1503: 點到圓弧的距離

分析：

先判斷點和圓心的連線是否在圓弧範圍內，如果在，最短距離即到圓心的距離減去半徑的絕對值；反之，為到端點的最短距離。

具體看註釋

#include <bits/stdc++.h>
using namespace std;

#define eps 1e-8
const double pi=acos(-1);

struct Point
{
    double x,y;
    Point(double a=0,double b=0)
    {
        x=a;
        y=b;
    }
};

Point 
 
operator - (Point a,Point b)
{
    return Point(a.x-b.x,a.y-b.y);
}

double dist(Point a,Point b)
{
    return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}

double multi(Point a,Point b)
{
    return a.x*b.x+a.y*b.y;
}

double cross(Point a,Point b)
{
    return a.x*b.y-a.y*b.x;
}

Point TriangleCircumCenter(Point a,Point b,Point c)
{
    Point res;
    
 
double a1=atan2(b.y-a.y,b.x-a.x)+pi/2;
    double a2=atan2(c.y-b.y,c.x-b.x)+pi/2;
    double ax=(a.x+b.x)/2;
    double ay=(a.y+b.y)/2;
    double bx=(c.x+b.x)/2;
    double by=(c.y+b.y)/2;
    double r1=(sin(a2)*(ax-bx)+cos(a2)*(by-ay))/(sin(a1)*cos(a2)-sin(a2)*cos(a1));
    return Point(ax+r1*cos(a1),ay+r1*sin(a1));
}

 
int main()
{
//    freopen("in.txt","r",stdin);
//    freopen("out.txt","w",stdout);
    int x1,y1,x2,y2,x3,y3,xp,yp;
    int kase=0;
    while(~scanf("%d%d%d%d%d%d%d%d",&x1,&y1,&x2,&y2,&x3,&y3,&xp,&yp))
    {
        Point p1=Point(x1,y1);
        Point p2=Point(x2,y2);
        Point p3=Point(x3,y3);
        Point pp=Point(xp,yp);
        Point pc=TriangleCircumCenter(p1,p2,p3);    //算圓心
        double temp=cross(p2-p1,p3-p1);
        if(temp<0)  //如果是順時針，把p1和p3點互換
        {
            Point t=p1;
            p1=p3;
            p3=t;
        }
        double cosA=multi(p1-pc,p3-pc)/(dist(p1,pc)*dist(p3,pc));
        if(fabs(cosA)>1)    //如果fabs(cosA)>1，那麽acos(cosA)算出的結果是不合法的
        {
            if(cosA<0) cosA+=eps;
            else cosA-=eps;
        }
        double maxd=acos(cosA); //算p1-pc與p3-pc的夾角
        if(cross(p1-pc,p3-pc)<0 && fabs(cross(p1-pc,p3-pc))>eps)
            maxd=2*pi-maxd;
        double cosB=multi(p1-pc,pp-pc)/(dist(p1,pc)*dist(pp,pc));
        if(fabs(cosB)>1)
        {
            if(cosB<0) cosB+=eps;
            else cosB-=eps;
        }
        double degree=acos(cosB);   //算p1-pc與pp-pc的夾角
        if(cross(p1-pc,pp-pc)<0 && fabs(cross(p1-pc,pp-pc))>eps)
            degree=2*pi-degree;
        if(degree<maxd)
            printf("Case %d: %.3lf\n",++kase,fabs(dist(pp,pc)-dist(p1,pc)));
        else
            printf("Case %d: %.3lf\n",++kase,min(dist(pp,p1),dist(pp,p3)));
    }
    return 0;
}

csu-acm 1503: 點到圓弧的距離