UVA 10652 Board Wrapping

题意：

有n个小矩形，求把他们包起来的最小多边形，并计算出这些矩形面积占总凸包面积的百分比。

求最小凸包，然后在处理即可。

代码:

#include <iostream>#include <cmath>#include <cstdio>#include <algorithm>using namespace std;const double eps = 1e-10;struct Point{    double x, y;    Point(double x = 0, double y = 0):x(x), y(y){}};typedef Point Vector;Vector operator +(Vector A, Vector B){    return Vector(A.x+B.x, A.y+B.y);}Vector operator -(Vector A, Vector B){    return Vector(A.x-B.x, A.y-B.y);}Vector operator *(Vector A, double p){    return Vector(A.x*p, A.y*p);}Vector operator /(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){//精度控制    if(fabs(x) < eps) return 0;    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 Dot(Vector A, Vector B){//点乘    return A.x*B.x + A.y*B.y;}double length(Vector A){    return sqrt(Dot(A, A));}double Angle(Vector A, Vector B){//向量夹角    return acos(Dot(A, B) / length(A) / length(B));}double Cross(Vector A, Vector B){//叉积    return A.x*B.y - A.y*B.x;}double torad(double deg){//角度化弧度    return deg/180 * acos(-1.0);}Vector Rotate(Vector A, double rad){//向量旋转    return Vector(A.x*cos(rad) - A.y*sin(rad), A.x*sin(rad) + A.y*cos(rad));}double  PolygonArea(Point *p, int n){//多边形的有向面积    double area = 0;    for(int i = 1; i < n-1; i++){        area += Cross(p[i]-p[0], p[i+1]-p[0]);    }        return area/2;}int ConvexHull(Point *p, int n, Point *ch)//凸包{    sort(p, p+n);    int m = 0;    for(int i = 0; i < n; i++)    {        while(m > 1 && dcmp (Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])) != 1) m--;        ch[m++] = p[i];    }    int k = m;    for(int i = n - 2; i >= 0; i--)    {        while(m > k && dcmp (Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])) !=1) m--;        ch[m++] = p[i];    }    if(n > 1) m--;    return m;}int main(){    int T;    Point P[2500], ch[2500];    cin >> T;    while(T--){        int n, pc = 0;        double area1 = 0;        cin >> n;        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);            P[pc++] = o + Rotate(Vector(-w/2, -h/2), ang);            P[pc++] = o + Rotate(Vector(w/2, -h/2), ang);            P[pc++] = o + Rotate(Vector(-w/2, h/2), ang);            P[pc++] = o + Rotate(Vector(w/2,h/2), ang);            area1 += w*h;        }        int m = ConvexHull(P, pc, ch);        double area2 = PolygonArea(ch, m);        printf("%.1f %%\n", area1*100/area2);    }    return 0;}