题意：

弄两个多边形覆盖图中所有点，要求里面多边形面积比上外面多边形面积值最大。

思路：
枚举用的是哪个多边形，则比值最大时，外面那个多边形覆盖所有点，里面那个多边形一个点都没有覆盖。二分就好了。

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <iostream>
 
using namespace std;
 
const double eps = 1e-8;
const double pi = acos(-1);

const int maxn = 1e3 + 7;
struct point
{
    double x,y;
    int id;
    point(){}
    point(double _x,double _y)
    {
        x = _x;y = _y;
    }
    point operator+(point a)
    {
        return point(x + a.x,y + a.y);
    }
    point operator-(point a)
    {
        return point(x - a.x,y - a.y);
    }
    double operator*(point a)
    {
        return x * a.y - y * a.x;
    }
    
}a[maxn],p[10][15];
int n;
bool dcmp(double x,double y)
{
    if(x - y < eps && x - y > -eps)
        return 0;
    if(x - y > 0)return 1;
    return -1;
}
 
double cal(point *p) { //算凸包面积
    double ans = 0;
    int cnt = p[0].id + 3;
    for(int i = 0;i < cnt - 1;i++)
    {
        ans += (p[i] - p[0]) * (p[i + 1] - p[0]);
    }
    return fabs(ans) / 2;
}

bool judge(point now,point *p,double mid) { //now是否在多边形内
    now.x /= mid;now.y /= mid;
    int cnt = p[0].id + 3;
    double ans = 0.0;
    for(int i = 0;i < cnt;i++) {
        point p1 = p[i % cnt],p2 = p[(i + 1) % cnt];
        ans += fabs((p1 - now) * (p2 - now));
    }
    ans = ans / 2;
    double area = cal(p);
    if(dcmp(area,ans) == 0) return true;
    return false;
}

bool check1(double mid,point *p) { //覆盖所有点
    for(int i = 0;i < n;i++) {
        if(!judge(a[i],p,mid)) return false;
    }
    return true;
}

bool check2(double mid,point *p) { //是否没有覆盖点
    for(int i = 0;i < n;i++) {
        if(judge(a[i],p,mid)) return false;
    }
    return true;
}

void init() {
    for(int i = 0;i <= 5;i++) {
        for(int j = 0;j < i + 3;j++) {
            p[i][j].id = i;
            double rad = 2 * pi / (i + 3) * j;
            double x = cos(rad),y = sin(rad);
            p[i][j].x = x;p[i][j].y = y;
        }    
    }
}
 
int main() {
    #ifndef ONLINE_JUDGE
    freopen("D:in.in", "r", stdin);
    freopen("D:out.out", "w", stdout);
    #endif
    init();
    scanf("%d",&n);
    for(int i = 0;i < n;i++) {
        scanf("%lf%lf",&a[i].x,&a[i].y);
    }

    double ans = 0.0;
    int pos = 0;
    for(int i = 0;i <= 5;i++) {
        double l = 0,r = 5e7;
        double ans1 = 0.0;
        double ans2 = 0.0;
        while(r - l > eps) { //外层比例
            double mid = (l + r) / 2;
            if(check1(mid,p[i])) {
                r = mid;
            } else {
                l = mid;
            }
        }
        ans1 = l * l;
        l = 0,r = 5e7;
        while(r - l > eps) {
            double mid = (l + r) / 2;
            if(check2(mid,p[i])) {
                l = mid;
            } else {
                r = mid;
            }
        }
        ans2 = r * r;

        if(ans < ans2 / ans1) {
            ans = ans2 / ans1;
            pos = i;
        }
    }

    printf("%d %.8f\n",pos + 3,ans);
    return 0;
}