是Graham的变种。水平扫描,分别构造上下凸壳,然后把两者接起来。
感觉比Graham好用。
复杂度O(nlog2n) (排序)
#include<cmath>
#include<cstdio>
#include<algorithm>
using namespace std;
const int maxn=1100;
const double eps=1e-9;
int dcmp(double x){
if(fabs(x)<eps) return 0;
return x<0?-1:1;
}
struct Point{
double x,y;
Point(double x=0,double y=0):x(x),y(y){}
bool operator < (const Point &b)const{
if(x<b.x) return true;
if(x>b.x) return false;
return y<b.y;
}
};
typedef Point Vector;
Vector operator - (Point A,Point B){ return Vector(A.x-B.x,A.y-B.y); }
double Cross(Vector A,Vector B){
return A.x*B.y-A.y*B.x;
}
double getDis(Point P1,Point P2){ return sqrt((P1.x-P2.x)*(P1.x-P2.x)+(P1.y-P2.y)*(P1.y-P2.y)); }
int n,tot;
double ans,L;
Point a[maxn],ch[maxn];
int Andrew(){
sort(a,a+n);
int len=0;
for(int i=0;i<=n-1;i++){
while(len>1&&dcmp(Cross(ch[len]-ch[len-1],a[i]-ch[len-1]))==-1) len--;
ch[++len]=a[i];
}
int k=len;
for(int i=n-2;i>=0;i--){
while(len>k&&dcmp(Cross(ch[len]-ch[len-1],a[i]-ch[len-1]))==-1) len--;
ch[++len]=a[i];
}
return len;
}
int main(){
freopen("poj1113.in","r",stdin);
freopen("poj1113.out","w",stdout);
scanf("%d%lf",&n,&L);
for(int i=0;i<=n-1;i++) scanf("%lf%lf",&a[i].x,&a[i].y);
int t=Andrew();
ans=0;
for(int i=1;i<=t-1;i++) ans+=getDis(ch[i],ch[i+1]);
printf("%.0lf\n",ans+2*3.14159*L);
return 0;
}