uva 11168 Airport

https://vjudge.net/problem/UVA-11168

 

给出n个点，求一条直线，使所有点在直线的同侧，且平均距离最小

输出最小的平均距离

 

直线一定是凸包的一条边

求出凸包每一条边一般式Ax+By+C

所有点到这条边的距离和=abs（A*sumx+B*sumy+C*n）/sqrt（A^2+B^2）

 

 

#include<cmath>
#include<cstdio>
#include<iostream>
#include<algorithm>

using namespace std;

#define N 10001

typedef long long LL;

const double eps=1e-10;

struct Point
{
    int x,y;
    Point (int x_=0,int y_=0) : x(x_),y(y_) { }
};

typedef Point Vector;

Point P[N],ch[N];

Vector operator - (Vector A,Vector B)  { return Vector(A.x-B.x,A.y-B.y); }

void read(int &x)
{
    x=0; int f=1; char c=getchar();
    while(!isdigit(c))  { if(c=='-') f=-1; c=getchar(); }
    while(isdigit(c)) { x=x*10+c-'0'; c=getchar(); }
    x*=f;
}

int dcmp(int x,int y)
{
    if(abs(x-y)<eps) return 0;
    return x<y ? -1 : 1;
}

bool cmp(Point A,Point B)
{
    if(!dcmp(A.x,B.x)) return A.y<B.y;
    return A.x<B.x;
}

LL Cross(Vector A,Vector B)
{
    return (LL)A.x*B.y-(LL)A.y*B.x;
}

int ConvexHull(Point *p,int n,Point *c)
{
    sort(p,p+n,cmp);
    int m=0;
    for(int i=0;i<n;++i)
    {
        while(m>1 && Cross(c[m-1]-c[m-2],p[i]-c[m-2])<=0) m--;
        c[m++]=p[i];
    }
    int k=m;
    for(int i=n-2;i>=0;--i)
    {
        while(m>k && Cross(c[m-1]-c[m-2],p[i]-c[m-2])<=0) m--;
        c[m++]=p[i];
    }
    if(n>1) m--;
    return m;
}

double solve(int n,int m)
{
    int sx=0,sy=0;
    for(int i=0;i<n;++i)
    {
        sx+=P[i].x;
        sy+=P[i].y;
    }
    double A,B,C;
    double ans=2e9;
    for(int i=0;i<m;++i)
    {
        if(!dcmp(ch[i].x,ch[i+1].x))
        {
            A=1;
            B=0;
            C=ch[i].x;
        }
        else
        {
            A=1.0*(ch[i].y-ch[i+1].y)/(ch[i].x-ch[i+1].x);
            B=-1;
            C=ch[i].y-ch[i].x*A;        
        }
        ans=min(ans,fabs(A*sx+B*sy+C*n)/sqrt(A*A+B*B));
    }
    return ans/n;
}

int main()
{
    int T,n,x,y;
    read(T);
    for(int t=1;t<=T;++t)
    {
        read(n);
        for(int i=0;i<n;++i)
        {
            read(x); read(y);
            P[i]=Point(x,y);
        }
        if(n<=2)
        {
            printf("Case #%d: 0.000\n",t);
            continue;
        }
        int m=ConvexHull(P,n,ch);
        printf("Case #%d: %.3lf\n",t,solve(n,m));
    }
}