SGU 277 Heroes(動態凸包維護)

題目連結：http://acm.sgu.ru/problem.php?contest=0&problem=277

題意：維護一個凸包，每次加一個點。輸出每次加入後的凸包面積。

思路：如下圖，找到內部一點，以每個點對這個點的極角建立set。每次查詢left和right，然後將中間的點刪掉，增加p。修改面積。

#include <iostream>
#include <cstdio>
#include <string.h>
#include <algorithm>
#include <cmath>
#include <vector>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <map>


#define max(x,y) ((x)>(y)?(x):(y))
#define min(x,y) ((x)<(y)?(x):(y))
#define abs(x) ((x)>=0?(x):-(x))
#define i64 long long
#define u32 unsigned int
#define u64 unsigned long long
#define clr(x,y) memset(x,y,sizeof(x))
#define CLR(x) x.clear()
#define ph(x) push(x)
#define pb(x) push_back(x)
#define Len(x) x.length()
#define SZ(x) x.size()
#define PI acos(-1.0)
#define sqr(x) ((x)*(x))
#define MP(x,y) make_pair(x,y)

#define FOR0(i,x) for(i=0;i<x;i++)
#define FOR1(i,x) for(i=1;i<=x;i++)
#define FOR(i,a,b) for(i=a;i<=b;i++)
#define DOW0(i,x) for(i=x;i>=0;i--)
#define DOW1(i,x) for(i=x;i>=1;i--)
#define DOW(i,a,b) for(i=a;i>=b;i--)
using namespace std;


void RD(int &x){scanf("%d",&x);}
void RD(i64 &x){scanf("%I64d",&x);}
void RD(u32 &x){scanf("%u",&x);}
void RD(double &x){scanf("%lf",&x);}
void RD(int &x,int &y){scanf("%d%d",&x,&y);}
void RD(i64 &x,i64 &y){scanf("%I64d%I64d",&x,&y);}
void RD(u32 &x,u32 &y){scanf("%u%u",&x,&y);}
void RD(double &x,double &y){scanf("%lf%lf",&x,&y);}
void RD(int &x,int &y,int &z){scanf("%d%d%d",&x,&y,&z);}
void RD(i64 &x,i64 &y,i64 &z){scanf("%I64d%I64d%I64d",&x,&y,&z);}
void RD(u32 &x,u32 &y,u32 &z){scanf("%u%u%u",&x,&y,&z);}
void RD(double &x,double &y,double &z){scanf("%lf%lf%lf",&x,&y,&z);}
void RD(char &x){x=getchar();}
void RD(char *s){scanf("%s",s);}
void RD(string &s){cin>>s;}


void PR(int x) {printf("%d\n",x);}
void PR(i64 x) {printf("%I64d\n",x);}
void PR(u32 x) {printf("%u\n",x);}
void PR(u64 x) {printf("%llu\n",x);}
void PR(double x) {printf("%.3lf\n",x);}
void PR(char x) {printf("%c\n",x);}
void PR(char *x) {printf("%s\n",x);}
void PR(string x) {cout<<x<<endl;}

int DB(double x)
{
    if(x>1e-10) return 1;
    if(x<-1e-10) return -1;
    return 0;
}

class point
{
public:
    i64 x,y;
    double ang;

    point(){}
    point(i64 _x,i64 _y)
    {
        x=_x;
        y=_y;
    }

    void read()
    {
        RD(x,y);
    }
    int operator<(const point &a) const
    {
        return DB(ang-a.ang)<0;
    }

    point operator-(point a)
    {
        return point(x-a.x,y-a.y);
    }

    i64 operator*(point a)
    {
        return x*a.y-y*a.x;
    }
};

set<point> p;
vector<point> q;
double X,Y;
int n,isTrangle;
point a;
i64 s;


i64 cross(point a,point b,point p)
{
    return (b-a)*(p-a);
}

int cmp(point a,point b)
{
    if(a.x!=b.x) return a.x<b.x;
    return a.y<b.y;
}

double getAng(point a)
{
    return atan2(a.y-Y,a.x-X);
}

void init()
{
    X=(q[0].x+q[1].x+q[2].x)/3.0;
    Y=(q[0].y+q[1].y+q[2].y)/3.0;
    int i;
    q[3]=q[0];
    FOR0(i,3)
    {
        q[i].ang=getAng(q[i]);
        p.insert(q[i]);
        s+=q[i]*q[i+1];
    }
    s=abs(s);
}


#define type set<point>::iterator

type last(type it)
{
    if(it==p.begin()) it=p.end();
    return --it;
}

type next(type it)
{
    if(++it==p.end()) it=p.begin();
    return it;
}

void update(point a)
{
    type it=last(p.lower_bound(a));
    point b=*it,x,y;
    if(cross(b,*next(it),a)>0) return;
    type L=it,R=it;
    while(cross(a,*next(R),*R)>=0) R=next(R);
    while(cross(a,*L,*last(L))>=0) L=last(L);
    for(it=L;it!=R;it=next(it))
    {
        x=*it;
        y=*next(it);
        s-=x*y;
    }
    for(it=next(L);it!=R;)
    {
        it=next(it);
        p.erase(last(it));
    }
    x=*L;y=*R;
    s+=x*a+a*y;
    p.insert(a);
}

int main()
{
    a.read(); q.pb(a);
    a.read(); q.pb(a);
    a.read(); q.pb(a);
    if(cross(q[0],q[1],q[2])) isTrangle=1,init();
    RD(n);
    while(n--)
    {
        a.read();
        if(isTrangle) a.ang=getAng(a),update(a);
        else if(cross(q[0],q[1],a))
        {
            isTrangle=1;
            sort(q.begin(),q.end(),cmp);
            q[1]=q[q.size()-1];
            q[2]=a;
            init();
        }
        else q.pb(a);
        PR(s);
    }
    return 0;
}