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| #include <cstdio>
#include <cmath>
#include <algorithm>
#include <vector>
#define pb push_back
using namespace std;
const int N = 1e5 + 10;
const double pi = acos(-1), eps = 1e-12, inf = 1e20;
int cmp (double a, double b)
{
if (a - b > eps) return 1;
if (b - a > eps) return -1;
return 0;
}
int sign (double a) { return cmp(a, 0); }
struct Point
{
double x, y;
Point () { }
Point (double a, double b)
{ x = a, y = b; }
void input () { scanf("%lf%lf", &x, &y); }
void output () { printf("%.10lf %.10lf\n", x + eps, y + eps); }
bool operator < (const Point &_) const
{
int t = cmp(x, _.x);
if (t == 1) return false;
if (t == -1) return true;
return y < _.y;
}
};
Point mid (Point a, Point b)
{ return Point((a.x + b.x) / 2, (a.y + b.y) / 2); }
struct Vector
{
double x, y;
Vector () { }
Vector (double a, double b)
{ x = a, y = b; }
Vector (Point a, Point b)
{ x = b.x - a.x, y = b.y - a.y; }
void input () { scanf("%lf%lf", &x, &y); }
void output () { printf("%.10lf %.10lf\n", x + eps, y + eps); }
Vector operator + (const Vector &_)
{ return Vector(x + _.x, y + _.y); }
Vector operator - (const Vector &_)
{ return Vector(x - _.x, y - _.y); }
Vector operator * (const double &_)
{ return Vector(x * _, y * _); }
Vector operator / (const double &_)
{ return Vector(x / _, y / _); }
double operator ^ (const Vector &_) const
{ return x * _.x + y * _.y; }
double operator & (const Vector &_) const
{ return x * _.y - y * _.x; }
double len () { return sqrt(*this ^ *this); }
Vector uint () { return *this / len(); }
Vector rotate (double th)
{ return Vector(x * cos(th) - y * sin(th), x * sin(th) + y * cos(th)); }
};
Point move (Point p, Vector t)
{ return Point(p.x + t.x, p.y + t.y); }
double area (Point a, Point b, Point c)
{ return abs(Vector(a, b) & Vector(a, c)); }
double angle (Vector a, Vector b) { return acos((a ^ b) / a.len() / b.len()); }
double dis (Point a, Point b)
{
double dx = a.x - b.x, dy = a.y - b.y;
return sqrt(dx * dx + dy * dy);
}
struct Segment
{
Point p; Vector t;
Segment () { }
Segment (Point a, Point b)
{ p = a, t = Vector(a, b); }
Segment (Point _p, Vector _t)
{ p = _p, t = _t; }
double angle () { return atan2(t.y, t.x); }
int on (Point _)
{ return sign(t & Vector(p, _)); }
bool operator < (Segment &_)
{
double a = angle(), b = _.angle();
if (!cmp(a, b)) return on(_.p) < 0;
return a < b;
}
Point proj (Point _)
{ return move(p, t * (t ^ Vector(p, _)) / (t ^ t)); }
double dis (Point _)
{ return abs(t & Vector(p, _)) / t.len(); }
};
Segment vertical (Point a, Point b)
{ return Segment(mid(a, b), Vector(a, b).rotate(pi / 2)); }
Point intersection (Segment a, Segment b)
{ return move(a.p, a.t * (b.t & Vector(b.p, a.p)) / (a.t & b.t)); }
struct Circle
{
Point p; double r;
Circle () { }
Circle (Point _p, double _r)
{ p = _p, r = _r; }
Circle (Point a, Point b, Point c)
{
p = intersection(vertical(a, b), vertical(a, c));
r = dis(p, a);
}
};
struct Polygon
{
vector <Point> p;
Polygon () { }
void input ()
{
int n; scanf("%d", &n);
p.resize(n);
for (int i = 0; i < n; ++i)
p[i].input();
}
double PolygonArea ()
{
double res = 0;
for (int i = 1; i + 1 < p.size(); ++i)
res += area(p[0], p[i], p[i + 1]);
return res / 2;
}
double PolygonCircumference ()
{
double res = dis(p.front(), p.back());
for (int i = 0; i + 1 < p.size(); ++i)
res += dis(p[i], p[i + 1]);
return res;
}
Polygon ConvexHull ()
{
if (p.size() < 3) return *this;
static bool vis[N];
sort(p.begin(), p.end());
static int top = 0, stk[N];
for (int i = 0; i < p.size(); ++i)
{
while (top >= 2 && Segment(p[stk[top - 1]], p[stk[top]]).on(p[i]) >= 0)
vis[stk[top--]] = false;
vis[stk[++top] = i] = true;
}
vis[0] = false;
for (int i = p.size() - 1; ~i; --i)
{
if (vis[i]) continue;
while (top >= 2 && Segment(p[stk[top - 1]], p[stk[top]]).on(p[i]) >= 0)
vis[stk[top--]] = false;
vis[stk[++top] = i] = true;
}
Polygon res;
for (int i = 1; i < top; ++i)
res.p.pb(p[stk[i]]);
return res;
}
double diameter ()
{
if (p.size() <= 2) return dis(p.front(), p.back());
double res = 0;
for (int i = 0, j = 1; i < p.size(); ++i)
{
Point d = p[i], e = p[(i + 1) % p.size()];
while (cmp(area(d, e, p[j]), area(d, e, p[(j + 1) % p.size()])) == -1)
j = (j + 1) % p.size();
res = max(res, max(dis(d, p[j]), dis(e, p[j])));
}
return res;
}
Circle CircleCover ()
{
random_shuffle(p.begin(), p.end());
Circle c;
c.p = p[0], c.r = 0;
for (int i = 1; i < p.size(); ++i)
{
if (cmp(c.r, dis(c.p, p[i])) >= 0) continue;
c.p = p[i], c.r = 0;
for (int j = 0; j < i; ++j)
{
if (cmp(c.r, dis(c.p, p[j])) >= 0) continue;
c.p = mid(p[i], p[j]), c.r = dis(p[i], p[j]) / 2;
for (int k = 0; k < j; ++k)
if (cmp(c.r, dis(c.p, p[k])) < 0)
c = Circle(p[i], p[j], p[k]);
}
}
return c;
}
Polygon RectangleCover ()
{
double mn = inf;
Polygon res; res.p.resize(4);
for (int i = 0, a = 2, b = 1, c = 2; i < p.size(); ++i)
{
Segment l(p[i], p[(i + 1) % p.size()]);
while (cmp(l.dis(p[a]), l.dis(p[(a + 1) % p.size()])) < 0)
a = (a + 1) % p.size();
while (cmp(l.t ^ Vector(l.p, p[b]), l.t ^ Vector(l.p, p[(b + 1) % p.size()])) < 0)
b = (b + 1) % p.size();
if (!i) c = a;
while (cmp(l.t ^ Vector(l.p, p[c]), l.t ^ Vector(l.p, p[(c + 1) % p.size()])) > 0)
c = (c + 1) % p.size();
double h = l.dis(p[a]), w = dis(l.proj(p[b]), l.proj(p[c]));
if (h * w < mn)
{
mn = h * w;
res.p[0] = l.proj(p[b]), res.p[1] = l.proj(p[c]);
Vector u = l.t.uint().rotate(-pi / 2) * h;
res.p[2] = move(res.p[1], u), res.p[3] = move(res.p[0], u);
}
}
return res;
}
};
Polygon HalfPlaneIntersection (vector <Segment> &l)
{
sort(l.begin(), l.end());
static int hd, tl, q[N];
hd = 0, tl = -1;
for (int i = 0; i < l.size(); ++i)
{
if (i && !cmp(l[i].angle(), l[i - 1].angle())) continue;
while (hd < tl && l[i].on(intersection(l[q[tl - 1]], l[q[tl]])) <= 0) --tl;
while (hd < tl && l[i].on(intersection(l[q[hd + 1]], l[q[hd]])) <= 0) ++hd;
q[++tl] = i;
}
while (hd + 1 < tl && l[q[hd]].on(intersection(l[q[tl - 1]], l[q[tl]])) <= 0) --tl;
while (hd + 1 < tl && l[q[tl]].on(intersection(l[q[hd + 1]], l[q[hd]])) <= 0) ++hd;
q[++tl] = q[hd];
Polygon res;
for (int i = hd; i < tl; ++i)
res.p.pb(intersection(l[q[i]], l[q[i + 1]]));
return res;
}
int main ()
{
return 0;
}
|