POJ 2540 Hotter Colder（半平面交）
题目链接：http://poj.org/problem?id=2540
题意：一个正方形，坐标为（0，0）、（10,0）、（10、10）、（0,10）。现在有A、B两人做一个游戏。B首先指定一个正方形中的目标位置P。开始时A在（0,0）点，每次A走到另一点上，B告诉A离目标位置远了（Colder）还是近了（Hotter）还是一样（Same），在B每次告诉A后输出目标位置可能的面积。
思路：每次走过的路线的中垂线和原多边形求交。根据Colder和Hotter判断是交左侧还是右侧。
int DB(double x)
{
if(x>1e-10) return 1;
if(x<-1e-10) return -1;
return 0;
}
struct point
{
double x,y;
point(){}
point(double _x,double _y)
{
x=_x;
y=_y;
}
void read()
{
RD(x,y);
}
void output()
{
printf("(%.2lf %.2lf)",x,y);
}
point operator+(point a)
{
return point(x+a.x,y+a.y);
}
point operator-(point a)
{
return point(x-a.x,y-a.y);
}
double operator*(point a)
{
return x*a.y-y*a.x;
}
point operator*(double t)
{
return point(x*t,y*t);
}
point operator/(double t)
{
return point(x/t,y/t);
}
bool operator==(point a)
{
return DB(x-a.x)==0&&DB(y-a.y)==0;
}
bool operator!=(point a)
{
return DB(x-a.x)||DB(y-a.y);
}
};
point a[N];
int n;
//t在ab的左侧返回正值
double cross(point a,point b,point t)
{
return point(b-a)*point(t-a);
}
point getCross(point a,point b,point p,point q)
{
double s1=(a-p)*(b-p);
double s2=(b-q)*(a-q);
double t=s1+s2;
return (p*s2+q*s1)/(s1+s2);
}
double getDist(point a,point b)
{
return sqrt(sqr(a.x-b.x)+sqr(a.y-b.y));
}
double getArea(point p[],int n)
{
double ans=0;
int i;
p[n]=p[0];
FOR0(i,n) ans+=p[i]*p[i+1];
return ans/2;
}
void moveSegment(point &p1,point &p2,double r)
{
r/=getDist(p1,p2);
point p=point(p1.y-p2.y,p2.x-p1.x)*r;
p1=p1+p;
p2=p2+p;
}
void deal(point a[],int &n,point p1,point p2,int flag)
{
point b[N],p;
int i,m=n,t1,t2;
FOR0(i,n) b[i]=a[i];
b[m]=b[0];
n=0;
FOR0(i,m)
{
t1=DB(cross(p1,p2,b[i]));
t2=DB(cross(p1,p2,b[i+1]));
p=getCross(p1,p2,b[i],b[i+1]);
if(flag) t1=-t1,t2=-t2;
if(t1>0&&!t2||t1>0&&t2>0||!t1&&t2>0)
{
a[n++]=b[i],a[n++]=b[i+1];
}
else if(t1>0&&t2<0) a[n++]=b[i],a[n++]=p;
else if(t1<0&&t2>0) a[n++]=p,a[n++]=b[i+1];
else if(!t1&&t2<0) a[n++]=b[i];
else if(t1<0&&!t2) a[n++]=b[i+1];
}
m=1;
FOR1(i,n-1) if(a[i]!=a[i-1]) a[m++]=a[i];
if(a[m-1]==a[0]) m--;
n=m;
}
void deal(point a[],int &n,point p1,point p2,char cmd[])
{
point mid=(p1+p2)/2,dir=point(p1.y-p2.y,p2.x-p1.x);
deal(a,n,mid,mid+dir,cmd[0]=='H');
}
int main()
{
point pre=point(0,0),cur;
char cmd[20];
int flag=0;
a[0]=point(0,0);
a[1]=point(10,0);
a[2]=point(10,10);
a[3]=point(0,10);
n=4;
while(scanf("%lf%lf%s",&cur.x,&cur.y,cmd)!=-1)
{
if(cmd[0]=='S'||flag)
{
puts("0.00");
flag=1;
continue;
}
deal(a,n,pre,cur,cmd);
printf("%.2lf\n",fabs(getArea(a,n)));
pre=cur;
}
return 0;
}