bzoj 2178

这题调精度真痛苦啊（向管理员要了数据才调出来）。

用的是hwd在WC2015上讲的方法，考虑将原图分割，根据每个圆的左右边界和圆与圆交点的横坐标来分割，这样原图就被分成很多竖着的长条，并且每一条中间都没有交点，这样就有一个性质：每一条都是"弓形-梯形-弓形 弓形-梯形-弓形..."的形式，然后从一个方向开始，记录当前进入的圆的数量，每当出来就就计算面积。

 /**************************************************************
     Problem: 2178
     User: idy002
     Language: C++
     Result: Accepted
     Time:1248 ms
     Memory:48560 kb
 ****************************************************************/

 #include <cstdio>
 #include <cstring>
 #include <cmath>
 #include <algorithm>
 #define eps 1e-11
 #define N 2010
 using namespace std;

 inline int sg( long double x ) { return (x>-eps)-(x<eps); }
 struct Vector {
     long double x, y;
     Vector(){}
     Vector( long double x, long double y ):x(x),y(y){}
     Vector operator+( const Vector & b ) const { return Vector(x+b.x,y+b.y); }
     Vector operator-( const Vector & b ) const { return Vector(x-b.x,y-b.y); }
     Vector operator*( long double b ) const { return Vector(x*b,y*b); }
     Vector operator/( long double b ) const { return Vector(x/b,y/b); }
     long double operator^( const Vector & b ) const { return x*b.y-y*b.x; }
     long double operator&( const Vector & b ) const { return x*b.x+y*b.y; }
     long double ang() { return atan2(y,x); }
     long double len() { return sqrt(x*x+y*y); }
     long double len2() { return x*x+y*y; }
 };
 typedef Vector Point;
 struct Circle {
     Point c;
     long double r;
     Circle(){}
     Circle( Point c, long double r ):c(c),r(r){}
     inline bool in( Point &p ) {
         Vector vv=p-c;
         return (vv.x*vv.x+vv.y*vv.y) < r*r*0.999;
     }
     Point pt( long double ang ) const {
         return c+Vector(cos(ang),sin(ang))*r;
     }
 };
 struct Arc {
     int cid, type;
     long double al, ar;
     Point pa, pb;
     Arc(){}
     Arc( int cid, int type, const Point &a, const Point &b );
     long double area();
 };

 int n;
 bool del[N], has[N];
 long double spt[N*N]; int stot;
 Circle cir[N];
 Arc arc[N+N];

 bool cmp_arc( const Arc &a, const Arc &b ) {
     if( sg(a.pa.y-b.pa.y)!= ) return sg(a.pa.y-b.pa.y)<;
     if( sg(a.pb.y-b.pb.y)!= ) return sg(a.pb.y-b.pb.y)<;
     if( a.type!=b.type ) return a.type>b.type;
     if( a.type== ) {
         return cir[a.cid].r < cir[b.cid].r;
     } else {
         return cir[a.cid].r > cir[b.cid].r;
     }
 }
 bool cmp_cir_r( const Circle &a, const Circle &b ) { return a.r<b.r; }
 Arc::Arc( int cid, int type, const Point &a, const Point &b ) {
     this->cid = cid;
     this->type = type;
     pa = a;
     pb = b;
     this->al = (a-cir[cid].c).ang();
     this->ar = (b-cir[cid].c).ang();
     if( pa.x>pb.x ) swap(pa,pb);
 }
 long double Arc::area() {
     long double da = ar-al;
     while( sg(da)<= ) da+=M_PI+M_PI;
     while( sg(da-M_PI-M_PI)> ) da-=M_PI+M_PI;
     return (da-sin(da))*cir[cid].r*cir[cid].r/2.0;
 }
 int ccinter( int ca, int cb, Point *p ) {
     if( cir[ca].r<cir[cb].r ) swap(ca,cb);
     long double cd = (cir[ca].c - cir[cb].c).len2();
     long double s1 = cir[ca].r-cir[cb].r;
     long double s2 = cir[ca].r+cir[cb].r;
     s1=s1*s1, s2=s2*s2;

     if( sg(cd-s1)< || sg(cd-s2)> ) return ;
     if( sg(cd-s1)== || sg(cd-s2)== ) {
         long double ang = (cir[cb].c-cir[ca].c).ang();
         p[] = cir[ca].pt(ang);
         return ;
     }
     long double r1 = cir[ca].r, r2 = cir[cb].r;
     long double base = (cir[cb].c-cir[ca].c).ang();
     long double delta = acos( (r1*r1+cd-r2*r2)/(2.0*r1*sqrt(cd)) );
     p[] = cir[ca].pt( base-delta );
     p[] = cir[ca].pt( base+delta );
     return ;
 }
 bool clinter( int c, long double xl, long double xr, Arc *arc ) {
     long double xlb = cir[c].c.x-cir[c].r;
     long double xrb = cir[c].c.x+cir[c].r;
     if( sg(xlb-xr)>= || sg(xrb-xl)<= ) return false;
     Point p = cir[c].c;
     long double r = cir[c].r;
     long double d1, d2;
     long double s1 = r*r-(p.x-xl)*(p.x-xl);
     long double s2 = r*r-(p.x-xr)*(p.x-xr);
     if( s1<0.0 ) s1=0.0;
     if( s2<0.0 ) s2=0.0;
     d1 = sqrt( s1 );
     d2 = sqrt( s2 );
     arc[] = Arc( c, -, Point(xr,p.y+d2), Point(xl,p.y+d1) );
     arc[] = Arc( c, +, Point(xl,p.y-d1), Point(xr,p.y-d2) );
     return true;
 }
 long double area( long double lf, long double rg ) {
     int m=;
     for( int i=; i<n; i++ )
         if( clinter(i,lf,rg,arc+m) )
             m += ;
     sort( arc, arc+m, cmp_arc );

     int cc = , top;
     long double rt = 0.0;
     for( int i=; i<m; i++ ) {
         if( cc== )
             top = i;
         cc += arc[i].type;
         if( cc== ) {
             rt += (rg-lf)*((arc[i].pa+arc[i].pb).y-(arc[top].pa+arc[top].pb).y)/2.0;
             rt += arc[top].area()+arc[i].area();
         }
     }
     return rt;
 }
 bool cmp_eq( long double x, long double y ) {
     return sg(x-y)==;
 }
 void clean() {
     int j=;
     for( int i=; i<n; i++ )
         if( !del[i] ) cir[j++]=cir[i];
     n = j;
 }
 long double area() {
     Point ip[];
     int ic;
     long double rt = 0.0;
     for( int i=; i<n; i++ ) {
         for( int j=i+; j<n; j++ ) {
             ic = ccinter( i, j, ip );
             if( ic<= ) continue;
             for( int k=; k<ic; k++ ) {
                 int q=n;
                 for( q=; q<n; q++ ) {
                     if( q==i || q==j ) continue;
                     if( cir[q].in(ip[k]) )
                         break;
                 }
                 if( q==n ) spt[stot++]=ip[k].x;
             }
         }
     }
     for( int i=; i<n; i++ ) {
         spt[stot++] = cir[i].c.x-cir[i].r;
         spt[stot++] = cir[i].c.x+cir[i].r;
     }
     sort( spt, spt+stot );
     stot = unique( spt, spt+stot, cmp_eq ) - spt;

     for( int i=; i<stot; i++ )
         rt += area( spt[i-], spt[i] );
     return rt;
 }
 void init() {
     sort( cir, cir+n, cmp_cir_r );
     for( int i=; i<n; i++ )
         for( int j=i+; j<n; j++ ) {
             long double dx = cir[i].c.x-cir[j].c.x;
             long double dy = cir[i].c.y-cir[j].c.y;
             long double dij = dx*dx+dy*dy;
             long double cc = cir[j].r-cir[i].r;
             cc = cc*cc;
             if( dij<cc ) del[i]=true;
         }
     clean();
 }
 int main() {
     scanf( "%d", &n );
     for( int i=; i<n; i++ )
         scanf( "%Lf%Lf%Lf", &cir[i].c.x, &cir[i].c.y, &cir[i].r );
     init();
     printf( "%.3Lf\n", area() );
 }