LA4127计算几何+离散化+点覆盖

/*
LA4127计算几何
离散化的思想。刘的书上已经说得很清楚。
重点是自己手写的函数：
1、判断线段和线段的交点
2、覆盖在最上面的线段的判断
离散化的思想和之前做的LA2527是一致的
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <ctype.h>
#include <string>
#include <iostream>
#include <sstream>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <list>
#include <set>
#include <algorithm>
#define INF 0x3f3f3f3f
#define eps 1e-7
#define eps2 1e-3
#define zero(x) (((x)>0?(x):-(x))<eps)
using namespace std;


struct Point
{
    double x,y;
    Point() {}
    Point(double xx,double yy)
    {
        x=xx;
        y=yy;
    }
    bool operator<(const Point& p) const{
        if (x==p.x) return y<p.y;
        else return x<p.x;
    }
};

typedef Point Vector;

struct Segment
{
    Point p1,p2;
    Segment(){}
    Segment(Point p11,Point p22)
    {
        p1=p11;p2=p22;
    }
    double getk()
    {
        return (p1.y-p2.y)/(p1.x-p2.x);
    }
}Seg[25005];

struct Line
{
    Point p;
    Vector v;
    Line(){}
    Line(Point pp,Vector vv)
    {
        v=vv;
        p=pp;
    }
};
bool operator==(Point A,Point B)
{
    if ((fabs(A.x-B.x)<eps) && (fabs(A.y-B.y)<eps)) return true;
    else return false;
}
Vector operator-(Point A,Point B)//表示A指向B
{
    return Vector(A.x-B.x,A.y-B.y);
}
Vector operator*(Vector A,double k)
{
    return Vector(A.x*k,A.y*k);
}
Vector operator+(Point A,Point B)//表示A指向B
{
    return Vector(B.x+A.x,B.y+A.y);
}
double Dot(Vector A,Vector B)
{
    return A.x*B.x+A.y*B.y;
}
double Length(Vector A)
{
    return sqrt(Dot(A,A));
}
double Cross(Vector A,Vector B)
{
    return A.x*B.y-A.y*B.x;
}
double Area2(Point A,Point B,Point C)
{
    return Cross(B-A,C-A);
}
int dcmp(double x)
{
    if(fabs(x)<eps) return 0;
    else if(x>0) return 1;
    else return -1;
}
double angle(Vector v)
{
    return atan2(v.y,v.x);
}
Vector Rotate(Vector A,double rad)//向量向逆时针旋转
{
    return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));
}
Point InterSection(Line L1,Line L2)//求直线交点
{
    Vector u=L1.p-L2.p;
    double t=Cross(L2.v,u)/Cross(L1.v,L2.v);
    return L1.p+L1.v*t;
}
bool SegInter(Segment l1,Segment l2,double* xx)
{
    Point jiao=(InterSection(Line(l1.p1,l1.p2-l1.p1),Line(l2.p1,l2.p2-l2.p1)));
    *xx=jiao.x;
    if ( *xx-l1.p1.x>=0 && l1.p2.x-*xx>=0 && *xx-l2.p1.x>=0 && l2.p2.x-*xx>=0) return true;else return false;
}
int findUpesetLine(int cnt,double a)//线段个数，中点横坐标，返回最上（后）覆盖这个点的线段序号
{
    int ans=-1;
    double my=-1;
    for(int i=0;i<cnt;i++)
    {
        double x1=Seg[i].p1.x,y1=Seg[i].p1.y,x2=Seg[i].p2.x,y2=Seg[i].p2.y;
        if (x1-a>0 || a-x2>0) continue;
        double k1=x1-a,k2=x2-a;
        double y=(k2*y1-k1*y2)/(-k1+k2);
        if (y-my>0)
        {
            my=y;
            ans=i;
        }
    }
    return ans;
}
int n,cas=0;
double x,h,b;
double X[25500];//离散的x坐标
int main()
{
    double ans=0;
    int cnt=0;//线段的个数
    int cnt2=0;//离散点的个数
    while(cin>>n && n>0)
    {
        cas++;
        ans=0;
        cnt=cnt2=0;
        for(int i=0;i<n;i++)//预处理
        {
            cin>>x>>h>>b;
            b=b/2;
            Seg[cnt++]=Segment(Point(x-b,0),Point(x,h));
            Seg[cnt++]=Segment(Point(x,h),Point(x+b,0));
            X[cnt2++]=x-b;X[cnt2++]=x;X[cnt2++]=x+b;
        }
        for(int i=1;i<cnt;i++)
        for(int j=0;j<i;j++)//线段两两求交点
        {
            double xx;
            bool ok=SegInter(Seg[i],Seg[j],&xx);
            if (ok) X[cnt2++]=xx;
        }
        sort(X,X+cnt2);
//        for(int i=0;i<cnt2;i++) cout<<X[i]<<" ";cout<<endl;
        for(int i=0;i<cnt2-1;i++)//枚举每两个相邻离散线段的中点
        {
            double px=(X[i]+X[i+1])/2;
            int num=findUpesetLine(cnt,px);
            if (num!=-1){
                double k=Seg[num].getk();//用斜率求线段长度
                ans+=(X[i+1]-X[i])*sqrt(1+k*k);
            }
        }
        printf("Case %d: %d

",cas,(int)(ans+0.5));
    }

}