point& _b) { Vec ap(_a, _p), ab(_a, _b); double u = ap * ab / ab.Squared_Norm(); return Translate(_a, ab.Scale(u)); } double Distance_To_Line(const Point& _p, const Point& _a, const Point& _b) { return Euclidean_Distance(_p, Closest_Point_In_Line(_p, _a, _b)); } Point Closest_Point_In_Line_Segment(const Point& _p, const Point& _a, const Point& _b) { Vec ap(_a, _p), ab(_a, _b); double u = ap * ab / ab.Squared_Norm(); if (u < 0.0) return {_a.x, _a.y}; if (u > 1.0) return {_b.x, _b.y}; return Translate(_a, ab.Scale(u)); } double Distance_To_Line_Segment(const Point& _p, const Point& _a, const Point& _b) { return Euclidean_Distance(_p, Closest_Point_In_Line_Segment(_p, _a, _b)); } double Angle(const Point& _a, const Point& _o, const Point& _b) { Vec oa(_o, _a), ob(_o, _b); return acos(oa * ob / sqrt(oa.Squared_Norm() * ob.Squared_Norm())); } double Angle_CCW_From_X_Axis(const Point& _a) { if (fabs(_a.x) < EPS) { if (fabs(_a.y) < EPS) return 0; if (_a.y > 0) return PI / 2.; return 3. * PI / 2.; } else if (fabs(_a.y) < EPS) { if (_a.x > 0) return 0; return PI; } double ans = atan(_a.y / _a.x); if (_a.y < 0) ans += PI; return ans; } bool Left_Of_Line(const Point& _p, const Point& _a, const Point& _b) { return Cross_Product(Vec(_a, _b), Vec(_a, _p)) > 0; } bool Collinear(const Point& _p, const Point& _a, const Point& _b) { return fabs(Cross_Product(Vec(_a, _b), Vec(_a, _p))) < EPS; } struct Circle { double radius, area, circumference; Point possible_center1, possible_center2; Circle(double radius) : radius(radius) {} void Init() { area = PI * radius * radius; circumference = 2. * PI * radius; } bool Get_Center(const Point& p1, const Point& p2) { double dSq = (p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y); double det = radius * radius / dSq - 0.25; if (det < 0.) return 0; double h = sqrt(det); possible_center1.x = (p1.x + p2.x) * .5 + (p1.y - p2.y) * h; possible_center1.y = (p1.y + p2.y) * .5 + (p2.x - p1.x) * h; possible_center2.x = (p1.x + p2.x) * .5 + (p2.y - p1.y) * h; possible_center2.y = (p1.y + p2.y) * .5 + (p1.x - p2.x) * h; return 1; } }; struct Triangle { Point p1, p2, p3; double area, s1, s2, s3, semip; void Init() { semip = (s1 + s2 + s3) / 2; area = sqrt(semip * (semip - s1) * (semip - s2) * (semip - s3)); } Triangle(double s1, double s2, double s3) : s1(s1), s2(s2), s3(s3) { Init(); } Triangle(const Point& p1, const Point& p2, const Point& p3) : p1(p1), p2(p2), p3(p3) { s1 = Euclidean_Distance(p1, p2); s2 = Euclidean_Distance(p2, p3); s3 = Euclidean_Distance(p1, p3); Init(); } double Incircle_Radius() { return area / semip; } double Circumcircle_Radius() { return s1 * s2 * s3 / (4. * area); } Point Circumcircle_Center() { Point ans; Point mid1 = Point((p1.x + p2.x) / 2, (p1.y + p2.y) / 2); Point mid2 = Point((p2.x + p3.x) / 2, (p2.y + p3.y) / 2); Line per1 = Perpendicular_Line(Line(p1, p2), mid1); Line per2 = Perpendicular_Line(Line(p2, p3), mid2); return Intersection(per1, per2); } Point Incircle_Center() { double ratio = s1 / s3; Point p = Translate(p2, Vec(p2, p3).Scale(ratio / (1 + ratio))); ratio = s1 / s2; p = Translate(p1, Vec(p1, p3).Scale(ratio / (1 + ratio))); return Intersection(Line(p1, p), Line(p2, p)); } }; struct Polygon { vector<Point> vp; Polygon() {} void Add(const Point& _p) { vp.push_back(_p); } double Perimeter() { double ans = 0.0; for (int i = 0; i < (int)vp.size() - 1; i++) ans += Euclidean_Distance(vp[i], vp[i + 1]); return ans; } double Area() { double ans = 0.0, x1, y1, x2, y2; for (int i = 0; i < (int)vp.size() - 1; i++) { x1 = vp[i].x; x2 = vp[i + 1].x; y1 = vp[i].y; y2 = vp[i + 1].y; ans += (x1 * y2 - x2 * y1); } return fabs(ans) / 2.0; } bool Convex() { int sz = (int)vp.size(); if (sz <= 3) return 0; bool isLeft = Left_Of_Line(vp[2], vp[0], vp[1]); for (int i = 1; i < sz - 1; i++) if (Left_Of_Line(vp[(i + 2) == sz ? 1 : i + 2], vp[i], vp[i + 1]) != isLeft) return 0; return 1; } bool Contains_Point(const Point& _p) { if ((int)vp.size() == 0) return 0; double sum = 0; for (int i = 0; i < (int)vp.size() - 1; i++) { if (Left_Of_Line(vp[i + 1], _p, vp[i])) sum += Angle(vp[i], _p, vp[i + 1]); else sum -= Angle(vp[i], _p, vp[i + 1]); } return fabs(fabs(sum) - 2. * PI) < EPS; } Point Line_Intersect_Seg(const Point& _p, const Point& _q, const Point& _A, const Point& _B) { double a, b, c, u, v; a = _B.y - _A.y; b = _A.x - _B.x; c = _B.x * _A.y - _A.x * _B.y; u = fabs(a * _p.x + b * _p.y + c); v = fabs(a * _q.x + b * _q.y + c); return Point((_p.x * v + _q.x * u) / (u + v), (_p.y * v + _q.y * u) / (u + v)); } Polygon Cut_Polygon(const Point& _a, const Point& _b) { Polygon ans; for (int i = 0; i < (int)vp.size(); i++) { double left1 = Cross_Product(Vec(_a, _b), Vec(_a, vp[i])), left2 = 0; if (i != (int)vp.size() - 1) left2 = Cross_Product(Vec(_a, _b), Vec(_a, vp[i + 1])); if (left1 > -EPS) ans.Add(vp[i]); if (left1 * left2 < -EPS) ans.Add(Line_Intersect_Seg(vp[i], vp[i + 1], _a, _b)); } if (!ans.vp.empty() && !(ans.vp.back() == ans.vp.front())) ans.Add(ans.vp.front()); return ans; } }; vector<Point> Convex_Hull(vector<Point> vp) { int i, j, n = (int)vp.size(); if (n <= 3) { if (!(vp[0] == vp[n - 1])) vp.push_back(vp[0]); return vp; } int P0 = 0; for (i = 1; i < n; i++) if (vp[i].y < vp[P0].y || (vp[i].y == vp[P0].y && vp[i].x > vp[P0].x)) P0 = i; swap(vp[0], vp[P0]); sort(vp.begin() + 1, vp.end(), [vp](const Point& _a, const Point& _b) { if (Collinear(vp[0], _a, _b)) return Euclidean_Distance(vp[0], _a) < Euclidean_Distance(vp[0], _b); double d1x = _a.x - vp[0].x, d1y = _a.y - vp[0].y; double d2x = _b.x - vp[0].x, d2y = _b.y - vp[0].y; return (atan2(d1y, d1x) - atan2(d2y, d2x)) < 0; }); vector<Point> ans; ans.push_back(vp[n - 1]); ans.push_back(vp[0]); ans.push_back(vp[1]); i = 2; while (i < n) { j = (int)ans.size() - 1; if (Left_Of_Line(vp[i], ans[j - 1], ans[j])) ans.push_back(vp[i++]); else ans.pop_back(); } return ans; } double Area_Of_Polygon(const vector<Point> vertices) { double sum = 0.; for (int i = 0; i < vertices.size(); i++) sum += Cross_Product(vertices[i], vertices[(i + 1) % vertices.size()]); return abs(sum) / 2.0; } int n; Point P; vector<Point> p; double Process() { double R = 0, r = Distance_To_Line_Segment(P, p[0], p.back()); for (auto x : p) R = max(R, Euclidean_Distance(x, P)); for (int i = 1; i < n; i++) r = min(r, Distance_To_Line_Segment(P, p[i - 1], p[i])); return PI * (R * R - r * r); } void Output() { double ans = Process(); cout << fixed << setprecision(12) << ans << "\n"; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); while (cin >> n) { cin >> P; p.resize(n); for (int i = 0; i < n; i++) cin >> p[i]; Output(); } return 0; }
#include <bits/stdc++.h> using namespace std; const int max_n = 100000; const double eps = 1e-9; const double pi = atan2(0, -1); int xs[max_n]; int ys[max_n]; double d2(double x1, double y1, double x2, double y2) { return (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2); } double d2_seg(double x, double y, double x1, double y1, double x2, double y2) { double a = (x2 - x1); double b = (y2 - y1); double t = (-1.0) * ((a * (x1 - x) + b * (y1 - y)) / (a * a + b * b)); if (fabs(t - 0.0) < eps) { return d2(x, y, x1, y1); } if (fabs(t - 1.0) < eps) { return d2(x, y, x2, y2); } if (t - 0.0 > -eps && t - 1.0 < eps) { double qx = x1 + a * t, qy = y1 + b * t; return d2(x, y, qx, qy); } return min(d2(x, y, x1, y1), d2(x, y, x2, y2)); } int main() { int N, px, py; scanf("%d %d %d", &N, &px, &py); for (int i = 0; i < N; i++) { scanf("%d %d", &xs[i], &ys[i]); } double farest_d2 = d2(px, py, xs[0], ys[0]); double nearest_d2 = d2_seg(px, py, xs[N - 1], ys[N - 1], xs[0], ys[0]); for (int i = 0; i < N; i++) { double dis2 = d2(px, py, xs[i], ys[i]); if (dis2 > farest_d2) farest_d2 = dis2; } for (int i = 0; i + 1 < N; i++) { double dis2_seg = d2_seg(px, py, xs[i], ys[i], xs[i + 1], ys[i + 1]); if (dis2_seg < nearest_d2) nearest_d2 = dis2_seg; } double area = pi * (farest_d2 - nearest_d2); printf("%.10lf\n", area); return 0; }
#include <bits/stdc++.h> using namespace std; struct pt { double x, y; } ar[100010]; double md(pt v, pt w, pt p) { const double l2 = (w.x - v.x) * (w.x - v.x) + (w.y - v.y) * (w.y - v.y); if (l2 == 0.0) return sqrt((p.x - v.x) * (p.x - v.x) + (p.y - v.y) * (p.y - v.y)); const double t = ((p.x - v.x) * (w.x - v.x) + (p.y - v.y) * (w.y - v.y)) / l2; if (t < 0.0) return sqrt((p.x - v.x) * (p.x - v.x) + (p.y - v.y) * (p.y - v.y)); else if (t > 1.0) return sqrt((p.x - w.x) * (p.x - w.x) + (p.y - w.y) * (p.y - w.y)); struct pt projection; projection.x = v.x + t * (w.x - v.x); projection.y = v.y + t * (w.y - v.y); return sqrt((p.x - projection.x) * (p.x - projection.x) + (p.y - projection.y) * (p.y - projection.y)); } int main() { double dma = -1.0, dmi = 1e20; int n; scanf("%d", &n); int px, py; scanf("%d %d", &px, &py); double PX = px, PY = py; pt P; P.x = PX; P.y = PY; for (int i = 0; i < n; i++) { int x, y; scanf("%d %d", &x, &y); double X = x, Y = y; ar[i].x = X; ar[i].y = Y; dma = max(dma, (X - PX) * (X - PX) + (Y - PY) * (Y - PY)); if (i != 0) dmi = min(dmi, md(ar[i], ar[i - 1], P) * md(ar[i], ar[i - 1], P)); } dmi = min(dmi, md(ar[n - 1], ar[0], P) * md(ar[n - 1], ar[0], P)); printf("%.10lf\n", acos(-1.0) * (dma - dmi)); return 0; }
#include <bits/stdc++.h> using namespace std; int n; struct point { double x, y; } p[100010], o; struct line { double k, b; }; inline double dis(point a, point b) { return (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y); } inline line make_line(point a, point b) { line ret; ret.k = (a.y - b.y) / (a.x - b.x); ret.b = a.y - a.x * ret.k; return ret; } inline double dis_ltop(point a, line b) { return abs(b.k * a.x + -1 * a.y + b.b) / sqrt(1 + b.k * b.k); } inline double dis_ltop(point a, point p, point q) { double d1 = (q.x - p.x) * (a.x - p.x) + (q.y - p.y) * (a.y - p.y); if (d1 <= 0) return dis(a, p); double d2 = dis(p, q); if (d1 >= d2) return dis(a, q); double r = d1 / d2; point pp; pp.x = p.x + (q.x - p.x) * r; pp.y = p.y + (q.y - p.y) * r; return dis(pp, a); } double mx = -1e18, mn = 1e18; int main() { cin >> n >> o.x >> o.y; for (int i = 1; i <= n; ++i) { scanf("%lf%lf", &p[i].x, &p[i].y); double r = dis(p[i], o); mx = max(mx, r); mn = min(mn, r); } for (int i = 1; i <= n; ++i) { int j = i + 1; if (j > n) j -= n; mn = min(mn, dis_ltop(o, p[i], p[j])); } printf("%.18lf", (mx - mn) * acos(-1)); }
#include <bits/stdc++.h> using namespace std; int n; struct node { double x, y; } a[101000], o; double lenmin = 20000000000, lenmax = 0, ans; double dis(node a, node b) { return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y)); } double get_dis(node a, node b, node c) { double alen = dis(b, c); double blen = dis(a, c); double clen = dis(a, b); if (alen * alen + clen * clen <= blen * blen) { return alen; } if (blen * blen + clen * clen <= alen * alen) { return blen; } double s = abs((a.x - c.x) * (b.y - c.y) - (a.y - c.y) * (b.x - c.x)); return s / clen; } void init() { cin >> n >> o.x >> o.y; for (int i = 0; i < n; i++) { cin >> a[i].x >> a[i].y; lenmax = max(lenmax, dis(a[i], o)); } for (int i = 0; i < n; i++) { int j = (i + 1) % n; lenmin = min(lenmin, get_dis(a[i], a[j], o)); } printf("%.10f\n", acos(-1.0) * (lenmax * lenmax - lenmin * lenmin)); } int main() { init(); return 0; }
#include <bits/stdc++.h> using namespace std; const bool testing = false; double pDistance(double x, double y, double x1, double y1, double x2, double y2) { double A = x - x1; double B = y - y1; double C = x2 - x1; double D = y2 - y1; double dot = A * C + B * D; double len_sq = C * C + D * D; double param = -1; if (len_sq != 0) param = dot / len_sq; double xx, yy; if (param < 0) { xx = x1; yy = y1; } else if (param > 1) { xx = x2; yy = y2; } else { xx = x1 + param * C; yy = y1 + param * D; } double dx = x - xx; double dy = y - yy; return dx * dx + dy * dy; } void program() { int n; cin >> n; double x, y; cin >> x >> y; double min = 10e14; double max = 0; double fa, fb, pa, pb; double a, b, c; cin >> fa >> fb; pa = fa; pb = fb; for (int i = 1; i < n; i++) { cin >> a >> b; c = pDistance(x, y, pa, pb, a, b); if (c < min) min = c; c = (x - a) * (x - a) + (y - b) * (y - b); if (c > max) max = c; pa = a; pb = b; } c = pDistance(x, y, fa, fb, a, b); if (c < min) min = c; c = (x - fa) * (x - fa) + (y - fb) * (y - fb); if (c > max) max = c; double r = max - min; r *= 3.141592653589793238463; cout.precision(20); cout << r << endl; } int main() { if (!testing) { program(); return 0; } FILE* fin = NULL; fin = fopen("in.txt", "w+"); fprintf(fin, "4 0 0\n1 1\n-1 1\n-1 2\n1 2\n"); fclose(fin); freopen("in.txt", "r", stdin); printf("test case(1) => expected : \n"); printf("12.566370614359172464\n"); printf("test case(1) => founded : \n"); program(); fin = fopen("in.txt", "w+"); fprintf(fin, "4 1 -1\n0 0\n1 2\n2 0\n1 1\n"); fclose(fin); freopen("in.txt", "r", stdin); printf("test case(2) => expected : \n"); printf("21.991148575128551812\n"); printf("test case(2) => founded : \n"); program(); return 0; }
#include <bits/stdc++.h> using namespace std; void err(istream_iterator<string> it) { cerr << endl; } template <typename T, typename... Args> void err(istream_iterator<string> it, T a, Args... args) { cerr << "[ " << *it << " = " << a << " ] "; err(++it, args...); } double find_dis(double x, double y, double a, double b) { return (x - a) * (x - a) + (y - b) * (y - b); } double find_height(double x, double y, double ax, double ay, double bx, double by) { double area = abs(x * ay + ax * by + bx * y - ax * y - bx * ay - x * by); double base = sqrt((ax - bx) * (ax - bx) + (ay - by) * (ay - by)); double a = find_dis(x, y, ax, ay); double b = find_dis(x, y, bx, by); if (a >= b + base * base or b >= a + base * base) return min(a, b); double h = area / base; return h * h; } int main() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); ; int n, i; double px, py, maxi = DBL_MIN, mini = DBL_MAX; cin >> n >> px >> py; vector<pair<double, double> > v(n + 1); for (i = 0; i < n; i++) { cin >> v[i].first >> v[i].second; maxi = max(maxi, find_dis(px, py, v[i].first, v[i].second)); } v[n] = v[0]; for (i = 0; i < n; i++) { mini = min(mini, find_height(px, py, v[i].first, v[i].second, v[i + 1].first, v[i + 1].second)); } cout << setprecision(15) << fixed << acos(-1) * (maxi - mini) << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int MAX_N = 100000; int N, X, Y; double R, r = 2e18; struct data { int x, y; } A[MAX_N + 5]; int main() { int i; long long a, b, c; double d; scanf("%d %d %d", &N, &X, &Y); for (i = 1; i <= N; i++) scanf("%d %d", &A[i].x, &A[i].y); A[N + 1] = A[1]; for (i = 1; i <= N; i++) { R = max(R, (double)(A[i].x - X) * (A[i].x - X) + (double)(A[i].y - Y) * (A[i].y - Y)); } for (i = 1; i <= N; i++) { r = min(r, (double)(A[i].x - X) * (A[i].x - X) + (double)(A[i].y - Y) * (A[i].y - Y)); } for (i = 1; i <= N; i++) { if (A[i].x == A[i + 1].x) { a = 1, b = 0, c = A[i].x; } else if (A[i].y == A[i + 1].y) { a = 0, b = -1, c = A[i].y; } else { a = (A[i + 1].y - A[i].y); b = -(A[i + 1].x - A[i].x); c = -(a * A[i].x + b * A[i].y); } d = (double)(a * X + b * Y + c) * (a * X + b * Y + c) / (double)(a * a + b * b); if ((double)(A[i].x - X) * (A[i].x - X) + (double)(A[i].y - Y) * (A[i].y - Y) < (double)(A[i + 1].x - X) * (A[i + 1].x - X) + (double)(A[i + 1].y - Y) * (A[i + 1].y - Y)) { if ((double)(A[i + 1].x - X) * (A[i + 1].x - X) + (double)(A[i + 1].y - Y) * (A[i + 1].y - Y) - d > (double)(A[i + 1].x - A[i].x) * (A[i + 1].x - A[i].x) + (double)(A[i + 1].y - A[i].y) * (A[i + 1].y - A[i].y)) continue; } else { if ((double)(A[i].x - X) * (A[i].x - X) + (double)(A[i].y - Y) * (A[i].y - Y) - d > (double)(A[i + 1].x - A[i].x) * (A[i + 1].x - A[i].x) + (double)(A[i + 1].y - A[i].y) * (A[i + 1].y - A[i].y)) continue; } r = min(r, d); } printf("%.12f", (R - r) * 3.14159265358979); return 0; }
#include <bits/stdc++.h> using namespace std; struct point { double x, y; } p[100005], t; int n; double dis(point a, point b) { return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y)); } double dot(point a, point b) { return a.x * b.x + a.y * b.y; } double len(point a) { return sqrt(dot(a, a)); } double point_to_segment(point a, point b, point c) { point v1, v2, v3; v1.x = c.x - b.x; v1.y = c.y - b.y; v2.x = a.x - b.x; v2.y = a.y - b.y; v3.x = a.x - c.x; v3.y = a.y - c.y; if (dot(v1, v2) < 0) return len(v2); else if (dot(v1, v3) > 0) return len(v3); else return fabs((v1.x * v2.y - v2.x * v1.y) / len(v1)); } int main() { scanf("%d", &n); scanf("%lf%lf", &t.x, &t.y); for (int i = 0; i < n; i++) scanf("%lf%lf", &p[i].x, &p[i].y); p[n].x = p[0].x; p[n].y = p[0].y; double Max = 0; double Min = 1000000000.0; for (int i = 0; i < n; i++) { Max = max(Max, dis(t, p[i])); Min = min(Min, point_to_segment(t, p[i], p[i + 1])); } printf("%0.10f\n", Max * Max * acos(-1.0) - Min * Min * acos(-1.0)); return 0; }
#include <bits/stdc++.h> using namespace std; const int M = 1000000007; const int MM = 998244353; const long double PI = acos(-1); template <typename T, typename U> static inline void amin(T &x, U y) { if (y < x) x = y; } template <typename T, typename U> static inline void amax(T &x, U y) { if (x < y) x = y; } template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &p) { return os << '(' << p.first << "," << p.second << ')'; } struct Point { long long x, y; Point() {} Point(long long x_, long long y_) { x = x_; y = y_; } friend istream &operator>>(istream &i, Point &p) { return i >> p.x >> p.y; } double dis(Point &p) { return sqrt(pow(p.x - x, 2) + pow(p.y - y, 2)); } long long cross(Point r) { return x * r.y - y * r.x; } }; Point operator-(Point &l, Point &r) { return Point(l.x - r.x, l.y - r.y); } int _runtimeTerror_() { int n; Point P; cin >> n >> P; vector<Point> p(n); for (int i = 0; i < n; ++i) cin >> p[i]; double max = 0, min = 1e9; for (int i = 0; i < n; ++i) { amax(max, P.dis(p[i])); amin(min, P.dis(p[i])); Point d = p[i] - p[(i + 1) % n]; swap(d.x, d.y); d.x *= -1; if (((p[i] - P).cross(d) > 0 ? 1 : -1) * ((p[(i + 1) % n] - P).cross(d) > 0 ? 1 : -1) < 0) amin(min, abs((p[i] - P).cross(p[(i + 1) % n] - p[i]) / p[i].dis(p[(i + 1) % n]))); } cout << fixed << setprecision(20); cout << acos(-1) * (max * max - min * min); return 0; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int TESTS = 1; while (TESTS--) _runtimeTerror_(); return 0; }
#include <bits/stdc++.h> using namespace std; using vi = vector<int>; using pi = pair<int, int>; using vs = vector<string>; using vpi = vector<pi>; using ll = long long int; template <typename T> string tostr(T x) { ostringstream oss; oss << x; return oss.str(); } template <typename T1, typename T2, typename T3> T1 modpow(T1 a, T2 p, T3 mod) { T1 ret = 1; a %= mod; for (; p > 0; p /= 2) { if (p & 1) ret = 1ll * ret * a % mod; a = 1ll * a * a % mod; } return ret; } int dx[]{-1, 0, 1, 0, 1, 1, -1, -1}; int dy[]{0, -1, 0, 1, 1, -1, 1, -1}; constexpr auto PI = 3.14159265358979323846L; constexpr auto oo = numeric_limits<ll>::max() / 2 - 10; constexpr auto eps = 1e-7; constexpr auto mod = 1000000007; constexpr int mx = 100005; struct PT { double x, y; PT() {} PT(double x, double y) : x(x), y(y) {} PT(const PT& p) : x(p.x), y(p.y) {} PT operator+(const PT& p) const { return PT(x + p.x, y + p.y); } PT operator-(const PT& p) const { return PT(x - p.x, y - p.y); } PT operator*(double c) const { return PT(x * c, y * c); } PT operator/(double c) const { return PT(x / c, y / c); } }; double dot(PT p, PT q) { return p.x * q.x + p.y * q.y; } double dist2(PT p, PT q) { return dot(p - q, p - q); } double cross(PT p, PT q) { return p.x * q.y - p.y * q.x; } PT RotateCCW90(PT p) { return PT(-p.y, p.x); } PT RotateCW90(PT p) { return PT(p.y, -p.x); } PT RotateCCW(PT p, double t) { return PT(p.x * cos(t) - p.y * sin(t), p.x * sin(t) + p.y * cos(t)); } PT ProjectPointLine(PT a, PT b, PT c) { return a + (b - a) * dot(c - a, b - a) / dot(b - a, b - a); } PT ProjectPointSegment(PT a, PT b, PT c) { double r = dot(b - a, b - a); if (fabs(r) < eps) return a; r = dot(c - a, b - a) / r; if (r < 0) return a; if (r > 1) return b; return a + (b - a) * r; } long double DistancePointSegment(PT a, PT b, PT c) { return sqrt(dist2(c, ProjectPointSegment(a, b, c))); } int main() { int px, py, n, x, y; long double r1, r2; r1 = oo, r2 = -oo; scanf("%d %d %d", &n, &px, &py); long double ans; PT last(-1, -1), cur, fs; for (auto i = 0, _i = (n); i < _i; ++i) { scanf("%d %d", &x, &y); ll dx = x - px, dy = y - py; r2 = max(r2, sqrt(1.0L * dx * dx + 1.0L * dy * dy)); cur = PT(x, y); if (i) { r1 = min(r1, DistancePointSegment(cur, last, PT(px, py))); } else { fs = cur; } last = cur; } r1 = min(r1, DistancePointSegment(fs, last, PT(px, py))); ; ans = PI * (r2 * r2 - r1 * r1); std::cout << std::fixed; std::cout << std::setprecision(9); cout << ans << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const double PI = 3.14159265358979311599796346854; struct point { double x, y; }; struct vect { double x, y; }; bool isABCSharp(point a, point b, point c) { vect ba = {a.x - b.x, a.y - b.y}; vect bc = {c.x - b.x, c.y - b.y}; double scalar = ba.x * bc.x + ba.y * bc.y; return scalar > 0; } double dist(point p, point a, point b) { double x0 = p.x, y0 = p.y, x1 = a.x, y1 = a.y, x2 = b.x, y2 = b.y, x, y; x = (x0 * (x1 - x2) * (x1 - x2) + y0 * (y1 - y2) * (x1 - x2) - (y1 - y2) * (x1 * y2 - x2 * y1)) / ((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)); y = (x0 * (x1 - x2) * (y1 - y2) + y0 * (y1 - y2) * (y1 - y2) + (x1 - x2) * (x1 * y2 - x2 * y1)) / ((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)); return sqrt((x - x0) * (x - x0) + (y - y0) * (y - y0)); } int main() { int n; cin >> n; point p; cin >> p.x >> p.y; vector<point> points(n); for (int i = 0; i < n; i++) cin >> points[i].x >> points[i].y; double far = 0, close = numeric_limits<double>::infinity(); for (int i = 0; i < n; i++) { point a = points[i], b = points[(i + 1) % n]; double min_dist, max_dist; if (isABCSharp(p, a, b) && isABCSharp(p, b, a)) min_dist = dist(p, a, b); else min_dist = min(sqrt((p.x - a.x) * (p.x - a.x) + (p.y - a.y) * (p.y - a.y)), sqrt((p.x - b.x) * (p.x - b.x) + (p.y - b.y) * (p.y - b.y))); max_dist = max(sqrt((p.x - a.x) * (p.x - a.x) + (p.y - a.y) * (p.y - a.y)), sqrt((p.x - b.x) * (p.x - b.x) + (p.y - b.y) * (p.y - b.y))); far = max(far, max_dist); close = min(close, min_dist); } cout << setprecision(30) << PI * (far * far - close * close) << endl; }
#include <bits/stdc++.h> using namespace std; double dist(double x1, double y1, double x2, double y2) { return sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1)); } int main() { long long n; double i, j, x1, y1, x, y, curx, cury, mind, maxd; cin >> n >> i >> j; cin >> x1 >> y1; curx = x1; cury = y1; mind = dist(i, j, x1, y1); maxd = dist(i, j, x1, y1); for (long long k = 1; k < n; k++) { cin >> x >> y; mind = min(dist(i, j, x, y), mind); if (((y - j) * (y - cury) + (x - curx) * (x - i)) * ((cury - j) * (y - cury) + (x - curx) * (curx - i)) < 0) mind = min(abs((j - cury) * (x - curx) - (y - cury) * (i - curx)) / sqrt((x - curx) * (x - curx) + (y - cury) * (y - cury)), mind); maxd = max(dist(i, j, x, y), maxd); curx = x; cury = y; } if (((y1 - j) * (y1 - cury) + (x1 - curx) * (x1 - i)) * ((cury - j) * (y1 - cury) + (x1 - curx) * (curx - i)) < 0) mind = min(abs((j - cury) * (x1 - curx) - (y1 - cury) * (i - curx)) / sqrt((x1 - curx) * (x1 - curx) + (y1 - cury) * (y1 - cury)), mind); cout << fixed << setprecision(18) << acos(-1.0) * (maxd * maxd - mind * mind); return 0; }
#include <bits/stdc++.h> #pragma comment(linker, "/stack:200000000") #pragma GCC optimize("Ofast") #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") using namespace std; const double PI = 3.14159265358979323846; const double maxN = 1e10; double sqr(double a) { return a * a; } struct Point { double x, y; long long int ind; Point(double x0 = 0, double y0 = 0, long long int ind = 0) { this->x = x0; this->y = y0; this->ind = ind; } }; bool operator==(const Point& a, const Point& b) { return a.x == b.x && a.y == b.y; } bool operator<(const Point& a, const Point& b) { return a.x < b.x || (a.x == b.x && a.y < b.y); } struct Vector { double x, y; long long int ind; Vector(double x0 = 0, double y0 = 0) { this->x = x0; this->y = y0; } Vector(const Point& A, const Point& B, long long int ind = 0) { this->x = B.x - A.x; this->y = B.y - A.y; this->ind = ind; } double len() { return sqrt(x * x + y * y); } double angle() const { return atan2(y, x); } }; struct Circle { double x, y, r; Circle(double x0 = 0, double y0 = 0, double r0 = 0) { this->x = x0; this->y = y0; this->r = r0; } Point get_center() { return Point(this->x, this->y); } double getSubS(double ang) { return ang * r; } }; bool operator==(Circle& a, Circle& b) { return a.x == b.x && a.y == b.y && a.r == b.r; } Vector operator/(Vector A, double d) { return Vector(A.x / d, A.y / d); }; Vector operator*(Vector A, double d) { return Vector(A.x * d, A.y * d); }; Point operator+(Point A, Vector B) { return Point(A.x + B.x, A.y + B.y); } struct Line { double a, b, c; Line(double a0 = 0, double b0 = 0, double c0 = 0) { this->a = a0; this->b = b0; this->c = c0; } Line(Point& A, Point& B) { Vector AB(A, B); b = -AB.x; a = AB.y; c = -a * A.x - b * A.y; } Line(Point& A, Vector& C) { Point B = A + C; Line(A, B); } Vector normal() { return Vector(a, b); } Point getPoint() { double x = -(a * c) / (a * a + b * b); double y = -(b * c) / (a * a + b * b); return Point(x, y); } double get(Point& A) { return a * A.x + b * A.y + c; } double perp_sz(const Point& C) { return (a * C.x + b * C.y + c) / sqrt(a * a + b * b); } Point proection(const Point& A) { double d = perp_sz(A); Vector n = normal(); n = n / n.len(); Vector n1 = n * d, n2 = n * (-d); Point A1 = A + n1, A2 = A + n2; if (get(A1) == 0) return A1; else return A2; } }; struct Ray { Point A, B; Ray(){}; Ray(Point& A, Point& B) { this->A = A; this->B = B; } }; istream& operator>>(istream& in, Circle& P) { return in >> P.x >> P.y >> P.r; } istream& operator>>(istream& in, Point& P) { return in >> P.x >> P.y; } istream& operator>>(istream& in, Vector& P) { return in >> P.x >> P.y; } istream& operator>>(istream& in, Line& P) { return in >> P.a >> P.b >> P.c; } ostream& operator<<(ostream& out, Point P) { out.precision(20); return out << P.x << " " << P.y; } ostream& operator<<(ostream& out, Vector P) { out.precision(20); return out << P.x << " " << P.y << endl; } ostream& operator<<(ostream& out, Line P) { out.precision(20); return out << P.a << " " << P.b << " " << P.c << endl; } double dot_product(const Vector& A, const Vector& B) { return A.x * B.x + A.y * B.y; } double cross_product(const Vector& A, const Vector& B) { return A.x * B.y - A.y * B.x; } double angle(Vector A, Vector B) { return fabs(atan2(cross_product(A, B), dot_product(A, B))); } Vector ort(Vector A) { return Vector(-A.y, A.x); } bool one(double a, double b) { return a * b >= 0; } Vector rotate_v(const Vector& A, double angle_rad) { return Vector((A.x * cos(angle_rad) - A.y * sin(angle_rad)), (A.x * sin(angle_rad) + A.y * cos(angle_rad))); } Point zero = Point(0, 0); vector<Point> intersect(Line& a, Line& b) { if (cross_product(a.normal(), b.normal()) == 0) return {}; double x = (b.c * a.b - b.b * a.c) / (b.b * a.a - a.b * b.a); double y = (b.c * a.a - a.c * b.a) / (a.b * b.a - b.b * a.a); return {Point(x, y)}; } vector<Point> intersect(Circle& c, Line& a) { if (a.perp_sz(c.get_center()) > c.r) return {}; else if (a.perp_sz(c.get_center()) == c.r) return {a.proection(c.get_center())}; else { Point S = a.proection(c.get_center()); Vector n = ort(a.normal()); n = n / n.len(); double sz = sqrt(sqr(c.r) - sqr(a.perp_sz(c.get_center()))); Vector n1 = n * sz; Vector n2 = n * (-sz); return {S + n1, S + n2}; } } vector<Point> intersect(Circle& a, Circle& b) { Vector AB(a.get_center(), b.get_center()); if (AB.len() > a.r + b.r) return {}; else { double la = 2 * a.x - 2 * b.x; double lb = 2 * a.y - 2 * b.y; double lc = sqr(b.x) + sqr(b.y) - sqr(b.r) - sqr(a.x) - sqr(a.y) + sqr(a.r); Line l(la, lb, lc); return intersect(a, l); } } bool cmpAndrew(const Point& a, const Point& b) { if (a.x == b.x) return a.y < b.y; return a.x < b.x; } bool cw(Point a, Point b, Point c) { return cross_product(Vector(b, a), Vector(b, c)) > 0; } bool ccw(Point a, Point b, Point c) { return cross_product(Vector(b, a), Vector(b, c)) < 0; } vector<Point> Andrew(vector<Point>& points) { sort(points.begin(), points.end(), cmpAndrew); vector<Point> up, down; up.push_back(points[0]); down.push_back(points[0]); Point p1 = points[0], p2 = points.back(); long long int n = (long long int)points.size(); for (long long int i = 1; i < n; i++) { if (i == n - 1 || cw(p1, points[i], p2)) { while (up.size() >= 2 && !cw(up[up.size() - 2], up[up.size() - 1], points[i])) { up.pop_back(); } up.push_back(points[i]); } if (i == n - 1 || ccw(p1, points[i], p2)) { while (down.size() >= 2 && !ccw(down[down.size() - 2], down[down.size() - 1], points[i])) { down.pop_back(); } down.push_back(points[i]); } } vector<Point> convexHall; for (auto i : down) convexHall.push_back(i); for (long long int i = (long long int)up.size() - 2; i >= 1; i--) convexHall.push_back(up[i]); return convexHall; } Point first; struct node { Point now, up, down; node(Point& now) { this->now = now; } node(Point& down, Point& now) { this->down = down; this->now = now; } }; bool cmpGraham(const Point& A, const Point& B) { Vector OA(first, A); Vector OB(first, B); return cross_product(OA, OB) > 0 || (cross_product(OA, OB) == 0 && OA.len() < OB.len()); } vector<node> Graham(vector<Point>& points, unordered_set<long long int>& ind) { first = Point(1e10, 1e10); long long int n = (long long int)points.size(); for (long long int i = 0; i < n; i++) { if (points[i] < first) first = points[i]; } sort(points.begin(), points.end(), cmpGraham); vector<node> convex = {node(points[0]), node(points[0], points[1])}; convex[0].up = points[1]; for (long long int i = 2; i < n; i++) { long long int l = (long long int)convex.size(); Vector oldV(convex[l - 2].now, convex[l - 1].now), newV(convex[l - 1].now, points[i]); while (cross_product(oldV, newV) < 0) { convex.pop_back(); l = (long long int)convex.size(); oldV = Vector(convex[l - 2].now, convex[l - 1].now); newV = Vector(convex[l - 1].now, points[i]); } Point down = convex.back().now; convex.back().up = points[i]; if (cross_product(oldV, newV) == 0) convex.pop_back(); convex.push_back(node(down, points[i])); } convex[0].down = convex.back().now; convex.back().up = convex[0].now; for (auto i : convex) ind.insert(i.now.ind); return convex; } vector<Point> convexHall; vector<Vector> up, down; bool cmpV(const Vector& a, const Vector& b) { return cross_product(a, b) > 0; } void preTangents(vector<Point>& points) { convexHall = Andrew(points); for (long long int i = 0; i < convexHall.size(); i++) { Point A = convexHall[i], B = convexHall[(i + 1) % convexHall.size()]; Vector AB(A, B, i); if (AB.angle() >= 0 || fabs(AB.angle()) == PI) up.push_back(AB); else down.push_back(AB); } sort(up.begin(), up.end(), cmpV); sort(down.begin(), down.end(), cmpV); } vector<Point> tangents(Line& l) { if (convexHall.size() == 1) return {convexHall[0], convexHall[0]}; else if (convexHall.size() == 2) return convexHall; else { Vector n1 = ort(l.normal()); Vector n2 = n1 * -1; long long int ind1, ind2; if (n1.angle() >= 0 || fabs(n1.angle()) == PI) { auto it = lower_bound(up.begin(), up.end(), n1, cmpV); if (it != up.end()) ind1 = (*it).ind; else ind1 = down[0].ind; } else { auto it = lower_bound(down.begin(), down.end(), n1, cmpV); if (it != down.end()) ind1 = (*it).ind; else ind1 = up[0].ind; } if (n2.angle() >= 0 || fabs(n2.angle()) == PI) { auto it = lower_bound(up.begin(), up.end(), n2, cmpV); if (it != up.end()) ind2 = (*it).ind; else ind2 = down[0].ind; } else { auto it = lower_bound(down.begin(), down.end(), n2, cmpV); if (it != down.end()) ind2 = (*it).ind; else ind2 = up[0].ind; } return {convexHall[ind1], convexHall[ind2]}; } } bool intersect_1(double a, double b, double c, double d) { if (a > b) swap(a, b); if (c > d) swap(c, d); return max(a, c) <= min(b, d); } bool intersect(Point& A, Point& B, Point& C, Point& D) { Vector AB(A, B), BA(B, A), AC(A, C), AD(A, D), BC(B, C), BD(B, D); Vector CD(C, D), DC(D, C), DA(D, A), DB(D, B), CA(C, A), CB(C, B); if (cross_product(AB, AC) == 0 && cross_product(AB, AD) == 0) { if (intersect_1(A.x, B.x, C.x, D.x) && intersect_1(A.y, B.y, C.y, D.y)) return true; else return false; } bool ans = (!one(cross_product(AB, AC), cross_product(AB, AD)) && !one(cross_product(CD, CA), cross_product(CD, CB))); return ans; } double dist(Point A, Point B) { Vector AB(A, B); return AB.len(); } double dist(Point A, Point B, Point C) { Vector BC(B, C), CB(C, B), BA(B, A), CA(C, A); Line l(B, C); if (dot_product(BC, BA) >= 0 && dot_product(CB, CA) >= 0) return fabs(l.perp_sz(A)); else if (dot_product(BC, BA) < 0) return dist(A, B); else return dist(A, C); } double dist(Point A, Ray Q) { Point B = Q.A, C = Q.B; Vector BC(B, C), BA(B, A); Line l(B, C); if (dot_product(BC, BA) < 0) return dist(A, B); else return fabs(l.perp_sz(A)); } double dist(Point A, Line L) { return fabs(L.perp_sz(A)); } double dist(Point A, Point B, Point C, Point D) { if (intersect(A, B, C, D)) return 0; else return min({dist(A, C, D), dist(B, C, D), dist(C, A, B), dist(D, A, B)}); } double dist(Point A, Point B, Ray Q) { Point C = Q.A, D = Q.B; Vector CD(C, D); CD = CD * maxN; D = D + CD; return dist(A, B, C, D); } double dist(Point A, Point B, Line L) { Point C = L.getPoint(); Vector n = ort(L.normal()); Vector n1 = n * maxN, n2 = n * (-maxN); C = C + n1; Point D = C + n2; return dist(A, B, C, D); } double dist(Ray Q1, Ray Q2) { Point A = Q1.A, B = Q1.B, C = Q2.A, D = Q2.B; Vector AB(A, B), CD(C, D); AB = AB * maxN; CD = CD * maxN; B = B + AB; D = D + CD; return dist(A, B, C, D); } double dist(Ray Q, Line L) { Point A = Q.A, B = Q.B, C = L.getPoint(); Vector AB(A, B); AB = AB * maxN; B = B + AB; Vector n = ort(L.normal()); Vector n1 = n * maxN, n2 = n * (-maxN); C = C + n1; Point D = C + n2; return dist(A, B, C, D); } double dist(Line L1, Line L2) { Point A = L1.getPoint(); Vector n = ort(L1.normal()); Vector n1 = n * maxN, n2 = n * (-maxN); A = A + n1; Point B = A + n2; Point C = L2.getPoint(); Vector m = ort(L2.normal()); Vector m1 = m * maxN, m2 = m * (-maxN); C = C + m1; Point D = C + m2; return dist(A, B, C, D); } signed main() { Point P; long long int n; cin >> n >> P; vector<Point> a(n); vector<double> b; for (long long int i = 0; i < n; i++) { cin >> a[i]; b.push_back(dist(P, a[i])); } for (long long int i = 0; i < n; i++) { Point A = a[i], B = a[(i + 1) % n]; b.push_back(dist(P, A, B)); } sort(b.begin(), b.end()); cout.precision(20); cout << PI * (b.back() * b.back() - b.front() * b.front()) << "\n"; return 0; }
#include <bits/stdc++.h> using namespace std; struct myk { double x; double y; double distance; }; myk a[100000 + 10]; int n, origin_x, origin_y; double xiao, da; double juli(double xx1, double yy1, double xx2, double yy2) { double xx0 = origin_x, yy0 = origin_y; double temp, temp2; temp = sqrt((xx2 - xx1) * (xx2 - xx1) + (yy2 - yy1) * (yy2 - yy1)); temp2 = (xx1 - xx0) * (yy2 - yy0) - (yy1 - yy0) * (xx2 - xx0); temp2 = fabs(temp2); return (temp2 / temp); } bool isruijiao(double xx1, double yy1, double xx2, double yy2) { int status = 1; double xx0 = origin_x, yy0 = origin_y; if ((xx0 - xx1) * (xx2 - xx1) + (yy0 - yy1) * (yy2 - yy1) < 0) status = 0; if ((xx1 - xx2) * (xx0 - xx2) + (yy1 - yy2) * (yy0 - yy2) < 0) status = 0; return status; } int main(void) { cin >> n >> origin_x >> origin_y; xiao = 1000000000; da = 0; for (int i = 0; i < n; i++) { scanf("%lf%lf", &a[i].x, &a[i].y); a[i].distance = sqrt(((a[i].x - origin_x) * (a[i].x - origin_x)) + ((a[i].y - origin_y) * (a[i].y - origin_y))); xiao = min(xiao, a[i].distance); da = max(da, a[i].distance); } for (int i = 1; i < n; i++) { if (isruijiao(a[i - 1].x, a[i - 1].y, a[i].x, a[i].y)) xiao = min(xiao, juli(a[i - 1].x, a[i - 1].y, a[i].x, a[i].y)); } if (isruijiao(a[0].x, a[0].y, a[n - 1].x, a[n - 1].y)) xiao = min(xiao, juli(a[0].x, a[0].y, a[n - 1].x, a[n - 1].y)); double temp = da * da - xiao * xiao; printf("%.15lf", acos(-1) * temp); return 0; }
#include <bits/stdc++.h> using namespace std; template <typename T, typename U> std::istream &operator>>(std::istream &i, pair<T, U> &p) { i >> p.first >> p.second; return i; } template <typename T> std::istream &operator>>(std::istream &i, vector<T> &t) { for (auto &v : t) { i >> v; } return i; } template <typename T> std::ostream &operator<<(std::ostream &o, const vector<T> &t) { if (t.empty()) o << '\n'; for (size_t i = 0; i < t.size(); ++i) { o << t[i] << " \n"[i == t.size() - 1]; } return o; } template <typename T, typename U> std::ostream &operator<<(std::ostream &o, pair<T, U> &p) { o << p.first << ' ' << p.second; return o; } template <typename T> using minheap = priority_queue<T, vector<T>, greater<T>>; template <typename T> using maxheap = priority_queue<T, vector<T>, less<T>>; template <typename T> bool in(T a, T b, T c) { return a <= b && b < c; } unsigned int logceil(int first) { return 8 * sizeof(int) - __builtin_clz(first); } namespace std { template <typename T, typename U> struct hash<pair<T, U>> { hash<T> t; hash<U> u; size_t operator()(const pair<T, U> &p) const { return t(p.first) ^ (u(p.second) << 7); } }; } // namespace std template <typename T, typename F> T bsh(T l, T h, const F &f) { T r = -1, m; while (l <= h) { m = (l + h) / 2; if (f(m)) { l = m + 1; r = m; } else { h = m - 1; } } return r; } template <typename F> double bshd(double l, double h, const F &f, double p = 1e-9) { unsigned int r = 3 + (unsigned int)log2((h - l) / p); while (r--) { double m = (l + h) / 2; if (f(m)) { l = m; } else { h = m; } } return (l + h) / 2; } template <typename T, typename F> T bsl(T l, T h, const F &f) { T r = -1, m; while (l <= h) { m = (l + h) / 2; if (f(m)) { h = m - 1; r = m; } else { l = m + 1; } } return r; } template <typename F> double bsld(double l, double h, const F &f, double p = 1e-9) { unsigned int r = 3 + (unsigned int)log2((h - l) / p); while (r--) { double m = (l + h) / 2; if (f(m)) { h = m; } else { l = m; } } return (l + h) / 2; } template <typename T> T gcd(T a, T b) { if (a < b) swap(a, b); return b ? gcd(b, a % b) : a; } template <typename T> class vector2 : public vector<vector<T>> { public: vector2() {} vector2(size_t a, size_t b, T t = T()) : vector<vector<T>>(a, vector<T>(b, t)) {} }; template <typename T> class vector3 : public vector<vector2<T>> { public: vector3() {} vector3(size_t a, size_t b, size_t c, T t = T()) : vector<vector2<T>>(a, vector2<T>(b, c, t)) {} }; template <typename T> class vector4 : public vector<vector3<T>> { public: vector4() {} vector4(size_t a, size_t b, size_t c, size_t d, T t = T()) : vector<vector3<T>>(a, vector3<T>(b, c, d, t)) {} }; template <typename T> class vector5 : public vector<vector4<T>> { public: vector5() {} vector5(size_t a, size_t b, size_t c, size_t d, size_t e, T t = T()) : vector<vector4<T>>(a, vector4<T>(b, c, d, e, t)) {} }; template <typename T> struct bounded_priority_queue { inline bounded_priority_queue(unsigned int X) : A(X), B(0), s(0) {} inline void push(unsigned int L, T V) { B = max(B, L); A[L].push(V); ++s; } inline const T &top() const { return A[B].front(); } inline void pop() { --s; A[B].pop(); while (B > 0 && A[B].empty()) --B; } inline bool empty() const { return A[B].empty(); } inline void clear() { s = B = 0; for (auto &a : A) a = queue<T>(); } inline unsigned int size() const { return s; } private: vector<queue<T>> A; unsigned int B; int s; }; constexpr double PI = 3.14159265358979323846; template <typename T> struct Segment; template <typename T> struct Point : public pair<T, T> { Point(T a = 0, T b = 0) : pair<T, T>(a, b) {} Point(const pair<T, T> &p) : pair<T, T>(p.first, p.second) {} Point(const Point<T> &p) = default; Point<T> &operator=(const Point<T> &p) = default; T squaredDistance(const Point<T> &o) const { return Segment<T>{*this, o}.squaredLength(); } double distance(const Point<T> &o) const { return Segment<T>{*this, o}.length(); } }; template <typename T> ostream &operator<<(ostream &o, const Point<T> &p) { o << p.first << ' ' << p.second; return o; } template <typename T> T ccw(const Point<T> &a, const Point<T> &b, const Point<T> &c) { return (b.first - a.first) * (c.second - a.second) - (b.second - a.second) * (c.first - a.first); } template <typename T> T area(const Point<T> &a, const Point<T> &b, const Point<T> &c) { return abs(ccw(a, b, c)); } template <typename T> double cosangle(const Point<T> &a, const Point<T> &b, const Point<T> &c) { return ((b.first - a.first) * (c.first - a.first) + (b.second - a.second) * (c.second - a.second)) / a.distance(b) / a.distance(c); } template <typename T> double angle(const Point<T> &a, const Point<T> &b, const Point<T> &c) { return acos(cosangle(a, b, c)); } template <typename T> int orientation(const Point<T> &a, const Point<T> &b, const Point<T> &c) { auto o = ccw(a, b, c); return (o > 1e-6) - (o < -1e-6); } template <typename T> bool collinear(const Point<T> &a, const Point<T> &b, const Point<T> &c) { return orientation(a, b, c) == 0; } template <typename T> struct Segment : public pair<Point<T>, Point<T>> { using pair<Point<T>, Point<T>>::first; using pair<Point<T>, Point<T>>::second; explicit Segment(Point<T> a = {0, 0}, Point<T> b = {0, 0}) : pair<Point<T>, Point<T>>(a, b) {} Segment(const Segment<T> &) = default; Segment<T> &operator=(const Segment<T> &) = default; inline T dx() const { return first.first - second.first; } inline T dy() const { return first.second - second.second; } T squaredLength() const { return dx() * dx() + dy() * dy(); } double length() const { return sqrt(squaredLength()); } bool contains(const Point<T> &q) const { return collinear(first, q, second) && ((q.first <= max(first.first, second.first) && q.first >= min(first.first, second.first)) || (q.second <= max(first.second, second.second) && q.second >= min(first.second, second.second))); } double distance(const Point<T> &p) const { double u = ((p.first - second.first) * dx() + (p.second - second.second) * dy()) / double(dx() * dx() + dy() * dy()); if (u > 1) u = 1; if (u < 0) u = 0; return Point<double>(p.first, p.second) .distance({second.first + u * dx(), second.second + u * dy()}); } bool intersect(const Segment<T> &s) const { return (orientation(first, second, s.first) != orientation(first, second, s.second) && orientation(s.first, s.second, first) != orientation(s.first, s.second, second)) || contains(s.first) || contains(s.second) || s.contains(first) || s.contains(second); } }; template <typename T> struct Line : public pair<Point<T>, Point<T>> { using pair<Point<T>, Point<T>>::first; using pair<Point<T>, Point<T>>::second; Line(Point<T> a = {0, 0}, Point<T> b = {0, 0}) : pair<Point<T>, Point<T>>(a, b) {} explicit Line(const Segment<T> &s) : pair<Point<T>, Point<T>>(s.first, s.second) {} Line(const Line<T> &p) = default; Line<T> &operator=(const Line<T> &p) = default; inline T dx() const { return first.first - second.first; } inline T dy() const { return first.second - second.second; } inline T c() const { return first.second * second.first - first.first * second.second; } double distance(const Point<T> &p) const { long long px = dx(), py = dy(), dL = px * px + py * py; return abs(py * p.first - px * p.second + second.first * first.second - second.second * first.first) / sqrt(dL); } Point<double> project(const Point<T> &p) const { double u = ((p.first - second.first) * dx() + (p.second - second.second) * dy()) / double(dx() * dx() + dy() * dy()); return {second.first + u * dx(), second.second + u * dy()}; } bool parallel(const Line<T> &l) const { return abs(l.dx() * dy() - l.dy() * dx()) < 1e-6; } Point<double> intersection(const Line<T> &l) { double det = l.dx() * dy() - l.dy() * dx(); if (abs(det) < 1e-6) return {1e300, 1e300}; else { double c1 = c(), c2 = l.c(); double first = -(c2 * dx() - l.dx() * c1) / det; double second = -(-l.dy() * c1 + c2 * dy()) / det; return {first, second}; } }; }; template <typename T> struct Circle { Point<T> center; T radius; bool intersect(const Circle<T> &o) const { return o.center.squaredDistance(center) <= (radius + o.radius) * (radius + o.radius); } bool contains(const Point<T> &p) const { return p.squaredDistance(center) <= radius * radius; } bool contains(const Circle<T> &o) const { return radius >= o.radius && center.squaredDistance(center) <= (radius - o.radius) * (radius - o.radius); } bool touches(const Circle<T> &o) const { T dist = center.squaredDistance(center); return dist == (radius - o.radius) * (radius - o.radius) || dist == (radius + o.radius) * (radius + o.radius); } }; template <typename T> struct Polygon : public vector<Point<T>> { using vector<Point<T>>::vector; using vector<Point<T>>::at; using vector<Point<T>>::front; using vector<Point<T>>::back; T doubleSignedArea() const { if (this->empty()) return T(0); T area = back().first * front().second - back().second * front().first; for (int i = 0; i < this->size() - 1; ++i) area += (at(i).first * at(i + 1).second - at(i + 1).first * at(i).second); return area; } double circumference() const { if (this->empty()) return T(0); T res = back().distance(front()); for (int i = 0; i < this->size() - 1; ++i) res += at(i).distance(at(i + 1)); return res; } }; template <typename T> Polygon<T> convexhull(const vector<Point<T>> &v) { unsigned int N = (unsigned int)v.size(); vector<Point<T>> w(N + 1); int lo = 0; for (int i = 0; i < N; ++i) if (v[i].second < v[lo].second) lo = i; Point<T> o = v[lo]; for (int i = 0; i < N; ++i) w[i + 1] = {v[i].first - o.first, v[i].second - o.second}; swap(w[1], w[lo + 1]); sort(w.begin() + 2, w.end(), [](Point<T> &a, Point<T> &b) { if (a.second == 0 && a.first > 0) return true; if (b.second == 0 && b.first > 0) return false; if (a.second > 0 && b.second < 0) return true; return !(a.second < 0 && b.second > 0) && (a.first * b.second - a.second * b.first) > 1e-6; }); w[0] = w[N]; unsigned int M = 1; for (int i = 2; i <= N; ++i) { while (ccw(w[M - 1], w[M], w[i]) <= 0) if (M > 1) --M; else if (i == N) break; else ++i; ++M; swap(w[M], w[i]); } Polygon<T> res(M); for (int i = 0; i < M; ++i) res[i] = {w[i + 1].first + o.first, w[i + 1].second + o.second}; return res; } class TaskA { public: void solve(istream &cin, ostream &cout) { int N; cin >> N; double lo = 1e12; double hi = 0; Point<long long> P; cin >> P; vector<Point<long long>> R(N); cin >> R; for (int i = 0; i < N; ++i) { double dist = R[i].distance(P); lo = min(lo, dist); hi = max(hi, dist); } for (int i = 0; i < N; ++i) { auto a = R[i]; auto b = R[(i + 1) % N]; Segment<long long> S{a, b}; double dist = S.distance(P); lo = min(lo, dist); hi = max(hi, dist); } double ans = PI * (hi * hi - lo * lo); cout << fixed << setprecision(10) << ans << endl; } }; int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); TaskA solver; std::istream &in(std::cin); std::ostream &out(std::cout); solver.solve(in, out); return 0; }
#include <bits/stdc++.h> using namespace std; using std::string; typedef long long ll; ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; } ll my_exp(ll a, ll b) { if (b == 0) { return 1; } else { ll temp = my_exp(a, b / 2); temp *= temp; if (b % 2 == 1) { temp *= a; } return temp; } } double FindDistanceToSegment(double x1, double y1, double x2, double y2, double pointX, double pointY) { double diffX = x2 - x1; float diffY = y2 - y1; if ((diffX == 0) && (diffY == 0)) { diffX = pointX - x1; diffY = pointY - y1; return sqrt(diffX * diffX + diffY * diffY); } float t = ((pointX - x1) * diffX + (pointY - y1) * diffY) / (diffX * diffX + diffY * diffY); if (t < 0) { diffX = pointX - x1; diffY = pointY - y1; } else if (t > 1) { diffX = pointX - x2; diffY = pointY - y2; } else { diffX = pointX - (x1 + t * diffX); diffY = pointY - (y1 + t * diffY); } return sqrt(diffX * diffX + diffY * diffY); } int main() { double n, mini = 10000000, maxi = 0; pair<double, double> p, a, first, b; std::cin >> n >> p.first >> p.second; std::cin >> a.first >> a.second; mini = min(mini, sqrt(pow(double(p.first - a.first), 2) + pow(double(p.second - a.second), 2))); maxi = max(maxi, sqrt(pow(double(p.first - a.first), 2) + pow(double(p.second - a.second), 2))); first = a; for (ll i = 1; i < n; i++) { b = a; std::cin >> a.first >> a.second; mini = min(min(mini, sqrt(pow(double(p.first - a.first), 2) + pow(double(p.second - a.second), 2))), FindDistanceToSegment(a.first, a.second, b.first, b.second, p.first, p.second)); maxi = max(maxi, sqrt(pow(double(p.first - a.first), 2) + pow(double(p.second - a.second), 2))); } mini = min(mini, FindDistanceToSegment(a.first, a.second, first.first, first.second, p.first, p.second)); std::cout << setprecision(20) << 3.141592653589793238462643383279502884197169399375105820974944592307816406286 * (maxi * maxi - mini * mini) << std::endl; return 0; }
#include <bits/stdc++.h> using namespace std; template <class T> int getbit(int i, T X) { return (X & (1 << (i - 1))); } template <class T> T onbit(int i, T X) { return (X | (1 << (i - 1))); } template <class T> T offbit(int i, T X) { return (X | (1 << (i - 1)) - (1 << (i - 1))); } template <class T> T sqr(T x) { return (x * x); } template <class T> T cube(T x) { return (x * x * x); } template <class T> T gcd(T a, T b) { T r; while (b != 0) { r = a % b; a = b; b = r; } return a; } template <class T> T lcm(T a, T b) { return a / gcd(a, b) * b; } int csx[4] = {0, 0, -1, 1}; int csy[4] = {-1, 1, 0, 0}; const int MOD = 1000000007; const long long infi = 1e18; const int maxn = 1e5; const long double PI = 2 * acos(0.0); int n; pair<long double, long double> G, P[maxn + 5]; void enter() { cin >> n; cin >> G.first >> G.second; for (int i = 1; i <= n; i++) cin >> P[i].first >> P[i].second; } long double distance(pair<long double, long double> A, pair<long double, long double> B, pair<long double, long double> C) { long double ans = sqr((A.first - C.first) * (B.second - A.second) - (B.first - A.first) * (A.second - C.second)) / (sqr(B.second - A.second) + sqr(B.first - A.first)); return ans; } long double dis(pair<long double, long double> A, pair<long double, long double> B) { return (sqr(A.first - B.first) + sqr(A.second - B.second)); } void solve() { long double fmax = -1; long double fmin = 1e18; P[n + 1] = P[1]; for (int i = 1; i <= n; i++) { fmax = max(fmax, dis(G, P[i])); fmin = min(fmin, dis(P[i], G)); } for (int i = 1; i <= n; i++) { double z = dis(P[i + 1], P[i]); double x = dis(G, P[i]); double y = dis(G, P[i + 1]); if (x + z < y) continue; if (y + z < x) continue; fmin = min(fmin, distance(P[i], P[i + 1], G)); } long double ans = PI * (fmax - fmin); cout << fixed; cout << setprecision(18) << ans; } int main() { enter(); solve(); return 0; }
#include <bits/stdc++.h> #pragma GCC optimize("O3") #pragma GCC target("tune=native") using namespace std; const int MAX = 1e5 + 5; const long long MOD = 1000000007; const long long MOD2 = 2010405347; const long long INF = 9e18; const int dr[] = {1, 0, -1, 0, 1, 1, -1, -1, 0}; const int dc[] = {0, 1, 0, -1, 1, -1, 1, -1, 0}; const double pi = acos(-1); const double EPS = 1e-9; const int block = 315; inline long long pw(long long x, long long y, long long md = MOD) { long long ret = 1; while (y) { if (y & 1) ret = ret * x % md; x = x * x % md, y >>= 1; } return ret; } inline void add(int &a, int b, int md = MOD) { a = a + b >= md ? a + b - md : a + b; } int n; array<long long, 2> p, x[MAX]; array<double, 2> c; long long mx, z; double mn, len, prj; long long dot(array<long long, 2> a, array<long long, 2> b) { return a[0] * b[0] + a[1] * b[1]; } int main() { cout << fixed << setprecision(10); ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n >> p[0] >> p[1]; mn = INF; for (int i = (1); i <= (n); ++i) { cin >> x[i][0] >> x[i][1]; z = (x[i][0] - p[0]) * (x[i][0] - p[0]) + (x[i][1] - p[1]) * (x[i][1] - p[1]); mx = max(mx, z); mn = min(mn, (double)z); } for (int i = (1); i <= (n); ++i) { int j = i == 1 ? n : i - 1; len = hypot(x[j][0] - x[i][0], x[j][1] - x[i][1]); prj = dot({x[j][0] - x[i][0], x[j][1] - x[i][1]}, {p[0] - x[i][0], p[1] - x[i][1]}) / len; if (prj < 0.0 || prj > len) continue; prj /= len; c = {x[i][0] + (x[j][0] - x[i][0]) * prj, x[i][1] + (x[j][1] - x[i][1]) * prj}; mn = min(mn, (p[0] - c[0]) * (p[0] - c[0]) + (p[1] - c[1]) * (p[1] - c[1])); } cout << (mx - mn) * pi << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; vector<pair<long double, long double> > v; pair<long double, long double> p; int n; bool valid(long double len) { bool posi = false; for (int i = 1; i <= n; i++) { long double x1, x2, y1, y2; y1 = v[i - 1].second - p.second; y2 = v[i].second - p.second; x1 = v[i - 1].first - p.first; x2 = v[i].first - p.first; long double p12, p22, p1p2; long double a, b, c; p12 = x1 * x1 + y1 * y1; p22 = x2 * x2 + y2 * y2; p1p2 = x1 * x2 + y1 * y2; a = p12 + p22 - p1p2 * 2.0; b = p1p2 * 2.0 - p12 * 2.0; c = p12 - len * len; if ((b * b - a * c * 4.0) < 0) continue; long double det = b * b - a * c * 4.0; det = sqrt(det); long double alpha = (-b + det) / (a * 2.0); long double beta = (-b - det) / (a * 2.0); if (0 <= alpha && alpha <= 1) posi = true; if (0 <= beta && beta <= 1) posi = true; } return posi; } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cin >> n >> p.first >> p.second; v.resize(n + 2); long double mn, mx = -1; int x, y; for (int i = 0; i < n; i++) { cin >> x >> y; v[i].first = x; v[i].second = y; long double x1, x2, y1, y2; y2 = v[i].second - p.second; x2 = v[i].first - p.first; mx = max(mx, sqrt(x2 * x2 + y2 * y2)); } v[n] = v[0]; long double lo = 0.0, hi = mx; long double mid; long double ans = -1; for (int i = 1; i <= 300; i++) { mid = (lo + hi) / 2; if (valid(mid) == true) { ans = mid; hi = mid; } else lo = mid; } mn = ans; long double pi = acos(-1); ans = pi * (mx * mx - mn * mn); cout << setprecision(32) << ans << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1e6; long long int n, xx0, yy0; long long int x[200010]; long long int y[200010]; long double pi = 3.1415926535897932384626433832795; long double eps = 1e-15; long long int dist(long long int ind) { return (xx0 - x[ind]) * (xx0 - x[ind]) + (yy0 - y[ind]) * (yy0 - y[ind]); } long double sqr(long double a) { return (a * a); } long double dist_p_p(long double ax, long double ay, long double bx, long double by) { return sqr(ax - bx) + sqr(ay - by); } long double dist_p_s(long double ox, long double oy, long double ax, long double ay, long double bx, long double by) { long double l, r, c, cx, cy, cz; l = 0.0; r = 1.0; do { c = (l + r) / 2.0; cx = ax + (bx - ax) * c; cy = ay + (by - ay) * c; if ((ox - cx) * (bx - cx) + (oy - cy) * (by - cy) > 0) l = c; else r = c; } while (r - l > eps); return dist_p_p(ox, oy, cx, cy); } int main() { cin >> n; cin >> xx0 >> yy0; for (int i = 0; i < n; i++) { cin >> x[i] >> y[i]; } int blz = 0; for (int i = 0; i < n; i++) { if (dist(i) < dist(blz)) blz = i; } int dal = 0; for (int i = 0; i < n; i++) { if (dist(i) > dist(dal)) dal = i; } long double distt = dist_p_s(xx0, yy0, x[0], y[0], x[1], y[1]); for (int i = 0; i < n; i++) { if (dist_p_s(xx0, yy0, x[i], y[i], x[(i + 1) % n], y[(i + 1) % n]) < distt) distt = dist_p_s(xx0, yy0, x[i], y[i], x[(i + 1) % n], y[(i + 1) % n]); } long double r1 = pi * distt; long double r2 = pi * dist(dal); printf("%.15llf", r2 - r1); }
#include <bits/stdc++.h> using namespace std; const int MAX_N = 1e6 + 10; const double PI = acos(-1.0); struct Point { double a, b; } p[MAX_N]; double getl(Point X, Point Y) { double d1 = (X.a - Y.a) * (X.a - Y.a); double d2 = (X.b - Y.b) * (X.b - Y.b); return sqrt(d1 + d2); } double getlength(Point A, Point B, Point C, double &temp) { double a = getl(A, C); double b = getl(B, C); double c = getl(A, B); temp = max(a, b); if (a * a >= b * b + c * c) return b; if (b * b >= a * a + c * c) return a; double pp = (a + b + c) / 2; double s = (pp - a) * (pp - b) * (pp - c) * pp; s = sqrt(s); double d = s * 2 / c; return d; } int main() { int n; scanf("%d", &n); Point T; scanf("%lf%lf", &T.a, &T.b); for (int i = 0; i < n; i++) scanf("%lf%lf", &p[i].a, &p[i].b); double maxx = -(double)10000000; double minn = (double)10000000; double temp; for (int i = 0; i < n; i++) { minn = min(minn, getlength(p[i], p[(i + 1) % n], T, temp)); maxx = max(maxx, temp); } double ans = maxx * maxx - minn * minn; ans *= PI; printf("%.10lf\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; int n, i; double p[2], poly[100005][2], minD = 1e18, maxD = 0, d, answer, lo, hi, EPS = 1e-12, mid1, mid2, x, y, d1, d2; int main() { scanf("%d %lf %lf", &n, &p[0], &p[1]); for (i = 0; i < n; i++) { scanf("%lf %lf", &poly[i][0], &poly[i][1]); d = (poly[i][0] - p[0]) * (poly[i][0] - p[0]) + (poly[i][1] - p[1]) * (poly[i][1] - p[1]); maxD = max(maxD, d); } for (i = 0; i < n; i++) { lo = 0; hi = 1; while (hi - lo > EPS) { mid1 = lo + (hi - lo) / 3; mid2 = mid1 + (hi - lo) / 3; x = poly[i][0] + (poly[(i + 1) % n][0] - poly[i][0]) * mid1; y = poly[i][1] + (poly[(i + 1) % n][1] - poly[i][1]) * mid1; d1 = (x - p[0]) * (x - p[0]) + (y - p[1]) * (y - p[1]); x = poly[i][0] + (poly[(i + 1) % n][0] - poly[i][0]) * mid2; y = poly[i][1] + (poly[(i + 1) % n][1] - poly[i][1]) * mid2; d2 = (x - p[0]) * (x - p[0]) + (y - p[1]) * (y - p[1]); if (d1 < d2) hi = mid2; else lo = mid1; } d = d1; minD = min(minD, d); } answer = acos(-1.0) * (maxD - minD); printf("%.18lf\n", answer); return 0; }
#include <bits/stdc++.h> template <typename T> using Vector2D = std::vector<std::vector<T>>; template <typename T> using Vector3D = std::vector<Vector2D<T>>; using PairInt = std::pair<int, int>; using PairInt64 = std::pair<int64_t, int64_t>; using MapInt = std::map<int, int>; using MMapInt = std::multimap<int, int>; using MMapInt64 = std::multimap<int64_t, int64_t>; using UMapIntString = std::unordered_map<int, std::string>; using SetInt = std::set<int>; using SetPairInt64 = std::set<PairInt64>; using VectorInt = std::vector<int>; using VectorInt2D = Vector2D<int>; using VectorInt64 = std::vector<int64_t>; using VectorUInt64 = std::vector<uint64_t>; using VectorInt642D = Vector2D<int64_t>; using VectorChar = std::vector<char>; using VectorChar2D = Vector2D<char>; using VectorString = std::vector<std::string>; using QueuePairInt = std::queue<PairInt>; using QueueInt = std::queue<int>; using VectorPairInt = std::vector<PairInt>; using VectorPairInt64 = std::vector<PairInt64>; using VectorPairInt2D = Vector2D<PairInt>; using SetInt = std::set<int>; using MSetInt = std::multiset<int>; using UMapChar = std::map<char, int>; using ListInt = std::list<int>; using VectorListInt = std::vector<ListInt>; using VectorDouble = std::vector<double>; double get_dist(int64_t x0, int64_t y0, int64_t x1, int64_t y1) { int64_t dx = std::abs(x0 - x1); int64_t dy = std::abs(y0 - y1); return std::sqrt(static_cast<double>(dx) * dx + dy * dy); } double get_h(double a, double b, double c) { double p = (a + b + c) / 2; double s = (p * (p - a) * (p - b) * (p - c)); return 2.0 * std::sqrt(s) / a; } bool is_angle_gt_90(double a, double b, double c) { return a * a > b * b + c * c; } int main() { std::ios::sync_with_stdio(false); int n; int64_t x0; int64_t y0; std::cin >> n >> x0 >> y0; int64_t x1; int64_t y1; std::cin >> x1 >> y1; double dist_x1 = get_dist(x0, y0, x1, y1); double dist_min = dist_x1; double dist_max = dist_x1; double dist_prev = dist_x1; int64_t x_prev = x1; int64_t y_prev = y1; for (int i = 1; i < n; ++i) { int64_t x; int64_t y; std::cin >> x >> y; double dist = get_dist(x0, y0, x, y); double dist_line = get_dist(x, y, x_prev, y_prev); if (!is_angle_gt_90(dist, dist_prev, dist_line) && !is_angle_gt_90(dist_prev, dist, dist_line)) { dist_min = std::min(dist_min, get_h(dist_line, dist, dist_prev)); } dist_min = std::min(dist_min, dist); dist_max = std::max(dist_max, dist); dist_prev = dist; x_prev = x; y_prev = y; } double dist_line = get_dist(x1, y1, x_prev, y_prev); if (!is_angle_gt_90(dist_x1, dist_prev, dist_line) && !is_angle_gt_90(dist_prev, dist_x1, dist_line)) { dist_min = std::min(dist_min, get_h(dist_line, dist_x1, dist_prev)); } double pi = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821; std::cout.precision(15); double s = pi * dist_max * dist_max - pi * dist_min * dist_min; std::cout << s; return 0; }
#include <bits/stdc++.h> using namespace std; int main() { long double const PI = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117; long n; cin >> n; long double Px, Py; cin >> Px >> Py; long double closest_dist = 1000000000000000000, longest_dist = 0; long double inputX, inputY, first_X, first_Y, lastX, lastY; cin >> inputX >> inputY; first_X = inputX; first_Y = inputY; lastX = inputX; lastY = inputY; long double dist = (inputX - Px) * (inputX - Px) + (inputY - Py) * (inputY - Py); closest_dist = min(closest_dist, dist); longest_dist = max(longest_dist, dist); for (long i = 0; i < n - 1; i++) { cin >> inputX >> inputY; dist = (inputX - Px) * (inputX - Px) + (inputY - Py) * (inputY - Py); if (lastX != inputX and lastY != inputY) { long double k = (lastY - inputY) / (long double)(lastX - inputX); long double k2 = -1 / k; long double U = (Py - (k2 * Px) - inputY + k * inputX) / (k - k2); if ((lastX >= U and inputX <= U) or (lastX <= U and inputX >= U)) { long double T = Py + k2 * (U - Px); closest_dist = min(closest_dist, ((Px - U) * (Px - U) + (Py - T) * (Py - T))); } } else { if (lastX == inputX) { if ((lastY >= Py and inputY <= Py) or (lastY <= Py and inputY >= Py)) { closest_dist = min(closest_dist, (inputX - Px) * (inputX - Px)); } } else { if ((lastX >= Px and inputX <= Px) or (lastX <= Px and inputX >= Px)) { closest_dist = min(closest_dist, (inputY - Py) * (inputY - Py)); } } } lastX = inputX; lastY = inputY; closest_dist = min(closest_dist, dist); longest_dist = max(longest_dist, dist); } inputX = first_X; inputY = first_Y; dist = (inputX - Px) * (inputX - Px) + (inputY - Py) * (inputY - Py); if (lastX != inputX and lastY != inputY) { long double k = (lastY - inputY) / (long double)(lastX - inputX); long double k2 = -1 / k; long double U = (Py - (k2 * Px) - inputY + k * inputX) / (k - k2); if ((lastX >= U and inputX <= U) or (lastX <= U and inputX >= U)) { long double T = Py + k2 * (U - Px); closest_dist = min(closest_dist, ((Px - U) * (Px - U) + (Py - T) * (Py - T))); } } else { if (lastX == inputX) { if ((lastY >= Py and inputY <= Py) or (lastY <= Py and inputY >= Py)) { closest_dist = min(closest_dist, (inputX - Px) * (inputX - Px)); } } else { if ((lastX >= Px and inputX <= Px) or (lastX <= Px and inputX >= Px)) { closest_dist = min(closest_dist, (inputY - Py) * (inputY - Py)); } } } cout << setprecision(55) << PI * longest_dist - PI * closest_dist; return 0; }
#include <bits/stdc++.h> using namespace std; double LenghtSq(double x, double y) { return (x * x + y * y); } bool Tup(complex<double> A, complex<double> B, complex<double> C) { return (((A - B).real() * (C - B).real()) + ((A - B).imag() * (C - B).imag())) < 0; } double Area(double a, double b, double c) { double s = (a + b + c) / 2; return sqrt(s * (s - a) * (s - b) * (s - c)); } double Dist(complex<double> A, complex<double> B1, complex<double> B2) { return 2 * Area(abs(A - B1), abs(A - B2), abs(B1 - B2)) / abs(B1 - B2); } int main() { int n; cin >> n; double x, y; cin >> x >> y; vector<complex<double> > a(n); for (int i = 0; i < n; i++) { double c, d; cin >> c >> d; a[i] = complex<double>(c, d); } double Farest = 0; for (double i = 0; i < n; i++) { Farest = max(Farest, LenghtSq(x - a[i].real(), y - a[i].imag())); } double Closest = 10000000000; for (int i = 0; i < n; i++) { complex<double> A = a[i], B = a[(i + 1) % n], C = complex<double>(x, y); if (Tup(A, B, C) || Tup(C, A, B)) { Closest = min(Closest, min(abs(A - C), abs(B - C))); } else Closest = min(Closest, Dist(C, A, B)); } cout << fixed; cout << setprecision(6) << (Farest - Closest * Closest) * 3.1415926535897932384 << endl; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 500100; struct PP { double x, y; PP() {} PP(long long xx, long long yy) { x = xx; y = yy; } void scan() { cin >> x >> y; } PP operator-(PP b) { return PP(x - b.x, y - b.y); } long long operator%(PP b) { return (x * b.y - y * b.x); } long long operator*(PP b) { return (x * b.x + y * b.y); } double len() { return x * x + y * y; } double len(PP p) { return (*this - p).len(); } } P; long long px, py; long long a, b, c; void make_line(PP p, PP q) { a = p.y - q.y; b = q.x - p.x; c = -(a * p.x + b * p.y); } bool f(PP p, PP q) { PP v1 = P - p, v2 = q - p; if (v1 * v2 < 0) return false; v1 = P - q, v2 = p - q; if (v1 * v2 < 0) return false; return true; } int main() { int n; cin >> n; P.scan(); PP p[n], M, m; double r, R; for (int i = 0; i < n; ++i) { p[i].scan(); if (i == 0) { R = p[i].len(P); r = p[i].len(P); } r = min(r, p[i].len(P)); R = max(R, p[i].len(P)); if (i && f(p[i], p[i - 1])) { make_line(p[i], p[i - 1]); double D = (a * P.x + b * P.y + c); D *= D; D /= (double)(a * a + b * b); r = min(r, D); } } if (f(p[0], p[n - 1])) { make_line(p[0], p[n - 1]); double D = (a * P.x + b * P.y + c); D *= D; D /= (double)(a * a + b * b); r = min(r, D); } printf("%.20lf\n", (R - r) * acos(-1.)); return 0; }
#include <bits/stdc++.h> using namespace std; double sq(double a) { return a * a; } struct pos { double y, x; double sqdis(const pos& b) const { return sq(x - b.x) + sq(y - b.y); } double dis(const pos& b) const { return sqrt(sqdis(b)); } double cj(const pos& b) const { return x * b.y - y * b.x; } }; pos p, ps[100000]; int main() { int n; double ty, tx, tmp, mx = 0, mi = 5e12; double dis[3]; int i; scanf("%d", &n); scanf("%lf%lf", &p.x, &p.y); for (i = 0; i < n; i++) { scanf("%lf%lf", &tx, &ty); ps[i].y = ty - p.y; ps[i].x = tx - p.x; } for (i = 0; i < n; i++) { tmp = sq(ps[i].y) + sq(ps[i].x); if (tmp > mx) mx = tmp; } for (i = 0; i < n; i++) { dis[0] = ps[i].sqdis(ps[(i + 1) % n]); dis[1] = ps[i].sqdis((pos){0, 0}); dis[2] = ps[(i + 1) % n].sqdis((pos){0, 0}); if (dis[0] + dis[1] < dis[2] || dis[0] + dis[2] < dis[1]) tmp = min(dis[1], dis[2]); else tmp = sq(ps[i].cj(ps[(i + 1) % n]) / ps[i].dis(ps[(i + 1) % n])); if (tmp < mi) mi = tmp; } printf("%.18lf\n", acos(-1) * (mx - mi)); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 5; const int inf = 0x3f3f3f3f; const double eps = 1e-6; const double pi = acos(-1.0); const int mod = 1e9 + 7; struct Point { double x, y; } p[N]; double dist_P_P(Point a, Point b) { return (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y); } double dist_P_L(Point a, Point b, Point c) { double l1 = dist_P_P(a, b); double l2 = dist_P_P(b, c); double l3 = dist_P_P(c, a); if (l2 * l2 >= l1 * l1 + l3 * l3) return l3; if (l3 * l3 >= l1 * l1 + l2 * l2) return l2; double A = a.y - b.y; double B = b.x - a.x; double C = a.x * b.y - a.y * b.x; double D = A * c.x + B * c.y + C; return fabs(D * D / (A * A + B * B)); } int main() { int n, i; double nea = 1e18, far = 0; scanf("%d", &n); for (i = 0; i <= n; ++i) scanf("%lf%lf", &p[i].x, &p[i].y); for (i = 1; i <= n; ++i) { if (i < n) nea = min(nea, dist_P_L(p[i], p[i + 1], p[0])); else nea = min(nea, dist_P_L(p[n], p[1], p[0])); far = max(far, dist_P_P(p[0], p[i])); } printf("%.18lf\n", pi * (far - nea)); return 0; }
#include <bits/stdc++.h> using namespace std; double esp = 1e-11; #pragma comment(linker, "/STACK:1024000000,1024000000") const double PI = acos(-1.0); const long long int INF = 0x3f3f3f3f3f3f3f3f; const long long int MOD = 1000000007; const int maxn = 100500; struct point { double x, y; point() { x = y = 0; } point(double x, double y) { this->x = x; this->y = y; } point operator*(const double &a) { return point(a * x, a * y); } point operator/(const double &a) { return point(x / a, y / a); } double operator*(const point &a) { return a.x * x + a.y * y; } point operator+(const point &a) { return point(x + a.x, y + a.y); } point operator-(const point &a) { return point(x - a.x, y - a.y); } bool operator<(const point &a) const { return x < a.x - esp || (abs(x - a.x) < esp && y < a.y - esp); } }; point operator*(double const &a, point const &b) { return point(a * b.x, a * b.y); } double cross(point a, point b) { return a.x * b.y - a.y * b.x; } double leng(point a) { return sqrt(a.x * a.x + a.y * a.y); } vector<point> m; double dmax = 0, dmin = INF * 1.0; void f(double ans) { dmax = max(dmax, ans); dmin = min(dmin, ans); } int main() { int n; scanf("%d", &n); int u, v; m.clear(); scanf("%d%d", &u, &v); point p(u, v); point tem; dmax = 0, dmin = INF; double s1, s2, s3, coth; for (int x = 1; x <= n; x++) { scanf("%d%d", &u, &v); tem.x = u; tem.y = v; m.push_back(tem); f(leng(tem - p)); } point a, b; for (int x = 1; x < n; x++) { a = m[x - 1]; b = m[x]; s1 = leng(b - a); s2 = leng(p - b); s3 = leng(p - a); coth = s1 * s1 + s3 * s3 - s2 * s2; coth /= (2.0 * s1 * s3); if (s3 * coth > -esp && s3 * coth < s1 + esp) f(s3 * sqrt(1 - coth * coth)); } a = m[0]; b = m[n - 1]; s1 = leng(b - a); s2 = leng(p - b); s3 = leng(p - a); coth = s1 * s1 + s3 * s3 - s2 * s2; coth /= (2.0 * s1 * s3); if (s3 * coth > -esp && s3 * coth < s1 + esp) f(s3 * sqrt(1 - coth * coth)); double ans = PI * dmax * dmax; ans -= PI * dmin * dmin; printf("%.7f\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; const int M = 500010, mod = 1000000007; const double PI = acos(-1.0); class PT { public: double first, second; PT() {} PT(double first, double second) : first(first), second(second) {} PT(const PT &p) : first(p.first), second(p.second) {} double Magnitude() { return sqrt(first * first + second * second); } PT operator+(const PT &p) const { return PT(first + p.first, second + p.second); } PT operator-(const PT &p) const { return PT(first - p.first, second - p.second); } PT operator*(double c) const { return PT(first * c, second * c); } PT operator/(double c) const { return PT(first / c, second / c); } }; double dot(PT p, PT q) { return p.first * q.first + p.second * q.second; } double dist2(PT p, PT q) { return dot(p - q, p - q); } double dist(PT p, PT q) { return sqrt(dist2(p, q)); } double cross(PT p, PT q) { return p.first * q.second - p.second * q.first; } double myAsin(double a, double b) { if (a / b > 1) return PI * 0.5; if (a / b < -1) return -PI * 0.5; return asin(a / b); } double myAtan(double a, double b) { if (b == 0) return PI * 0.5; return atan(a / b); } ostream &operator<<(ostream &os, const PT &p) { os << "(" << p.first << "," << p.second << ")"; } PT scale(PT p, PT pivot, double c) { PT trans = p - pivot; trans = (trans * c) / trans.Magnitude(); return trans + pivot; } PT RotateCCW90(PT p) { return PT(-p.second, p.first); } PT RotateCW90(PT p) { return PT(p.second, -p.first); } PT RotateCCW(PT p, double t) { return PT(p.first * cos(t) - p.second * sin(t), p.first * sin(t) + p.second * cos(t)); } PT RotateAroundPointCCW(PT p, PT pivot, double t) { PT trans = p - pivot; PT ret = RotateCCW(trans, t); ret = ret + pivot; return ret; } PT Reflection(PT ray, PT normal) { ray = ray / ray.Magnitude(); normal = normal / normal.Magnitude(); return normal * (2 * dot(ray, normal)) - ray; } PT ProjectPointLine(PT a, PT b, PT c) { return a + (b - a) * dot(c - a, b - a) / dot(b - a, b - a); } double DistancePointLine(PT a, PT b, PT c) { return dist(c, ProjectPointLine(a, b, c)); } PT ProjectPointSegment(PT a, PT b, PT c) { double r = dot(b - a, b - a); if (fabs(r) < 1e-12) return a; r = dot(c - a, b - a) / r; if (r < 0) return a; if (r > 1) return b; return a + (b - a) * r; } double DistancePointSegment(PT a, PT b, PT c) { return sqrt(dist2(c, ProjectPointSegment(a, b, c))); } double DistancePointPlane(double first, double second, double z, double a, double b, double c, double d) { return fabs(a * first + b * second + c * z - d) / sqrt(a * a + b * b + c * c); } bool LinesParallel(PT a, PT b, PT c, PT d) { return fabs(cross(b - a, c - d)) < 1e-12; } bool LinesCollinear(PT a, PT b, PT c, PT d) { return LinesParallel(a, b, c, d) && fabs(cross(a - b, a - c)) < 1e-12 && fabs(cross(c - d, c - a)) < 1e-12; } bool SegmentsIntersect(PT a, PT b, PT c, PT d) { if (LinesCollinear(a, b, c, d)) { if (dist2(a, c) < 1e-12 || dist2(a, d) < 1e-12 || dist2(b, c) < 1e-12 || dist2(b, d) < 1e-12) return true; if (dot(c - a, c - b) > 0 && dot(d - a, d - b) > 0 && dot(c - b, d - b) > 0) return false; return true; } if (cross(d - a, b - a) * cross(c - a, b - a) > 0) return false; if (cross(a - c, d - c) * cross(b - c, d - c) > 0) return false; return true; } PT ComputeLineIntersection(PT a, PT b, PT c, PT d) { b = b - a; d = c - d; c = c - a; assert(dot(b, b) > 1e-12 && dot(d, d) > 1e-12); return a + b * cross(c, d) / cross(b, d); } PT ComputeCircleCenter(PT a, PT b, PT c) { b = (a + b) / 2; c = (a + c) / 2; return ComputeLineIntersection(b, b + RotateCW90(a - b), c, c + RotateCW90(a - c)); } bool PointInPolygon(const vector<PT> &p, PT q) { bool c = 0; for (int i = 0; i < p.size(); i++) { int j = (i + 1) % p.size(); if ((p[i].second <= q.second && q.second < p[j].second || p[j].second <= q.second && q.second < p[i].second) && q.first < p[i].first + (p[j].first - p[i].first) * (q.second - p[i].second) / (p[j].second - p[i].second)) c = !c; } return c; } bool PointOnPolygon(const vector<PT> &p, PT q) { for (int i = 0; i < p.size(); i++) if (dist2(ProjectPointSegment(p[i], p[(i + 1) % p.size()], q), q) < 1e-12) return true; return false; } vector<PT> CircleLineIntersection(PT a, PT b, PT c, double r) { vector<PT> ret; b = b - a; a = a - c; double A = dot(b, b); double B = dot(a, b); double C = dot(a, a) - r * r; double D = B * B - A * C; if (D < -1e-12) return ret; ret.push_back(c + a + b * (-B + sqrt(D + 1e-12)) / A); if (D > 1e-12) ret.push_back(c + a + b * (-B - sqrt(D)) / A); return ret; } vector<PT> CircleCircleIntersection(PT a, PT b, double r, double R) { vector<PT> ret; double d = sqrt(dist2(a, b)); if (d > r + R || d + min(r, R) < max(r, R)) return ret; double first = (d * d - R * R + r * r) / (2 * d); double second = sqrt(r * r - first * first); PT v = (b - a) / d; ret.push_back(a + v * first + RotateCCW90(v) * second); if (second > 0) ret.push_back(a + v * first - RotateCCW90(v) * second); return ret; } double ComputeSignedArea(const vector<PT> &p) { double area = 0; for (int i = 0; i < p.size(); i++) { int j = (i + 1) % p.size(); area += p[i].first * p[j].second - p[j].first * p[i].second; } return area / 2.0; } double ComputeArea(const vector<PT> &p) { return fabs(ComputeSignedArea(p)); } PT ComputeCentroid(const vector<PT> &p) { PT c(0, 0); double scale = 6.0 * ComputeSignedArea(p); for (int i = 0; i < p.size(); i++) { int j = (i + 1) % p.size(); c = c + (p[i] + p[j]) * (p[i].first * p[j].second - p[j].first * p[i].second); } return c / scale; } bool IsSimple(const vector<PT> &p) { for (int i = 0; i < p.size(); i++) { for (int k = i + 1; k < p.size(); k++) { int j = (i + 1) % p.size(); int l = (k + 1) % p.size(); if (i == l || j == k) continue; if (SegmentsIntersect(p[i], p[j], p[k], p[l])) return false; } } return true; } double PAngle(PT a, PT b, PT c) { PT temp1(a.first - b.first, a.second - b.second), temp2(c.first - b.first, c.second - b.second); double ans = asin((temp1.first * temp2.second - temp1.second * temp2.first) / (temp1.Magnitude() * temp2.Magnitude())); if ((ans < 0 && (temp1.first * temp2.first + temp1.second * temp2.second) < 0) || (ans >= 0 && (temp1.first * temp2.first + temp1.second * temp2.second) < 0)) ans = PI - ans; ans = ans < 0 ? 2 * PI + ans : ans; return ans; } double SignedArea(PT a, PT b, PT c) { PT temp1(b.first - a.first, b.second - a.second), temp2(c.first - a.first, c.second - a.second); return 0.5 * (temp1.first * temp2.second - temp1.second * temp2.first); } bool XYasscending(PT a, PT b) { if (abs(a.first - b.first) < 1e-12) return a.second < b.second; return a.first < b.first; } void MakeConvexHull(vector<PT> given, vector<PT> &ans) { int i, n = given.size(), j = 0, k = 0; vector<PT> U, L; ans.clear(); sort(given.begin(), given.end(), XYasscending); for (i = 0; i < n; i++) { while (true) { if (j < 2) break; if (SignedArea(L[j - 2], L[j - 1], given[i]) <= 0) j--; else break; } if (j == L.size()) { L.push_back(given[i]); j++; } else { L[j] = given[i]; j++; } } for (i = n - 1; i >= 0; i--) { while (1) { if (k < 2) break; if (SignedArea(U[k - 2], U[k - 1], given[i]) <= 0) k--; else break; } if (k == U.size()) { U.push_back(given[i]); k++; } else { U[k] = given[i]; k++; } } for (i = 0; i < j - 1; i++) ans.push_back(L[i]); for (i = 0; i < k - 1; i++) ans.push_back(U[i]); } vector<PT> p; double maxdist(PT a, PT p, PT q) { return max(dist(a, p), dist(a, q)); } double mindist(PT a, PT p, PT q) { PT lt, rt; int loop = 250; while (loop--) { lt.first = (p.first * 2.0 + q.first) / 3.0; lt.second = (p.second * 2.0 + q.second) / 3.0; rt.first = (p.first + q.first * 2.0) / 3.0; rt.second = (p.second + q.second * 2.0) / 3.0; if (dist(a, lt) < dist(a, rt)) q = rt; else p = lt; } return dist(a, p); } int main() { ios_base::sync_with_stdio(false); int n, i, j, k; PT a, tmp; cin >> n >> a.first >> a.second; for (i = 0; i < n; i++) { cin >> tmp.first >> tmp.second; p.push_back(tmp); } double maxx = -10000000000000011; for (i = 0; i < n; i++) { j = (i + 1) % n; maxx = max(maxx, maxdist(a, p[i], p[j])); } double minn = 10000000000000011; for (i = 0; i < n; i++) { j = (i + 1) % n; minn = min(minn, mindist(a, p[i], p[j])); } cout << fixed << setprecision(10); cout << PI * (maxx * maxx - minn * minn) << endl; return 0; }
#include <bits/stdc++.h> using namespace std; long long n, px, py; double dist(long long px, long long py, long long x1, long long y1, long long x2, long long y2) { double d2 = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2); if (d2 == 0.0) return ((x1 - px) * (x1 - px) + (y1 - py) * (y1 - py)); double t = ((double)((px - x1) * (x2 - x1) + (py - y1) * (y2 - y1))) / d2; if (t < 0.0) return ((px - x1) * (px - x1) + (py - y1) * (py - y1)); else if (t > 1.0) return ((px - x2) * (px - x2) + (py - y2) * (py - y2)); double nx = x1 + t * (x2 - x1); double ny = y1 + t * (y2 - y1); return ((nx - px) * (nx - px) + (ny - py) * (ny - py)); } int main() { const double PI = atan(1.0) * 4; cin >> n >> px >> py; vector<long long> d(n); vector<double> d2(n); vector<double> cs(0), xs(n), ys(n); double x1, x2, y1, y2; for (int i = 0; i < n; i++) { long long x, y; cin >> x >> y; xs[i] = x; ys[i] = y; d[i] = (x - px) * (x - px) + (y - py) * (y - py); } for (int i = 0; i < n; i++) { x1 = xs[i]; x2 = xs[(i + 1) % n]; y1 = ys[i]; y2 = ys[(i + 1) % n]; double dd = dist(px, py, x1, y1, x2, y2); d2[i] = dd; } double maxd = max_element(d.begin(), d.end()) - d.begin(); double mind = min_element(d2.begin(), d2.end()) - d2.begin(); double res; res = PI * (d[maxd] - d2[mind]); cout.precision(20); cout << res; }
#include <bits/stdc++.h> using namespace std; int n, m; double px, py; vector<pair<double, double> > points; double get_radius(int i) { return (px - points[i].first) * (px - points[i].first) + (py - points[i].second) * (py - points[i].second); } double get_dist(double x1, double y1, double x2, double y2) { return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)); } int main() { scanf("%d %lf %lf", &n, &px, &py); points.resize(n); for (int i = 0; i < n; i++) { scanf("%lf %lf", &points[i].first, &points[i].second); } double max_area = -100000000000000000; double min_area = 100000000000000000; for (int i = 0; i < n; i++) { double radius = get_radius(i); double area = 3.14159265358979323846 * radius; max_area = max(max_area, area); int j = (i + 1) % n; double m1 = (points[j].second - points[i].second) / (points[j].first - points[i].first); double c1 = points[i].second - m1 * points[i].first; double m2 = -1.0 / m1; double c2 = py - px * m2; double xp, yp; if (points[i].first == points[j].first) { xp = points[i].first; yp = py; } else if (points[i].second == points[j].second) { xp = px; yp = points[i].second; } else { xp = (c2 - c1) / (m1 - m2), yp = m2 * xp + c2; } if (get_dist(points[i].first, points[i].second, xp, yp) + get_dist(points[j].first, points[j].second, xp, yp) - get_dist(points[i].first, points[i].second, points[j].first, points[j].second) <= 1e-9) { double rad = (px - xp) * (px - xp) + (py - yp) * (py - yp); min_area = min(min_area, 3.14159265358979323846 * rad); } else { double r1 = get_radius(i), r2 = get_radius(j); min_area = min(min_area, 3.14159265358979323846 * min(r1, r2)); } } printf("%.20lf\n", max_area - min_area); return 0; }
#include <bits/stdc++.h> using namespace std; const double eps = 1e-8; const double inf = 1e20; const double pi = acos(-1.0); int sgn(double x) { if (fabs(x) < eps) return 0; if (x < 0) return -1; else return 1; } double mysqrt(double x) { return sqrt(max(x, 0.0)); } struct point { double x, y; point(double x = 0, double y = 0) : x(x), y(y) {} bool operator==(const point &b) const { return sgn(x - b.x) == 0 && sgn(y - b.x) == 0; } bool operator<(const point &b) const { return sgn(x - b.x) == 0 ? sgn(y - b.y) < 0 : sgn(x - b.x) < 0; } point operator+(const point &b) const { return point(x + b.x, y + b.y); } point operator-(const point &b) const { return point(x - b.x, y - b.y); } point operator*(const double &k) const { return point(x * k, y * k); } point operator/(const double &k) const { return point(x / k, y / k); } double operator^(const point &b) const { return x * b.y - y * b.x; } double operator*(const point &b) const { return x * b.x + y * b.y; } double dist(point b) { return hypot(x - b.x, y - b.y); } double rad(point a, point b) { point p = *this; return fabs(atan2(fabs((a - p) ^ (b - p)), (a - p) * (b - p))); } point trunc(double r) { double l = hypot(x, y); if (!sgn(l)) return *this; r /= l; return point(x * r, y * r); } point rotleft() { return point(-y, x); } point rotright() { return point(y, -x); } point rotate(point p, double angle) { point v = (*this) - p; double c = cos(angle), s = sin(angle); return point(p.x + v.x * c - v.y * s, p.y + v.x * s + v.y * c); } void input() { scanf("%lf%lf", &x, &y); } }; struct line { point s, e; line() {} line(point s, point e) : s(s), e(e) {} bool operator==(const line &v) { return (s == v.s) && (e == v.e); } line(point p, double angle) { s = p; if (sgn(angle - pi / 2) == 0) { e = (s + point(0, 1)); } else { e = (s + point(1, tan(angle))); } } line(double a, double b, double c) { if (sgn(a) == 0) { s = point(0, -c / b); e = point(1, -c / b); } else if (sgn(b) == 0) { s = point(-c / a, 0); e = point(-c / a, 1); } else { s = point(0, -c / b); e = point(1, (-c - a) / b); } } void adjust() { if (e < s) swap(s, e); } double length() { return s.dist(e); } double dispointtoline(point p) { return fabs((p - s) ^ (e - s)) / length(); } double dispointtoseg(point p) { if (sgn((p - s) * (e - s)) < 0 || sgn((p - e) * (s - e) < 0)) return min(p.dist(s), p.dist(e)); return dispointtoline(p); } }; const int N = 1e5 + 10; point pp[N]; int main() { int n; point p; scanf("%d", &n); p.input(); double minn = inf, maxx = 0; for (int i = 1; i <= n; i++) { pp[i].input(); } for (int i = 1; i <= n; i++) { maxx = max(p.dist(pp[i]), maxx); int j = i == n ? 1 : i + 1; line line1 = line(pp[i], pp[j]); minn = min(minn, line1.dispointtoseg(p)); } printf("%lf\n", pi * (maxx * maxx - minn * minn)); return 0; }
#include <bits/stdc++.h> using namespace std; pair<double, double> center; long long n; inline double sqdist(pair<double, double> &a, pair<double, double> &b) { return (a.first - b.first) * (a.first - b.first) + (a.second - b.second) * (a.second - b.second); } inline double dotProduct(pair<double, double> &a, pair<double, double> &b) { return (center.first - a.first) * (b.first - a.first) + (center.second - a.second) * (b.second - a.second); } inline double distFromLine(pair<double, double> &a, pair<double, double> &b) { double c = a.first, d = a.second; double e = b.first, first = b.second; double x = center.first, y = center.second; double denom = (first - d) * (first - d) + (c - e) * (c - e); double num = ((first - d) * x + (c - e) * y - ((first - d) * c + (c - e) * d)); num = num * num; return num / denom; } inline double nearest(vector<pair<double, double> > &points, vector<double> &distances) { double ans = 1e15; long long i1, i2; for (long long i = 0; i < n; ++i) { i1 = i; i2 = i + 1; if (i2 == n) i2 = 0; double dp = dotProduct(points[i1], points[i2]); double len = sqdist(points[i1], points[i2]); if (dp >= 0 && dp < len) ans = min(ans, distFromLine(points[i1], points[i2])); } return ans; } signed main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cin >> n >> center.first >> center.second; vector<pair<double, double> > points(n); for (long long i = 0; i < n; i++) cin >> points[i].first >> points[i].second; vector<double> distances(n); for (long long i = 0; i < n; i++) distances[i] = sqdist(points[i], center); double ri2, ro2; ro2 = *max_element(distances.begin(), distances.end()); ri2 = *min_element(distances.begin(), distances.end()); ri2 = min(ri2, nearest(points, distances)); cout << fixed << setprecision(18); ; cout << 3.141592653589793238 * (ro2 - ri2); }
#include <bits/stdc++.h> using namespace std; const int maxn = 1e5 + 10; struct Point { double x, y; Point(double x = 0, double y = 0) : x(x), y(y) {} void input() { scanf("%lf%lf", &this->x, &this->y); } }; Point operator+(Point A, Point B) { return Point(A.x + B.x, A.y + B.y); } Point operator-(Point A, Point B) { return Point(A.x - B.x, A.y - B.y); } Point operator*(Point A, double p) { return Point(A.x * p, A.y * p); } Point operator/(Point A, double p) { return Point(A.x / p, A.y / p); } bool operator<(const Point &a, const Point &b) { return a.x < b.x || (a.x == b.x && a.y < b.y); } int dcmp(double x) { if (fabs(x) < 1e-8) return 0; else return x < 0 ? -1 : 1; } bool operator==(const Point &a, const Point &b) { return !dcmp(a.x - b.x) && !dcmp(a.y - b.y); } double Dot(Point A, Point B) { return A.x * B.x + A.y * B.y; } double Length(Point A) { return sqrt(Dot(A, A)); } double Angle(Point A, Point B) { return acos(Dot(A, B) / Length(A) / Length(B)); } double Cross(Point A, Point B) { return A.x * B.y - A.y * B.x; } double Area2(Point A, Point B, Point C) { return Cross(B - A, C - A); } Point Rotate(Point A, double rad) { return Point(A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad)); } double DistanceToSegment(Point p, Point A, Point B) { if (A == B) return Length(p - A); Point v1 = B - A, v2 = p - A, v3 = p - B; if (dcmp(Dot(v1, v2)) < 0) return Length(v2); else if (dcmp(Dot(v1, v3)) > 0) return Length(v3); else return fabs(Cross(v1, v2)) / Length(v1); } Point p0, p[maxn]; int main() { int n; scanf("%d", &n); p0.input(); double maxdis = -1, mindis = 1e9 + 7; for (int i = 0; i < n; i++) { p[i].input(); maxdis = max(maxdis, Length(p0 - p[i])); } p[n] = p[0]; for (int i = 0; i < n; i++) { mindis = min(mindis, DistanceToSegment(p0, p[i], p[i + 1])); } printf("%.8lf\n", acos(-1) * (maxdis * maxdis - mindis * mindis)); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 2e5; const long double Pi = 3.1415926535897932; struct point { int x, y; } p, a[N]; int n; long double mx, mn; long double dist(point a, point b) { long double ans; ans = sqrt(1.0 * (a.x - b.x) * (a.x - b.x) + 1.0 * (a.y - b.y) * (a.y - b.y)); return ans; } struct node { long double x, y; } v[4]; long double F() { long double ans = Pi * (mx * mx - mn * mn); return ans; } long double len(node a) { return sqrt(1.0 * a.x * a.x + 1.0 * a.y * a.y); } node do_it(point a, point b) { node result; result.x = b.x - a.x; result.y = b.y - a.y; return result; } long double dot(node a, node b) { return 1.0 * a.x * b.x + 1.0 * a.y * b.y; } long double cross(node a, node b) { return 1.0 * a.x * b.y - 1.0 * b.x * a.y; } long double dist_Point_line(point a, point b, point c) { v[0] = do_it(a, b); v[1] = do_it(a, c); double area = fabs(cross(v[0], v[1])); return area / (len(v[0])); } long double dist_Point_segment(point a, point b, point c) { v[0] = do_it(a, b); v[1] = do_it(a, c); v[2] = do_it(b, a); v[3] = do_it(b, c); if (dot(v[0], v[1]) >= 0 && dot(v[2], v[3]) >= 0) return dist_Point_line(a, b, c); else return min(len(v[1]), len(v[3])); } int main() { scanf("%d%d%d", &n, &p.x, &p.y); mn = 1e40; for (int i = 1; i <= n; i++) { scanf("%d%d", &a[i].x, &a[i].y); mx = max(mx, dist(a[i], p)); mn = min(mn, dist(a[i], p)); } a[n + 1] = a[1]; for (int i = 1; i <= n; i++) { int nxt = i + 1; if (nxt > n) nxt = 1; mx = max(mx, dist_Point_segment(a[i], a[nxt], p)); mn = min(mn, dist_Point_segment(a[i], a[nxt], p)); } cout << fixed << setprecision(15) << F() << endl; return 0; }
#include <bits/stdc++.h> using namespace std; int main() { ios_base::sync_with_stdio(0); cin.tie(0); int n; cin >> n; long double x, y; cin >> x >> y; long double maxi = 0, mini = 1e17; long double prx = -1.5, pry = -1.5; long double fx, fy; for (int i = 0; i <= n; ++i) { long double px, py; if (i != n) cin >> px >> py; else px = fx, py = fy; if (i == 0) fx = px, fy = py; maxi = max(maxi, abs(abs((px - x) * (px - x)) + abs((py - y) * (py - y)))); if (prx == -1.5) { prx = px; pry = py; continue; } long double pr1 = prx, pr2 = pry; long double diffX = px - prx; long double diffY = py - pry; long double x1 = prx, x2 = px, y1 = pry, y2 = py; if ((diffX == 0) && (diffY == 0)) { diffX = x - prx; diffY = y - pry; mini = min(diffX * diffX + diffY * diffY, mini); prx = px; pry = py; continue; } long double t = ((x - x1) * diffX + (y - y1) * diffY) / (diffX * diffX + diffY * diffY); if (t < 0) { diffX = x - x1; diffY = y - y1; } else if (t > 1) { diffX = x - x2; diffY = y - y2; } else { diffX = x - (x1 + t * diffX); diffY = y - (y1 + t * diffY); } mini = min(diffX * diffX + diffY * diffY, mini); prx = px; pry = py; } long double PI = acos(-1.0); if (n == 1) { cout << fixed << setprecision(10) << 0 << "\n"; } else { long double fans = PI * (maxi - mini); cout << fixed << setprecision(10) << fans << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; long long d(long long x1, long long y1, long long x2, long long y2) { return (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1); } long long x[110000], y[110000]; int n; double t(int idx, long long x0, long long y0) { return -(double)((y[(idx + 1) % n] - y[idx]) * (y[idx] - y0) + (x[(idx + 1) % n] - x[idx]) * (x[idx] - x0)) / (double)d(x[(idx + 1) % n], y[(idx + 1) % n], x[idx], y[idx]); } bool lies(int idx, long long x0, long long y0) { if (-((y[(idx + 1) % n] - y[idx]) * (y[idx] - y0) + (x[(idx + 1) % n] - x[idx]) * (x[idx] - x0)) >= 0 && -((y[(idx + 1) % n] - y[idx]) * (y[idx] - y0) + (x[(idx + 1) % n] - x[idx]) * (x[idx] - x0)) <= d(x[(idx + 1) % n], y[(idx + 1) % n], x[idx], y[idx])) return true; else return false; } int main() { long long x0, y0, dist_max = 0ll; double dist_min = INFINITY; scanf("%d %lld %lld", &n, &x0, &y0); for (int i = 0; i < n; i++) { scanf("%lld %lld", &x[i], &y[i]); dist_max = max(dist_max, d(x[i], y[i], x0, y0)); } for (int i = 0; i < n; i++) { if (lies(i, x0, y0)) { double m_t = t(i, x0, y0); double dist1 = (double)x[i] + m_t * (double)(x[(i + 1) % n] - x[i]) - x0; dist1 *= dist1; double dist2 = (double)y[i] + m_t * (double)(y[(i + 1) % n] - y[i]) - y0; dist2 *= dist2; dist_min = min(dist_min, dist1 + dist2); } else { dist_min = min(dist_min, (double)d(x[i], y[i], x0, y0)); dist_min = min(dist_min, (double)d(x[(i + 1) % n], y[(i + 1) % n], x0, y0)); } } double solution = (double)dist_max * M_PI; solution -= dist_min * M_PI; printf("%.15f\n", solution); }
#include <bits/stdc++.h> using namespace std; const int maxn = 100010; inline void readchar(char &ch) { while ((ch = getchar()) == ' ' || ch == '\n') ; } inline void read(int &x) { char ch; while ((ch = getchar()) < '0' || ch > '9') ; x = ch - '0'; while ((ch = getchar()) <= '9' && ch >= '0') x = x * 10 + ch - '0'; } long long x[maxn], y[maxn]; int n, px, py, cnt; double R, r; template <class T> double sqr(T x) { return (double)x * x; } int main() { scanf("%d%d%d", &n, &px, &py); for (int i = 1; i <= n; i++) scanf("%I64d%I64d", &(x[i]), &(y[i])), (x[i]) -= px, (y[i]) -= py; x[n + 1] = x[1]; y[n + 1] = y[1]; for (int i = 1; i <= n; i++) R = max(R, sqr((x[i])) + sqr((y[i]))); r = 1e100; for (int i = 1; i <= n; i++) { if ((x[i]) == 0 && (x[i + 1]) == 0) { if ((y[i]) * (y[i + 1]) <= 0) r = 0; else r = min(r, min(fabs((y[i])), fabs((y[i + 1])))); continue; } double x0 = (double)((x[i + 1]) * (y[i]) - (x[i]) * (y[i + 1])) * ((y[i]) - (y[i + 1])) / (double)(((x[i]) - (x[i + 1])) * ((x[i]) - (x[i + 1])) + ((y[i]) - (y[i + 1])) * ((y[i]) - (y[i + 1]))); if (x0 >= (x[i]) && x0 <= (x[i + 1]) || x0 >= (x[i + 1]) && x0 <= (x[i])) r = min(r, sqr((x[i + 1]) * (y[i]) - (x[i]) * y[i + 1]) / (sqr((x[i]) - (x[i + 1])) + sqr((y[i]) - (y[i + 1])))); else r = min( r, min(sqr((x[i])) + sqr((y[i])), sqr((x[i + 1])) + sqr((y[i + 1])))); } printf("%lf\n", 4 * atan(1) * (R - r)); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1001000; const double eps = 1e-10, inf = 1e20, pi = acos(-1); struct poi { double x, y; } c, p[maxn]; poi operator-(const poi &a, const poi &b) { return (poi){a.x - b.x, a.y - b.y}; } int dcmp(double x) { return fabs(x) < eps ? 0 : x < 0 ? -1 : 1; } double dot(poi a, poi b) { return a.x * b.x + a.y * b.y; } double cross(poi a, poi b) { return a.x * b.y - a.y * b.x; } int n; double mxd = -1, mnd = inf; double poi_dis_to_seg(poi p, poi a, poi b) { poi AB = b - a, AP = p - a, BP = p - b; if (dcmp(dot(AB, AP)) < 0) return dot(AP, AP); if (dcmp(dot(AB, BP)) > 0) return dot(BP, BP); return pow(fabs(cross(AB, AP) / sqrt(dot(AB, AB))), 2); } int main() { scanf("%d%lf%lf", &n, &c.x, &c.y); for (int i = 1; i <= n; i++) scanf("%lf%lf", &p[i].x, &p[i].y); for (int i = 1; i <= n; i++) { mxd = max(mxd, dot(p[i] - c, p[i] - c)); double dis = poi_dis_to_seg(c, p[i % n + 1], p[i]); mnd = min(mnd, dis); } printf("%.12lf\n", pi * (mxd - mnd)); return 0; }
#include <bits/stdc++.h> long double pi = acos(-1.0); using namespace std; long double dist(long long x1, long long y1, long long x2, long long y2) { return sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1)); } long double dist2(long long x, long long y, pair<long long, long long> p1, pair<long long, long long> p2) { return 0; } int main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); int n; cin >> n; long long x, y; cin >> x >> y; long double mn = 1e18, mx = -1e18; vector<pair<long long, long long>> xy; for (long long(i) = 0; (i) < n; (i)++) { long long xx, yy; cin >> xx >> yy; xx -= x; yy -= y; mx = max(mx, dist(0, 0, xx, yy)); xy.push_back({xx, yy}); } x = 0, y = 0; for (long long(i) = 0; (i) < n; (i)++) { pair<long long, long long> p1 = xy[i]; pair<long long, long long> p2 = xy[(i + 1) % n]; long double a = dist(p1.first, p1.second, p2.first, p2.second); long double b = dist(x, y, p1.first, p1.second); long double c = dist(x, y, p2.first, p2.second); pair<long long, long long> v1 = make_pair(p1.first - p2.first, p1.second - p2.second); pair<long long, long long> v2 = make_pair(p2.first, p2.second); pair<long long, long long> v3 = make_pair(p1.first, p1.second); long double alpha1 = acos((v2.first * v1.first + v2.second * v1.second) / (c * a)); v1.first *= -1; v1.second *= -1; long double alpha2 = acos((v3.first * v1.first + v3.second * v1.second) / (b * a)); int q1 = 1, q2 = 1; if (alpha1 > pi / 2.0) { q1 = -1; } if (alpha2 > pi / 2.0) { q2 = -1; } bool ok1 = q1 * q2 > 0; mn = min({mn, b, c}); if (ok1) { if (b > c) swap(b, c); long double pp = (a + b + c) / 2.0; long double s = sqrt(pp * (pp - a) * (pp - b) * (pp - c)); long double h = 2 * s / a; mn = min(mn, h); } } cout << setprecision(20) << fixed << pi * (mx * mx - mn * mn); return 0; }