Description
有n个圆盘从天而降，后面落下的可以盖住前面的。求最后形成的封闭区域的周长。看下面这副图, 所有的红色线条的总长度即为所求.
Input
n ri xi y1 ... rn xn yn
Output
最后的周长，保留三位小数
Sample Input
2
1 0 0
1 1 0
Sample Output
10.472
数据规模
n<=1000
调了一晚上外加下午（弱菜写计算几何，tan函数都抄错了）
对每一个圆计算覆盖区间，然后排序，再区间合并，注意范围，我是全部弄到0到2π里
再膜拜一下z55250825，最后还是他看出错误来的
1 uses math; 2 const 3 maxn=1010; 4 eps=1e-7; 5 var 6 r,x,y,ll,rr:array[0..maxn*2]of double; 7 n,tot:longint; 8 ans:double; 9 10 procedure init; 11 var 12 i:longint; 13 begin 14 read(n); 15 for i:=1 to n do 16 read(r[i],x[i],y[i]); 17 end; 18 19 function angle(a,b,c:double):double; 20 begin 21 exit(arccos((a*a+b*b-c*c)/(2*a*b))); 22 end; 23 24 function tan(x,y:double):double; 25 var 26 a:double; 27 begin 28 if abs(x)<eps then 29 begin 30 if y>-eps then exit(pi/2) 31 else exit(pi*3/2); 32 end; 33 if abs(y)<eps then 34 begin 35 if x>-eps then exit(0) 36 else exit(pi); 37 end; 38 a:=arctan(y/x); 39 if a<-eps then a:=-a; 40 if x>-eps then 41 if y>-eps then exit(a) 42 else exit(2*pi-a) 43 else 44 if y>-eps then exit(pi-a) 45 else exit(pi+a); 46 end; 47 48 procedure swap(var x,y:double); 49 var 50 t:double; 51 begin 52 t:=x;x:=y;y:=t; 53 end; 54 55 procedure sort(l,r:longint); 56 var 57 i,j:longint; 58 y:double; 59 begin 60 i:=l; 61 j:=r; 62 y:=ll[(l+r)>>1]; 63 repeat 64 while ll[i]+eps<y do 65 inc(i); 66 while ll[j]>y+eps do 67 dec(j); 68 if i<=j then 69 begin 70 swap(ll[i],ll[j]); 71 swap(rr[i],rr[j]); 72 inc(i); 73 dec(j); 74 end; 75 until i>j; 76 if i<r then sort(i,r); 77 if l<j then sort(l,j); 78 end; 79 80 procedure work; 81 var 82 i,j:longint; 83 d,a,b,sum,xx,yy:double; 84 cover:boolean; 85 begin 86 for i:=1 to n do 87 begin 88 tot:=0; 89 cover:=false; 90 for j:=i+1 to n do 91 begin 92 d:=sqrt((x[i]-x[j])*(x[i]-x[j])+(y[i]-y[j])*(y[i]-y[j])); 93 if (r[i]+r[j]-d<eps)or(d+r[j]-r[i]<eps) then continue; 94 if d+r[i]-r[j]<eps then 95 begin 96 cover:=true; 97 break; 98 end; 99 a:=tan(x[j]-x[i],y[j]-y[i]); 100 b:=angle(d,r[i],r[j]); 101 inc(tot); 102 ll[tot]:=a-b; 103 rr[tot]:=a+b; 104 if ll[tot]<-eps then 105 begin 106 ll[tot+1]:=2*pi+ll[tot]; 107 rr[tot+1]:=2*pi; 108 ll[tot]:=0; 109 inc(tot); 110 end; 111 if rr[tot]>2*pi+eps then 112 begin 113 rr[tot+1]:=rr[tot]-2*pi; 114 ll[tot+1]:=0; 115 rr[tot]:=2*pi; 116 inc(tot); 117 end; 118 end; 119 if cover then continue; 120 sort(1,tot); 121 inc(tot); 122 ll[tot]:=100; 123 rr[tot]:=100; 124 sum:=0; 125 xx:=0; 126 yy:=0; 127 for j:=1 to tot do 128 if ll[j]+eps<=yy then 129 begin 130 if rr[j]+eps<=yy then continue; 131 yy:=rr[j]; 132 end 133 else 134 begin 135 sum:=sum+yy-xx; 136 xx:=ll[j]; 137 yy:=rr[j]; 138 end; 139 ans:=ans+(2*pi-sum)*r[i]; 140 end; 141 write(ans:0:3); 142 end; 143 144 begin 145 init; 146 work; 147 end.