Uyuw's Concert

题目链接：http://poj.org/problem?id=2451

题意：要搭建舞台举行晚会，公园里有很多长椅，每条长椅的位置由一条线段表示，椅子是固定的，搬不动。现在要求所有座位都能看到舞台，求舞台的最大面积是多少。

思路：先用半平面交求出凸变形，然后再根据差积求面积即可。

#include<bits/stdc++.h>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<vector>
#include<map>
#include<iostream>
#include<algorithm>
using namespace std;
const int maxn=20010;
const int bound=10000;
const double esp= 1e-10;
struct point
{
    double x,y;
};
struct node
{
    point a,b;
};
node pp[maxn];
int cnt,id[maxn],n;
double at[maxn];
int q[maxn*2],front,rear,dg;
point dpg[maxn];
void add(double x1,double y1,double x2,double y2)
{
    pp[cnt].a.x =x1;
    pp[cnt].a .y =y1;
    pp[cnt].b.x =x2;
    pp[cnt++].b.y =y2;
}
void read()
{
    scanf("%d",&n);
    cnt=0;
    double x1,x2,y1,y2;
    for(int i=0; i<n; i++)
    {
        scanf("%lf%lf%lf%lf",&x1,&y1,&x2,&y2);
        add(x1,y1,x2,y2);
    }
    n+=4;
    add(0,0,bound,0);
    add(bound,0,bound,bound);
    add(bound,bound,0,bound);
    add(0,bound,0,0);
}
int is0(double a)
{
    if(a<=esp&&a>=-esp)
        return 0;
    if(a>esp)
        return 1;
    return -1;
}
double det(double x1,double y1,double x2,double y2)
{
    return x1*y2-x2*y1;
}

double ana(point p0,point p1,point p2)
{
    return det(p1.x-p0.x,p1.y -p0.y,p2.x -p0.x,p2.y -p0.y );
}
bool cmp(int a,int b)
{
    if(at[a]<at[b])
        return true;
    if(is0(at[a]-at[b])==0)
        if(is0(ana(pp[b].a,pp[b].b,pp[a].a ))>=0)
            return true;
    return false;
}
void deal()
{
    for(int i=0; i<n; i++)
    {
        at[i]=atan2(pp[i].b.y-pp[i].a.y,pp[i].b.x -pp[i].a.x );
        id[i]=i;
    }
    sort(id,id+n,cmp);
    int temp=1;
    for(int i=1; i<n; i++)
        if(is0(at[id[i-1]]-at[id[i]])!=0)
            id[temp++]=id[i];
    n=temp;
}
point APP(node &t1,node &t2)
{
    double d1,d2;
    point s1,e1,s2,e2;
    s1=t1.a ;
    e1=t1.b ;
    s2=t2.a ;
    e2=t2.b ;
    point temp;
    d1=ana(s2,e1,s1);
    d2=ana(e1,e2,s1);
    temp.x =(s2.x *d2+e2.x *d1)/(d2+d1);
    temp.y =(s2.y *d2+e2.y *d1)/(d2+d1);
    return temp;
}
bool judge(int x,int y,int now)
{
    point temp=APP(pp[x],pp[y]);
    double d=ana(pp[now].a,pp[now].b,temp);
    if(is0(d)<0)
        return true;
    return false;
}
void solve()
{
    int i;
    front=0;
    rear=1;
    q[0]=id[0];
    q[1]=id[1];
    for(i=2; i<n; i++)
    {
        while(front<rear&&judge(q[rear-1],q[rear],id[i]))
            rear--;
        while(front<rear&&judge(q[front],q[front+1],id[i]))
            front++;
        q[++rear]=id[i];
    }
    while(front<rear&&judge(q[rear-1],q[rear],q[front]))
        rear--;
    while(front<rear&&judge(q[front],q[front+1],q[rear]))
        front++;
    q[++rear]=q[front];
    dg=0;
    for(i=front+1; i<=rear; i++)
        dpg[dg++]=APP(pp[q[i-1]],pp[q[i]]);
}
double  area()
{
    double ans=0;
    for(int i=0; i<dg; i++)
        ans+=dpg[i].x*dpg[(i+1)%dg].y -dpg[(i+1)%dg].x *dpg[i].y ;
    ans=fabs(ans)/2.0;
    return ans;
}
int main()
{
    read();
    deal();
    solve();
    printf("%.1f\n",area());
    return 0;
}