## Solución al problema número 10002 de UVA - 10002.

Cualquier duda no dudes en contactar.

``````#include <bits/stdc++.h>
#define INF 0x3f3f3f3f
#define EPS 1e-10
#define PI acos(-1.0)
using namespace std;

struct point{
double x,y;
point(){x=y=0;}
point(double _x,double _y){x=_x,y=_y;}
};

double cross(point o, point a, point b) {
return (a.x-o.x)*(b.y-o.y) - (a.y-o.y)*(b.x-o.x);
}
bool cmp(point a,point b){
if(a.x!=b.x) return a.x<b.x;
return a.y<b.y;
}
double area(const vector<point> &P) {
double result = 0.0, x1, y1, x2, y2;
for (int i = 0; i < (int)P.size()-1; i++) {
x1 = P[i].x; x2 = P[i+1].x;
y1 = P[i].y; y2 = P[i+1].y;
result += (x1 * y2 - x2 * y1);
}
return result / 2.0; }
vector<point> CH(vector<point> P){
vector<point> res;
sort(P.begin(),P.end(),cmp);
int n = P.size();
int m=0;
for (int i=0;i<n;i++){
while (m>1&&cross(res[m-2], res[m-1], P[i]) <= 0)res.pop_back(),m--;
res.push_back(P[i]),m++;
}
for (int i = n-1, t = m+1; i >= 0; i--) {
while (m>=t&&cross(res[m-2], res[m-1], P[i]) <= 0)res.pop_back(),m--;
res.push_back(P[i]),m++;
}
return res;
}

point centroid(vector<point> g)		//center of mass
{
double cx = 0.0, cy = 0.0;
for(unsigned int i = 0; i < g.size() - 1; i++)
{
double x1 = g[i].x, y1 = g[i].y;
double x2 = g[i+1].x, y2 = g[i+1].y;

double f = x1 * y2 - x2 * y1;
cx += (x1 + x2) * f;
cy += (y1 + y2) * f;
}
double res = area(g);		//remove abs
cx /= 6.0 * res;
cy /= 6.0 * res;
return point(cx, cy);
}

int main()
{
int n;
while(scanf("%d",&n)==1 && n>2)
{
vector<point> V;
double x,y;
for(int i=0; i<n;i++)
{
scanf("%lf%lf",&x,&y);
V.push_back(point(x,y));
}
V = CH(V);
point res = centroid(V);
printf("%.3lf %.3lf\n",res.x,res.y);
}
return 0;
}
``````