[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 > 0? 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) < 0 && cd.cross(ca) * cd.cross(cb) < 0; } 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 < 0) return v2.abs(); if (v1 * v3 > 0) 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 < 0; } }; 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) * 2, g = b * b + d * d - C.r * C.r; Real delta = f * f - e * g * 4; Real t1, t2; if (delta < 0) return 0; if (delta == 0) { t1 = t2 = -f / (e * 2); sol.push_back(L.point(t1)); return 1; } t1 = (-f - sqrt(delta.get())) / (e * 2); sol.push_back(L.point(t1)); t2 = (-f + sqrt(delta.get())) / (e * 2); sol.push_back(L.point(t2)); return 2; } Real turningAngle(Point a, Point b) { Vector ca = a - c, cb = b - c; if (ca.abs() == 0 || cb.abs() == 0) return 0;//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) >= 0? angle : -angle; } }; const int maxn = 1e3 + 7; 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 = 0; i < n; i ++) { p[i].read(); } Circle c; c.read(); vector<Point> vs; for (int i = 0; i < n; i ++) { vs.pb(p[i]); vector<Point> v; Point a = p[i], b = p[(i + 1) % n]; c.getLineIntersection(Line(a, b - a), v); for (int i = 0; i < v.size(); i ++) { if (Segment(a, b).containPoint(v[i])) vs.pb(v[i]); } } Real ans = 0; for (int i = 0; i < vs.size(); i ++) { int j = (i + 1) % 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 0; }
