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来源：互联网发布：sql注入防止php 编辑：程序博客网时间：2024/05/18 17:40
#include <iostream>#include <stdio.h>#include <string.h>#include <algorithm>#include <stdlib.h>#include <cmath>#define MAXN 100000#define EPS 1e-5using namespace std;int n;struct Point{    double x,y;    Point(){}    Point(double _x,double _y):x(_x),y(_y){}};struct Circle{    Point o;    double r;    Circle(){}    Circle(Point _o,double _r):o(_o),r(_r){}}circles[MAXN],tmp[MAXN];pair<double,double>intervals[MAXN];int tot=0,st,ed;bool cmp(Circle a,Circle b){    if(fabs(a.o.x-a.r-b.o.x+b.r)<EPS) return a.o.x+a.r<b.o.x+b.r;    return a.o.x-a.r<b.o.x-b.r;}bool cmp2(Circle a,Circle b){    return a.r>b.r;}bool check(Circle a,Circle b){    return (a.o.x-b.o.x)*(a.o.x-b.o.x)+(a.o.y-b.o.y)*(a.o.y-b.o.y)<=(a.r-b.r)*(a.r-b.r);}void prework(){    sort(circles+1,circles+n+1,cmp2);    int cnt=0;    for(int i=1;i<=n;i++)    {        bool flag=true;        for(int j=1;j<=cnt;j++)            if(check(tmp[j],circles[i]))            {                flag=false;                break;            }        if(flag) tmp[++cnt]=circles[i];    }    n=cnt;    for(int i=1;i<=n;i++)        circles[i]=tmp[i];}void getCircleIntersec(Circle a,double x){    intervals[++tot]=make_pair(a.o.y-sqrt(a.r*a.r-(x-a.o.x)*(x-a.o.x)),a.o.y+sqrt(a.r*a.r-(x-a.o.x)*(x-a.o.x)));}double f(double x){    tot=0;    for(int i=st;i<=ed;i++)        if(x<circles[i].o.x+circles[i].r&&x>circles[i].o.x-circles[i].r)            getCircleIntersec(circles[i],x);    sort(intervals+1,intervals+tot+1);    double ans=0,start=-1e12,end=-1e12;    for(int i=1;i<=tot;i++)    {        if(intervals[i].first>end)        {            ans+=end-start;            start=intervals[i].first,end=intervals[i].second;        }        else end=max(intervals[i].second,end);    }    ans+=end-start;    return ans;}double calc(double len,double fL,double fM,double fR){    return (fL+4*fM+fR)*len/6;}double Simpson(double L,double M,double R,double fL,double fM,double fR,double sqr){    double M1=(L+M)/2,M2=(M+R)/2;    double fM1=f(M1),fM2=f(M2);    double g1=calc(M-L,fL,fM1,fM),g2=calc(R-M,fM,fM2,fR);    if(fabs(sqr-g1-g2)<EPS) return g1+g2;    return Simpson(L,M1,M,fL,fM1,fM,g1)+Simpson(M,M2,R,fM,fM2,fR,g2);}int main(){    double ans=0;    scanf("%d",&n);    for(int i=1;i<=n;i++)        scanf("%lf%lf%lf",&circles[i].o.x,&circles[i].o.y,&circles[i].r);    prework();    sort(circles+1,circles+n+1,cmp);    for(int i=1,j;i<=n;i++)    {        double L=circles[i].o.x-circles[i].r,R=circles[i].o.x+circles[i].r;        for(j=i+1;j<=n;j++)        {            if(circles[j].o.x-circles[j].r>R) break;            else R=max(R,circles[i].o.x+circles[i].r);        }        double M=(L+R)/2;        st=i,ed=j-1;        i=j-1;        double fL=f(L),fM=f(M),fR=f(R);        ans+=Simpson(L,M,R,fL,fM,fR,calc(R-L,fL,fM,fR));    }    printf("%.3lf\n",ans);    return 0;}
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