题目链接:UVa 10652 Board Wrapping
比较简单的求凸包的题,重要的是记下刘汝佳的模版。。
#include <iostream> #include <cstdio> #include <cmath> #include <cstring> #include <vector> #include <algorithm> using namespace std; const double eps = 1e-10; const double PI = acos(-1); struct Point { double x, y; Point(double x=0, double y=0):x(x),y(y) { } }; typedef Point Vector; Vector operator + (const Vector& A, const Vector& B) { return Vector(A.x+B.x, A.y+B.y); } Vector operator - (const Point& A, const Point& B) { return Vector(A.x-B.x, A.y-B.y); } Vector operator * (const Vector& A, double p) { return Vector(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) < eps) return 0; else return x < 0 ? -1 : 1; } bool operator == (const Point& a, const Point &b) { return dcmp(a.x-b.x) == 0 && dcmp(a.y-b.y) == 0; } double Cross(const Vector& A, const Vector& B) { return A.x*B.y - A.y*B.x; } double Dot(const Vector& A, const Vector& B) { return A.x*B.x + A.y*B.y; } double Length(const Vector& A) { return sqrt(Dot(A, A)); } // 点集凸包 // 如果不希望在凸包的边上有输入点,把两个 <= 改成 < // 如果不介意点集被修改,可以改成传递引用 vector<Point> ConvexHull(vector<Point> p) { // 预处理,删除重复点 sort(p.begin(), p.end()); p.erase(unique(p.begin(), p.end()), p.end()); int n = p.size(); int m = 0; vector<Point> ch(n+1); for(int i = 0; i < n; i++) { while(m > 1 && Cross(ch[m-1]-ch[m-2], p[i]-ch[m-2]) <= 0) m--; ch[m++] = p[i]; } int k = m; for(int i = n-2; i >= 0; i--) { while(m > k && Cross(ch[m-1]-ch[m-2], p[i]-ch[m-2]) <= 0) m--; ch[m++] = p[i]; } if(n > 1) m--; ch.resize(m); return ch; } // 多边形的有向面积 double PolygonArea(vector<Point> p) { double area = 0; int n = p.size(); for(int i = 1; i < n-1; i++) area += Cross(p[i]-p[0], p[i+1]-p[0]); return area/2; } double torad(double deg) { return deg/180 * PI; } Vector Rotate(const Vector& A, double rad) { return Vector(A.x*cos(rad)-A.y*sin(rad), A.x*sin(rad)+A.y*cos(rad)); } int main() { int T; scanf("%d", &T); while(T--) { int n; double area1 = 0; scanf("%d", &n); vector <Point> P; for(int i = 0; i < n; i++) { double x, y, w, h, j, ang; scanf("%lf%lf%lf%lf%lf", &x, &y, &w, &h, &j); Point o(x,y); ang = -torad(j); //题意是顺时针旋转,Rotate是逆时针旋转,所以需要转化 P.push_back(o + Rotate(Vector(-w / 2,-h / 2), ang)); P.push_back(o + Rotate(Vector(w / 2,-h / 2), ang)); P.push_back(o + Rotate(Vector(-w / 2,h / 2), ang)); P.push_back(o + Rotate(Vector(w / 2,h / 2), ang)); area1 += w * h; } double area2 = PolygonArea(ConvexHull(P)); printf("%.1lf %%\n", area1*100/area2); } return 0; }