#include<bits/stdc++.h>
using namespace std;
typedef unsigned long long ull;
int solve();
int main() {
#ifdef Yinku
freopen("Yinku.in","r",stdin);
#endif // Yinku
solve();
}
//不要输出-0.0之类的数
const double eps=1e-8;
const double pi=acos(-1.0);
//判断浮点数的符号
inline int cmp(double x) {
return (fabs(x)<eps)?0:((x>0.0)?1:-1);
}
inline double sqr(double x) {
return x*x;
}
struct Point {
double x,y;
Point() {};
Point(const double x,const double y):x(x),y(y) {};
friend Point operator+(const Point &a,const Point &b) {
return Point(a.x+b.x,a.y+b.y);
}
friend Point operator-(const Point &a,const Point &b) {
return Point(a.x-b.x,a.y-b.y);
}
friend Point operator*(const Point &p,const double k) {
return Point(p.x*k,p.y*k);
}
friend Point operator*(const double k,const Point &p) {
return Point(p.x*k,p.y*k);
}
friend Point operator/(const Point &p,const double k) {
return Point(p.x/k,p.y/k);
}
friend bool operator==(const Point &a,const Point &b) {
return cmp(a.x-b.x)==0&&cmp(a.y-b.y)==0;
}
Point rotate(double A) {
//向量绕原点旋转A弧度
return Point(x*cos(A)-y*sin(A),x*sin(A)+y*cos(A));
}
double norm() {
return sqrt(sqr(x)+sqr(y));
}
};
double det(const Point &a,const Point &b) {
return a.x*b.y-a.y*b.x;
}
double dot(const Point &a,const Point &b) {
return a.x*b.x+a.y*b.y;
}
double dist(const Point &a,const Point &b) {
return sqrt(sqr(a.x-b.x)+sqr(a.y-b.y));
}
struct Line {
Point a,b;
Line() {};
Line(const Point &a,const Point &b):a(a),b(b) {};
Line move_dist(const double &d) {
//向法向平移d单位长度
//单位法向量n,从a指向b
Point n=b-a;
n=n/n.norm();
//左旋90度
n=n.rotate(pi/2.0);
return Line(a+n*d,b+n*d);
}
};
double dist_point_to_line(const Point &p,const Line &l) {
Point a=l.a,b=l.b;
//当a与b可以重合时,这里要加上下面的语句
/*if(a==b)
return a.dist(p);*/
if(cmp(dot(p-a,b-a))<0)
return dist(p,a);
if(cmp(dot(p-b,a-b))<0)
return dist(p,b);
return fabs(det(a-p,b-p)/dist(a,b));
}
Point point_project_on_line(const Point &p,const Line &l) {
Point a=l.a,b=l.b;
double r=dot(b-a,p-a)/dot(b-a,b-a);
return a+(b-a)*r;
}
bool point_on_line(const Point &p,const Line &l) {
Point a=l.a,b=l.b;
//这里的line是线段
//第一个cmp意思是叉积等于0,意味着直线穿过该点
//第二个cmp的<=意思是点在线段内(含端点),当改为<为点在线段内(不含端点)
return cmp(det(p-a,b-a))==0&&cmp(dot(p-a,p-b))<=0;
}
bool parallel(const Line &tl,const Line &l) {
Point a=tl.a,b=tl.b;
//叉积等于0,意味着向量平行
return !cmp(det(a-b,l.a-l.b));
}
bool intersect(const Line &tl,const Line &l,Point &p) {
Point a=tl.a,b=tl.b;
//判断直线是否相交,相交则求出交点(不需要交点可以直接return)
if(parallel(tl,l))
return false;
double s1=det(a-l.a,l.b-l.a);
double s2=det(b-l.a,l.b-l.a);
p=(b*s1-a*s2)/(s1-s2);
return true;
}
const int MAXN=10005;
struct Polygon {
int n;
Point a[MAXN];
Polygon() {};
double perimeter() {
double sum=0.0;
a[n]=a[0];
for(int i=0; i<n; i++)
sum+=(a[i+1]-a[i]).norm();
return sum;
}
double area() {
double sum=0.0;
a[n]=a[0];
for(int i=0; i<n; i++)
sum+=det(a[i+1],a[i]);
return sum/2.0;
}
Point masscenter() {
Point ans(0.0,0.0);
//在这里,当多边形面积为0,返回的是原点
if(cmp(area())==0)
return ans;
a[n]=a[0];
for(int i=0; i<n; i++)
ans=ans+(a[i]+a[i+1])*det(a[i+1],a[i]);
return ans/area()/6.0;
}
//下面两个只有格点多边形能用
int border_point_num() {
int num=0;
a[n]=a[0];
for(int i=0; i<n; i++)
num+=__gcd(abs(int(a[i+1].x-a[i].x)),abs(int(a[i+1].y-a[i].y)));
return num;
}
int inside_point_num() {
return (int)area()+1-border_point_num()/2;
}
};
int point_in_polygon(Point &p,Polygon &po) {
Point *a=po.a;
int n=po.n;
int num=0,d1,d2,k;
a[n]=a[0];
for(int i=0; i<n; i++) {
if(point_on_line(p,Line(a[i],a[i+1])))
return 2;
k=cmp(det(a[i+1]-a[i],p-a[i]));
d1=cmp(a[i].y-p.y);
d2=cmp(a[i+1].y-p.y);
if(k>0&&d1<=0&&d2>0)
num++;
if(k<0&&d2<=0&&d1>0)
num--;
}
return num!=0;
}
struct Polygon_Convex {
vector<Point> P;
Polygon_Convex(int Size=0) {
P.resize(Size);
}
Polygon to_polygon() {
//注意多边形的最大点数要够
Polygon p;
p.n=P.size();
for(int i=0; i<p.n; i++) {
p.a[i]=P[i];
}
return p;
}
};
bool comp_less(const Point&a,const Point &b) {
//水平序
return cmp(a.x-b.x)<0||cmp(a.x-b.x)==0&&cmp(a.y-b.y)<0;
}
Polygon_Convex convex_hull(vector<Point> a) {
Polygon_Convex res(2*a.size()+5);
sort(a.begin(),a.end(),comp_less);
a.erase(unique(a.begin(),a.end()),a.end());
int m=0;
for(int i=0; i<a.size(); ++i) {
while(m>1&&cmp(det(res.P[m-1]-res.P[m-2],a[i]-res.P[m-2]))<=0)
--m;
res.P[m++]=a[i];
}
int k=m;
for(int i=int(a.size())-2; i>=0; --i) {
while(m>k&&cmp(det(res.P[m-1]-res.P[m-2],a[i]-res.P[m-2])<=0))
--m;
res.P[m++]=a[i];
}
//当只有一个点时,凸包保留一个点,否则结尾和开头重复了
res.P.resize(m-(a.size()>1));
return res;
}
int solve() {
int n;
scanf("%d",&n);
vector<Point> a(n);
for(int i=0; i<n; i++) {
scanf("%lf%lf",&a[i].x,&a[i].y);
}
printf("%.2f\n",convex_hull(a).to_polygon().perimeter());
return 0;
}
Template - Computational Geometry (Collection)
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Origin www.cnblogs.com/Yinku/p/10954747.html
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