POJ2451

#include<cmath>
#include<cstring>
#include<vector>
#include<cstdio>
#include<iostream>
#include<algorithm>

using namespace std;

#define db double

const db eps=1e-6;
const int N=1e6+7;

inline db sqr(db x){
    return x*x;
}

inline int dcmp(const db &x){
    if(fabs(x)<eps)return 0;
    return x>0?1:-1;
}

struct Point{
    db x,y;

    inline Point(){}
    inline Point(db _x,db _y):x(_x),y(_y){}

};

#define Vec Point

inline Vec operator +(const Vec &a,const Vec &b){
    return Vec(a.x+b.x,a.y+b.y);
}

inline Vec operator -(const Vec &a,const Vec &b){
    return Vec(a.x-b.x,a.y-b.y);
}

inline void operator +=(Vec &a,const Vec &b){
    a.x+=b.x,a.y+=b.y;
}

inline void operator -=(Vec &a,const Vec &b){
    a.x-=b.x,a.y-=b.y;
}

inline Vec operator *(const Vec &a,const db &b){
    return Vec(a.x*b,a.y*b);
}

inline Vec operator /(const Vec &a,const db &b){
    return Vec(a.x/b,a.y/b);
}

inline db Cross(const Vec &a,const Vec &b){
    return a.x*b.y-a.y*b.x;
}

inline db Angle(const Vec &a){
    return atan2(a.y,a.x);
}

struct Line{
    Point S,T;
    db theta;

    inline Line(){}
    inline Line(const Point &A,const Point &B):S(A),T(B),theta(Angle(B-A)){}

};

#define Seg Line

inline bool operator < (const Line &A,const Line &B){
    double alpha=A.theta-B.theta;
    if(dcmp(alpha))return dcmp(alpha)==-1;
    return dcmp(Cross(A.T-A.S,B.S-A.S))==-1;
}

inline bool check(const Line &a,const Line &b){
    return dcmp(Cross(a.T-a.S,b.T-b.S))==0;
}

inline Point LineCross(const Line &a,const Line &b){
    Vec u=a.T-a.S;
    Vec v=b.T-b.S;
    Vec w=a.S-b.S;
    db t=Cross(v,w)/Cross(u,v);
    return a.S+u*t;
}
//on the right or not
inline bool Direction(const Line &a,const Point &A){
    return dcmp(Cross(a.T-a.S,A-a.S))==-1;
}

Line Q1[N];
Point Q2[N];

inline bool Half(Line *A,int n,Point *B,int &m){
    int head=0,tail=0;
    sort(A+1,A+n+1);
    Q1[0]=A[1];
    for(int i=2;i<=n;++i){
        if(!dcmp(A[i].theta-A[i-1].theta))continue;
        while(head<tail&&Direction(A[i],Q2[tail-1]))--tail;
        while(head<tail&&Direction(A[i],Q2[head]))++head;
        Q1[++tail]=A[i];
        Q2[tail-1]=LineCross(A[i],Q1[tail-1]);
    }
    while(head<tail&&Direction(Q1[head],Q2[tail-1]))--tail;
    while(head<tail&&Direction(Q1[tail],Q2[head]))++head;
    Q2[tail]=LineCross(Q1[head],Q1[tail]);
    m=0;
    for(int i=head;i<=tail;++i)B[++m]=Q2[i];
    return 1;
}

inline db Area(Point *A,int n){
    db sum=Cross(A[n],A[1]);
    for(int i=1;i<n;++i){
        sum+=Cross(A[i],A[i+1]);
    }
    return sum/2;
}

const db Limit=10000;

Line A[N];
Point B[N];

int main(){
//  freopen(".in","r",stdin);
//  freopen(".out","w",stdout);
    int n;scanf("%d",&n);
    for(int i=1;i<=n;++i){
        db a,b,c,d;
        scanf("%lf%lf%lf%lf",&a,&b,&c,&d);
        A[i]=Line(Point(a,b),Point(c,d));
    }
    Point a(0,0);
    Point b(Limit,0);
    Point c(Limit,Limit);
    Point d(0,Limit);
    A[++n]=Line(a,b);
    A[++n]=Line(b,c);
    A[++n]=Line(c,d);
    A[++n]=Line(d,a);
    printf("%.1lf",Half(A,n,B,n)?Area(B,n):0);
    return 0;
}
/*
3
10000 10000 0 5000
10000 5000 5000 10000
0 5000 5000 0

*/