「Luogu P2742」【模板】二维凸包

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字数统计: 637 | 阅读时长 ≈ 3

给定一个点集，求它的凸包的周长。

链接

Luogu P2742

题解

二维凸包的模板题，没有什么好说的。
不会凸包的右转这里
但是最后求周长是一定要算点的距离，而不是向量的长度。被卡了两次

代码

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#include<bits/stdc++.h>
using namespace std;
typedef int ll;
typedef double db;
const ll MAXN=1e4+51;
struct Point{
    db x,y;
    Point(ll x=0,ll y=0)
    {
        this->x=x,this->y=y;
    }
    inline bool operator <(const Point &rhs)const
    {
        return y==rhs.y?x<rhs.x:y<rhs.y;
    }
    inline db polar()
    {
        return atan2(y,x);
    }
};
typedef Point Vector;
Point p[MAXN];
ll cnt,minn;
db res;
inline ll read()
{
    register ll num=0,neg=1;
    register char ch=getchar();
    while(!isdigit(ch)&&ch!='-')
    {
        ch=getchar();
    }
    if(ch=='-')
    {
        neg=-1;
        ch=getchar();
    }
    while(isdigit(ch))
    {
        num=(num<<3)+(num<<1)+(ch-'0');
        ch=getchar();
    }
    return num*neg;
}
inline Vector operator +(Vector x,Vector y)
{
    return Vector(x.x+y.x,x.y+y.y);
}
inline Vector operator -(Vector x,Vector y)
{
    return Vector(x.x-y.x,x.y-y.y);
}
inline Vector operator *(Vector x,db y)
{
    return Vector(x.x*y,x.y*y);
}
inline Vector operator /(Vector x,db y)
{
    return Vector(x.x/y,x.y/y);
}
inline db dot(Vector x,Vector y)
{
    return x.x*y.x+x.y*y.y;
}
inline db length(Vector x)
{
    return sqrt(dot(x,x));
}
inline db angle(Vector x,Vector y)
{
    return acos(dot(x,y)/length(x)/length(y));
}
inline db cross(Vector x,Vector y)
{
    return x.x*y.y-x.y*y.x;
}
inline db dist(Vector x,Vector y)
{
    db xx=x.x-y.x,yy=x.y-y.y;
    return sqrt(xx*xx+yy*yy);
}
inline bool cmp(Point x,Point y)
{
    double xx=cross(x-p[1],y-p[1]);
    if(xx>0)
    {
        return 1;
    }
    if(!xx&&length(x-p[1])<length(y-p[1]))
    {
        return 1;
    }
    return 0;
}
inline deque<Point> convexHull(Point *p,ll size)
{
    Point top;
    deque<Point>vec;
    if(size==1)
    {
        vec.push_back(p[1]);
        return vec;
    }
    if(size==2)
    {
        vec.push_back(p[1]),vec.push_back(p[2]);
        return vec;
    }
    vec.push_back(p[1]),vec.push_back(p[2]);
    for(register int i=3;i<=size;i++)
    {
        top=vec.back();
        while(cross(top-vec[vec.size()-2],p[i]-top)<0)
        {
            vec.pop_back(),top=vec.back();
        }
        vec.push_back(p[i]);
    }
    return vec;
}
int main()
{
    cnt=read();
    p[0].x=p[0].y=100000000000.0;
    if(cnt==0)
    {
        printf("0.00");
        return 0;
    }
    for(register int i=1;i<=cnt;i++)
    {
        scanf("%lf%lf",&p[i].x,&p[i].y);
        if(p[i]<p[minn])
        {
            minn=i;
        }
    }
    swap(p[minn],p[1]),sort(p+2,p+cnt+1,cmp);
    deque<Point>pt=convexHull(p,cnt);
    if(pt.size()==1)
    {
        printf("%.2lf",0.0);
    }
    else
    {
        for(register int i=1;i<pt.size();i++)
        {
            res+=dist(pt[i],pt[i-1]);
        }
        res+=dist(pt[0],pt[pt.size()-1]);
        printf("%.2lf",res);
    }
}