# BZOJ 1043 [HAOI2008]下落的圆盘 ——计算几何

QAQ

#include <map>
#include <cmath>
#include <queue>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
#define F(i,j,k) for (int i=j;i<=k;++i)
#define D(i,j,k) for (int i=j;i>=k;--i)
#define eps 1e-8
#define sqr(x) x*x
#define ll long long
#define mp make_pair

const double pi=acos(-1.0);

struct Vector{
double x,y;
void print()
{
printf("Vector -> (%.3f,%.3f)\n",x,y);
}
};

struct Point{
double x,y;
void print()
{
printf("Point . (%.3f,%.3f)\n",x,y);
}
};

Vector operator + (Vector a,Vector b)
{Vector ret;ret.x=a.x+b.x;ret.y=a.y+b.y;return ret;}

Vector operator - (Vector a,Vector b)
{Vector ret;ret.x=a.x-b.x;ret.y=a.y-b.y;return ret;}

Point operator + (Point a,Vector b)
{Point ret;ret.x=a.x+b.x;ret.y=a.y+b.y;return ret;}

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

Vector operator * (Vector a,double b)
{Vector ret;ret.x=a.x*b;ret.y=a.y*b;return ret;}

double operator * (Vector a,Vector b)
{return a.x*b.y-a.y*b.x;}

Vector Turn(Vector a,double b)
{
Vector ret;
ret.x=a.x*cos(b)-a.y*sin(b);
ret.y=a.x*sin(b)+a.y*cos(b);
return ret;
}

int n;

struct Circle{
double x,y,r;
void print()
{
printf("Circle (%.3f,%.3f) r = %.3f\n",x,y,r);
}
}a[1005];

double dst(double x1,double y1,double x2,double y2)
{return sqrt((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1));}

int dcmp(double x)
{
if (x>eps) return 1;
if (fabs(x)<eps) return 0;
return -1;
}

bool in(Circle a,Circle b)
{
if (dcmp(dst(a.x,a.y,b.x,b.y)-(b.r-a.r))<=0) return true;
return false;
}

struct Cut_Cir{
double l,r;
void print()
{
printf("Ang (%.3f,%.3f)\n",l,r);
}
}sta[1000005];
int top=0;

double nege(double x)
{
if (dcmp(x)==-1) x+=2*pi;
while (dcmp(x-2*pi)>=0) x-=2*pi;
return x;
}

void Cut(int pos)
{
top=0; double dist; Vector v0,v1,v2;
F(i,pos+1,n)
if ((dist=dst(a[pos].x,a[pos].y,a[i].x,a[i].y))<a[pos].r+a[i].r)
{
double ang; ang=(sqr(a[pos].r)+sqr(dist)-sqr(a[i].r))/(2*a[pos].r*dist);
if (ang>1.0) continue;
ang=acos(ang);
v0.x=a[i].x-a[pos].x;v0.y=a[i].y-a[pos].y;
v0=v0*(1.0/sqrt(sqr(v0.x)+sqr(v0.y))*a[pos].r);
v1=Turn(v0,ang);
v2=Turn(v0,-ang);
double t1=atan2(v1.y,v1.x),t2=atan2(v2.y,v2.x);
t1+=pi;t2+=pi;
while (t1>2*pi) t1-=2*pi;
while (t2>2*pi) t2-=2*pi;
if (t1<t2)
{
++top;
sta[top].l=0;
sta[top].r=t1;
++top;
sta[top].l=t2;
sta[top].r=2*pi;
}
else
{
++top;
sta[top].l=t2;
sta[top].r=t1;
}
}
}

double C(Circle a)
{return a.r*2*pi;}

bool cmp2(Cut_Cir a,Cut_Cir b)
{return a.l<b.l;}

double cal(double r)
{
sort(sta+1,sta+top+1,cmp2);
double now=0,ret=0;
F(i,1,top)
{
now=max(now,sta[i].l);
ret+=max(0.0,sta[i].r-now);
now=max(now,sta[i].r);
}
return ret*r;
}

double ans=0;

int main()
{
scanf("%d",&n);
F(i,1,n) scanf("%lf%lf%lf",&a[i].r,&a[i].x,&a[i].y);
F(i,1,n)
{
int flag=1;
F(j,i+1,n) if (in(a[i],a[j]))
flag=0;
if (!flag) continue;
Cut(i);
ans+=C(a[i]);
ans-=cal(a[i].r);
}
printf("%.3f\n",ans);
}


posted @ 2017-04-06 17:03  SfailSth  阅读(96)  评论(0编辑  收藏  举报