2019.02.21 bzoj1249: SGU277 HERO 动态凸包（set+凸包）

传送门

题意：动态插入点，维护凸包面积。

---

思路：用setsetset维护极角序来支持面积查询即可。

然后注意选原点的时候要从初始三个点随机平均系数来避免精度误差。

代码：

#include<bits/stdc++.h>
#define ri register ll
using namespace std;
typedef long long ll;
inline ll read(){
    ll ans=0;
    bool f=1;
    char ch=getchar();
    while(!isdigit(ch)){if(ch=='-')f^=1;ch=getchar();}
    while(isdigit(ch))ans=(ans<<3)+(ans<<1)+(ch^48),ch=getchar();
    return f?ans:-ans;
}
struct pot{
    ll x,y;
    double ang;
    pot(ll _x=0,ll _y=0):x(_x),y(_y){}
    pot(ll _x,ll _y,double _ang):x(_x),y(_y),ang(_ang){}
    friend inline pot operator+(const pot&a,const pot&b){return pot(a.x+b.x,a.y+b.y);}
    friend inline pot operator-(const pot&a,const pot&b){return pot(a.x-b.x,a.y-b.y);}
    friend inline ll operator^(const pot&a,const pot&b){return (ll)a.x*b.y-(ll)a.y*b.x;}
    friend inline bool operator<(const pot&a,const pot&b){return a.ang<b.ang;}
}a[5];
set<pot>S;
typedef set<pot>::iterator It;
ll n;
ll ans=0;
inline ll Area(const pot&a,const pot&b,const pot&c){return (a-c)^(b-c);}
inline ll labs(const ll&x){return x>0?x:-x;}
inline pot Pre(const pot&now){
    if(S.count(now)>0)return now;
    It it=S.lower_bound(now);
    if(it==S.begin())it=S.end();
    return *(--it);
}
inline pot Suf(const pot&now){
    It it=S.upper_bound(now);
    if(it==S.end())it=S.begin();
    return *it;
}
inline bool check(const pot&x){return Area(x,Suf(x),Pre(x))<=0;}
inline void insert(const pot&x){
    if(check(x))return;
    ans+=labs(Area(x,Suf(x),Pre(x)));
    while(1){
        pot p1=Pre(x),p2;
        S.erase(p1);
        p2=Pre(x);
        if(Area(x,p2,p1)>=0){S.insert(p1);break;}
        ans+=labs(Area(x,p2,p1));
    }
    while(1){
        pot p1=Suf(x),p2;
        S.erase(p1);
        p2=Suf(x);
        if(Area(x,p2,p1)<=0){S.insert(p1);break;}
        ans+=labs(Area(p1,p2,x));
    }
    S.insert(x);
}
signed main(){
    srand(time(NULL));
    ll xxx=rand(),yyy=rand(),zzz=rand(),ttt=xxx+yyy+zzz;
    double X,Y;
    a[1].x=read(),a[1].y=read();
    a[2].x=read(),a[2].y=read();
    a[3].x=read(),a[3].y=read();
    X=(double)((ll)a[1].x*xxx+(ll)a[2].x*yyy+(ll)a[3].x*zzz)/ttt;
    Y=(double)((ll)a[1].y*xxx+(ll)a[2].y*yyy+(ll)a[3].y*zzz)/ttt;
    for(ri i=1;i<=3;++i)S.insert(pot(a[i].x,a[i].y,atan2(a[i].y-Y,a[i].x-X)));
    ans=labs(Area(a[1],a[2],a[3]));
    for(ri x,y,tt=read();tt;--tt){
        x=read(),y=read();
        insert(pot(x,y,atan2(y-Y,x-X)));
        cout<<ans<<'\n';
    }
    return 0;
}