【模板】凸包——poj1113

凸包性质

如果把凸包的一点放到原点，那么剩下所有点只会经过三个象限，且每个象限内的点极角递增或递减

#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<vector>
using namespace std;
#define N 200005

typedef double db;
const db eps=1e-6;
const db pi=acos(-1);
int sign(db k){if (k>eps) return 1; else if (k<-eps) return -1; return 0;}
int cmp(db k1,db k2){return sign(k1-k2);}
int inmid(db k1,db k2,db k3){return sign(k1-k3)*sign(k2-k3)<=0;}// k3 在 [k1,k2] 内 
struct point{
    db x,y;
    point operator + (const point &k1) const{return (point){k1.x+x,k1.y+y};}
    point operator - (const point &k1) const{return (point){x-k1.x,y-k1.y};}
    point operator * (db k1) const{return (point){x*k1,y*k1};}
    point operator / (db k1) const{return (point){x/k1,y/k1};}
    bool operator < (const point k1) const{
        int a=cmp(x,k1.x);
        if (a==-1) return 1; else if (a==1) return 0; else return cmp(y,k1.y)==-1;
    }
    db abs(){return sqrt(x*x+y*y);}
    db abs2(){return x*x+y*y;}
    db dis(point k1){return ((*this)-k1).abs();}
};
int inmid(point k1,point k2,point k3){return inmid(k1.x,k2.x,k3.x)&&inmid(k1.y,k2.y,k3.y);}
db cross(point k1,point k2){return k1.x*k2.y-k1.y*k2.x;}
db dot(point k1,point k2){return k1.x*k2.x+k1.y*k2.y;}
int onS(point k1,point k2,point q){return inmid(k1,k2,q) && sign(cross(k1-q,k2-k1))==0;}

vector<point> ConvexHull(vector<point> A, int flag){
    int n=A.size();vector<point> ans(n*2);
    sort(A.begin(),A.end());
    int now=-1;
    for(int i=0;i<A.size();i++){//下凸包 
        while(now>0 && sign(cross(ans[now]-ans[now-1],A[i]-ans[now-1]))<flag)
            now--;
        ans[++now]=A[i];
    }
    int pre=now;
    for(int i=n-2;i>=0;i--){//上凸包 
        while(now>pre && sign(cross(ans[now]-ans[now-1],A[i]-ans[now-1]))<flag)
            now--;
        ans[++now]=A[i]; 
    } 
    ans.resize(now);
    return ans;
}

vector<point> p;
int n;
db L,ans;

int main(){
    while(cin>>n>>L){
        for(int i=1;i<=n;i++){
            point pp;
            scanf("%lf%lf",&pp.x,&pp.y);
            p.push_back(pp);
        }
        vector<point> res=ConvexHull(p,1);
        
        ans=0;
        for(int i=0;i<res.size();i++)
            ans+=res[i].dis(res[(i+1)%res.size()]);
        ans+=2*pi*L;
        printf("%d
",(int)(ans+0.5));
    }
}