[hihoCoder1231 2015BeijingOnline]求圆与多边形公共部分的周长

题意：如题

思路：离散。将所有交点求出来，相当于将多变形的边切成了很多条元边，对每条元边，有两种情况

• 在圆内，答案加上此边长
• 在圆外，答案加上此边相对于圆心的"有向转弧"

#include <bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
    #include "local.h"
#endif
#define X first
#define Y second
#define pb(x) push_back(x)
#define mp(x, y) make_pair(x, y)
#define all(a) (a).begin(), (a).end()
#define mset(a, x) memset(a, x, sizeof(a))
#define mcpy(a, b) memcpy(a, b, sizeof(a))
typedef long long ll;
template<typename T>bool umax(T&a, const T&b){return b<=a?false:(a=b,true);}
template<typename T>bool umin(T&a, const T&b){return b>=a?false:(a=b,true);}

namespace ConstSet {
    const double PI = acos(-1.0);
    const double e = 2.718281828459045;
}

const double eps = 1e-8;
struct Real {
    double x;
    double get() { return x; }
    int read() { return scanf("%lf", &x); }
    Real(const double &x) { this->x = x; }
    Real() {}
    Real abs() { return x > ? x : -x; }

    Real operator + (const Real &that) const { return Real(x + that.x);}
    Real operator - (const Real &that) const { return Real(x - that.x);}
    Real operator * (const Real &that) const { return Real(x * that.x);}
    Real operator / (const Real &that) const { return Real(x / that.x);}
    Real operator - () const { return Real(-x); }

    Real operator += (const Real &that) { return Real(x += that.x); }
    Real operator -= (const Real &that) { return Real(x -= that.x); }
    Real operator *= (const Real &that) { return Real(x *= that.x); }
    Real operator /= (const Real &that) { return Real(x /= that.x); }

    bool operator < (const Real &that) const { return x - that.x <= -eps; }
    bool operator > (const Real &that) const { return x - that.x >= eps; }
    bool operator == (const Real &that) const { return x - that.x > -eps && x - that.x < eps; }
    bool operator <= (const Real &that) const { return x - that.x < eps; }
    bool operator >= (const Real &that) const { return x - that.x > -eps; }

    friend ostream& operator << (ostream &out, const Real &val) {
        out << val.x;
        return out;
    }
    friend istream& operator >> (istream &in, Real &val) {
        in >> val.x;
        return in;
    }
};

struct Point {
    Real x, y;
    int read() { return scanf("%lf%lf", &x.x, &y.x); }
    Point(const Real &x, const Real &y) { this->x = x; this->y = y; }
    Point() {}
    Point operator + (const Point &that) const { return Point(this->x + that.x, this->y + that.y); }
    Point operator - (const Point &that) const { return Point(this->x - that.x, this->y - that.y); }
    Real operator * (const Point &that) const { return x * that.x + y * that.y; }
    Point operator * (const Real &that) const { return Point(x * that, y * that); }
    Point operator / (const Real &that) { return Point(x / that, y / that); }
    Point operator += (const Point &that)  { return Point(this->x += that.x, this->y += that.y); }
    Point operator -= (const Point &that)  { return Point(this->x -= that.x, this->y -= that.y); }
    Point operator *= (const Real &that)  { return Point(x *= that, y *= that); }
    Point operator /= (const Real &that) { return Point(x /= that, y /= that); }

    bool operator == (const Point &that) const { return x == that.x && y == that.y; }

    Real cross(const Point &that) const { return x * that.y - y * that.x; }
    Real abs() { return sqrt((x * x + y * y).get()); }
};
typedef Point Vector;

struct Segment {
    Point a, b;
    Segment(const Point &a, const Point &b) { this->a = a; this->b = b; }
    Segment() {}
    bool intersect(const Segment &that) const {
        Point c = that.a, d = that.b;
        Vector ab = b - a, cd = d - c, ac = c - a, ad = d - a, ca = a - c, cb = b - c;
        return ab.cross(ac) * ab.cross(ad) <  && cd.cross(ca) * cd.cross(cb) < ;
    }
    Point getSegmentIntersection(const Segment &that) const {
        Vector u = a - that.a, v = b - a, w = that.b - that.a;
        Real t = w.cross(u) / v.cross(w);
        return a + v * t;
    }
    Real Distance(Point P) {
        Point A = a, B = b;
        if (A == B) return (P - A).abs();
        Vector v1 = B - A, v2 = P - A, v3 = P - B;
        if (v1 * v2 < ) return v2.abs();
        if (v1 * v3 > ) return v3.abs();
        return v1.cross(v2).abs() / v1.abs();
    }
    bool containPoint(const Point &p) const {
        Vector ap = p - a, bp = p - b;
        return ap * bp < ;
    }
};

struct Line {
    Point p;
    Vector v;
    Line(Point p, Vector v): p(p), v(v) {}
    Line() {}
    Point point(Real a) {
        return p + v * a;
    }
};
struct Circle {
    Point c;
    Real r;
    Circle(Point c, Real r): c(c), r(r) {}
    Circle() {}
    void read() {
        c.read();
        scanf("%lf", &r.x);
    }
    Point point(Real a) {
        return Point(c.x + r * cos(a.get()), c.y + r * sin(a.get()));
    }
    int getLineIntersection(Line L, vector<Point> &sol) {
        Circle C = *this;
        Real a = L.v.x, b = L.p.x - C.c.x, c = L.v.y, d = L.p.y - C.c.y;
        Real e = a * a + c * c, f = (a * b + c * d) * , g = b * b + d * d - C.r * C.r;
        Real delta = f * f - e * g * ;
        Real t1, t2;
        if (delta < ) return ;
        if (delta == ) {
            t1 = t2 = -f / (e * ); sol.push_back(L.point(t1));
            return ;
        }
        t1 = (-f - sqrt(delta.get())) / (e * ); sol.push_back(L.point(t1));
        t2 = (-f + sqrt(delta.get())) / (e * ); sol.push_back(L.point(t2));
        return ;
    }
    Real turningAngle(Point a, Point b) {
        Vector ca = a - c, cb = b - c;
        if (ca.abs() ==  || cb.abs() == ) return ;//一个点和圆心重合，计算转角是没意义的
        Real angle = acos((ca * cb / ca.abs() / cb.abs()).get());
        return ca.cross(cb) >= ? angle : -angle;
    }
};

const int maxn = 1e3 + ;

Point p[maxn];

int main() {
#ifndef ONLINE_JUDGE
    freopen("in.txt", "r", stdin);
    //freopen("out.txt", "w", stdout);
#endif // ONLINE_JUDGE
    int n;
    while (cin >> n, n) {
        for (int i = ; i < n; i ++) {
            p[i].read();
        }
        Circle c;
        c.read();
        vector<Point> vs;
        for (int i = ; i < n; i ++) {
            vs.pb(p[i]);
            vector<Point> v;
            Point a = p[i], b = p[(i + ) % n];
            c.getLineIntersection(Line(a, b - a), v);
            for (int i = ; i < v.size(); i ++) {
                if (Segment(a, b).containPoint(v[i])) vs.pb(v[i]);
            }
        }
        Real ans = ;
        for (int i = ; i < vs.size(); i ++) {
            int j = (i + ) % vs.size();
            Point mid = (vs[i] + vs[j]) * 0.5;
            Real length = (mid - c.c).abs();
            if (length < c.r) ans += (vs[j] - vs[i]).abs();
            else ans += c.r * -c.turningAngle(vs[i], vs[j]);
        }
        cout << (ll)(ans.get() + 0.5) << endl;
    }
    return ;
}