Circle vs Triangle SPOJ - AREA1 [模拟退火]

题意: 给定一个三角形,给定一个圆,可以任意移动.求圆与三角形的最大面积交

思路:

一开始想的是圆固定,三角形在动,但发现找不到一个固定的点

三角形固定(2点固定在x轴,再根据两方程求解第三个点的坐标),圆在动,从圆心的状态开始延展.再套圆与多边形交的模板

#include<cstdio>
#include<vector>
#include<cmath>
#include<math.h>
#include<string>
#include<string.h>
#include<iostream>
#include<algorithm>
#include<map>
#define PI acos(-1.0)
#define pb push_back
#define F first
#define S second
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const int N=1005;
const int MOD=1e9+7;
const double EPS=1e-10;
int sign(double x) {  //三态函数，减少精度问题
    return abs(x) < EPS ? 0 : x < 0 ? -1 : 1;
}
struct Point { //点的定义
    double x, y;
    Point(double x=0.0, double y=0.0) : x(x), y(y) {}
    Point operator + (const Point &rhs) const {  //向量加法
        return Point(x + rhs.x, y + rhs.y);
    }
    Point operator - (const Point &rhs) const {  //向量减法
        return Point(x - rhs.x, y - rhs.y);
    }
    Point operator * (double p) const {  //向量乘以标量
        return Point(x * p, y * p);
    }
    Point operator / (double p) const {  //向量除以标量
        return Point(x / p, y / p);
    }
    bool operator < (const Point &rhs) const {  //点的坐标排序
        return x < rhs.x || (x == rhs.x && y < rhs.y);
    }
    bool operator == (const Point &rhs) const {  //判断同一个点
        return sign(x - rhs.x) == 0 && sign(y - rhs.y) == 0;
    }
};
struct Circle {  //圆的定义
    Point c;  //圆心
    double r;  //半径
    Circle() {}
    Circle(Point c, double r) : c(c), r(r) {}
    Point point(double a) {  //圆上的一点
        return Point(c.x+cos(a)*r, c.y+sin(a)*r);
    }
};
typedef Point Vector;
Point p[N];

double dot(Vector A,Vector B){
    return A.x*B.x+A.y*B.y;
}
double length(Vector A){
    return sqrt(dot(A,A));
}
double cross(Vector A,Vector B){
    return A.x*B.y-A.y*B.x;
}
double Angle(Vector A,Vector B){
    double t=dot(A,B)/length(A)/length(B);
    return acos(t);
}
bool on_seg(Point p, Point a, Point b) {  //判断点在线段上（不包含端点），两点式
    return sign(cross(a-p, b-p)) == 0 && sign(dot(a-p, b-p)) <= 0;  //点p是否在线段ab上
}

double CulArea( Point A, Point B,Circle C)
{
    Vector OA = A-C.c, OB = B-C.c;
    Vector BA = A-B, BC = C.c-B;
    Vector AB = B-A, AC = C.c-A;
    double DOA = length(OA), DOB = length(OB),DAB = length(AB), r = C.r;
    if(sign(cross(OA,OB)) == 0) return 0;
    if(sign(DOA-C.r) < 0 && sign(DOB-C.r) < 0) return cross(OA,OB)*0.5;
    else if(DOB < r && DOA >= r) {

        double x = (dot(BA,BC) + sqrt(r*r*DAB*DAB-cross(BA,BC)*cross(BA,BC)))/DAB;
        double TS = cross(OA,OB)*0.5;
        return asin(TS*(1-x/DAB)*2/r/DOA)*r*r*0.5+TS*x/DAB;
    }
    else if(DOB >= r && DOA < r) {
        double y = (dot(AB,AC)+sqrt(r*r*DAB*DAB-cross(AB,AC)*cross(AB,AC)))/DAB;
        double TS = cross(OA,OB)*0.5;
        return asin(TS*(1-y/DAB)*2/r/DOB)*r*r*0.5+TS*y/DAB;
    }
    else if(fabs(cross(OA,OB)) >= r*DAB || dot(AB,AC) <= 0 || dot(BA,BC) <= 0) {
        if(dot(OA,OB) < 0){
            if(cross(OA,OB) < 0) return (-acos(-1.0)-asin(cross(OA,OB)/DOA/DOB))*r*r*0.5;
            else return ( acos(-1.0)-asin(cross(OA,OB)/DOA/DOB))*r*r*0.5;
        }
        else return asin(cross(OA,OB)/DOA/DOB)*r*r*0.5;
    }
    else {
        double x = (dot(BA,BC)+sqrt(r*r*DAB*DAB-cross(BA,BC)*cross(BA,BC)))/DAB;
        double y = (dot(AB,AC)+sqrt(r*r*DAB*DAB-cross(AB,AC)*cross(AB,AC)))/DAB;
        double TS = cross(OA,OB)*0.5;
        return(asin(TS*(1-x/DAB)*2/r/DOA)+asin(TS*(1-y/DAB)*2/r/DOB))*r*r*0.5 + TS*((x+y)/DAB-1);
    }
}
double myrand(){
    return rand()%10000/10000.0;
}
int main(void){
    double a,b,c,r;
    srand(time(0));
    while((scanf("%lf%lf%lf%lf",&a,&b,&c,&r))==4){
        if(!a && !b && !c && !r)    break;
        int n=3;
        p[0]=Point(0,0);
        p[1]=Point(a,0);
        double x=(a*a+c*c-b*b)/2/a;
        double y=sqrt(c*c-x*x);
        p[2]=Point(x,y);
//        for(int i=0;i<3;i++)    printf("%f %f\n",p[i].x,p[i].y);
        double sx=0.0,sy=0.0;
        double E=0.0;
        double T=100;
        for(int i=0;i<n;i++)    E+=CulArea(p[i],p[(i+1)%n],Circle({sx,sy},r));
//        cout << E << endl;
        while(T>EPS){
            double mx=0.0;
            double nextx,nexty;
            for(int i=0;i<100;i++){
                double ang=2*PI*myrand();
                double nx=sx+cos(ang)*T;
                double ny=sy+sin(ang)*T;
                double nE=0;
                for(int i=0;i<n;i++)    nE+=CulArea(p[i],p[(i+1)%n],Circle({nx,ny},r));
                if(nE>mx){
                    mx=nE;
                    nextx=nx;
                    nexty=ny;
                }
            }
            if(sign(mx-E)>0 || exp(mx-E)/T>myrand()){
                E=mx;
                sx=nextx;
                sy=nexty;
            }
            T*=0.8;
        }
        printf("%.10f\n",E);
    }

    return 0;
}