bzoj 2178 自适应Simpson积分

Posted 2020-09-01 SD_le

 1 #include<iostream>
 2 #include<algorithm>
 3 #include<cstdio>
 4 #include<cstring>
 5 #include<algorithm>
 6 #include<cmath>
 7 using namespace std;
 8 int n;
 9 const double eps = 1e-13;
10 struct node
11 {
12     double x,y,r;
13 }b[1006],a[1006];int cnt;
14 bool cmp1(node aa,node bb)
15 {
16     return aa.r<bb.r;    
17 }
18 bool v[1005];
19 double dis(int x,int y)
20 {
21     return sqrt((b[x].x-b[y].x)*(b[x].x-b[y].x)+(b[x].y-b[y].y)*(b[x].y-b[y].y));
22 }
23 double lmin,rmax;
24 pair<double,double>q[1005];
25 double mx(double x,double y)
26 {
27     return x<y?y:x;
28 }
29 double f(double x)
30 {
31     int top=0;double len=0;
32     for(int i=1;i<=cnt;i++)
33     {
34         double xx=fabs(a[i].x-x);
35         if(fabs(xx)<=a[i].r)
36         {
37             double ww=sqrt(a[i].r*a[i].r-xx*xx);
38             q[++top].first=a[i].y-ww;
39             q[top].second=a[i].y+ww;
40         }
41     }
42     sort(q+1,q+top+1);len+=q[1].second-q[1].first;
43     double rs=q[1].second;
44     for(int i=2;i<=top;i++)if(q[i].second>rs)len+=q[i].second-mx(q[i].first,rs),rs=q[i].second;
45     return len;
46 }
47 double asr(double l,double mid,double r,double A,double B,double C)
48 {
49     double s=((r-l)/6)*(A+4*B+C),lf=f((l+mid)/2),rf=f((mid+r)/2);
50     double ls=((mid-l)/6)*(A+B+4*lf),rs=((r-mid)/6)*(B+C+4*rf);
51     if(fabs(s-ls-rs)<=eps)return s;
52     return asr(l,(l+mid)/2,mid,A,lf,B)+asr(mid,(r+mid)/2,r,B,rf,C);
53 }
54 int main()
55 {
56     scanf("%d",&n);
57     for(int i=1;i<=n;i++)
58     {
59         scanf("%lf%lf%lf",&b[i].x,&b[i].y,&b[i].r);
60         lmin=min(lmin,b[i].x-b[i].r);rmax=max(rmax,b[i].x+b[i].r);
61     }
62     sort(b+1,b+n+1,cmp1);
63     for(int i=1;i<=n;i++)
64     {
65         for(int j=1;j<i;j++)
66         {
67             if(dis(i,j)<=b[i].r-b[j].r)v[j]=1;
68         }
69     }
70     for(int i=1;i<=n;i++)if(!v[i])a[++cnt]=b[i];
71     printf("%.3f\n",asr(lmin,(lmin+rmax)/2,rmax,0,f((lmin+rmax)/2),0));
72     return 0;
73 }