SGU 277 Heroes(动态凸包维护)
题目链接：http://acm.sgu.ru/problem.php?contest=0&problem=277
题意：维护一个凸包，每次加一个点。输出每次加入后的凸包面积。
思路：如下图，找到内部一点，以每个点对这个点的极角建立set。每次查找left和right，然后将中间的点删掉，增加p。修改面积。
#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;
}