[poj][2187][Beauty Contest]

#include <iostream>
#include <cstdio>
#include <math.h>
#include <cstring>
#include <algorithm>

#define sqr(x) ((x)*(x))
using namespace std;

const double eps = 1e-8;
const int pi = acos(-1.0);
const int N = 500000+10;

int dcmp(double x) {
if (x < -eps) return -1;
else return x > eps;
}

struct cpoint {
double x, y;
cpoint() {}
cpoint(double x, double y):x(x),y(y) {}
cpoint operator + (const cpoint &u) const {
return cpoint(x + u.x, y + u.y);
}
cpoint operator - (const cpoint &u) const {
return cpoint(x - u.x, y - u.y);
}
double operator * (const cpoint &u) const {
return x * u.y - y * u.x;
}
double operator ^ (const cpoint &u) const {
return x * u.x + y * u.y;
}
bool operator == (const cpoint& u) const {
return dcmp(x - u.x) == 0 && dcmp(y - u.y) == 0;
}
bool operator < (const cpoint& u) const {
if (dcmp(x - u.x)) return x < u.x;
else return dcmp(y - u.y) < 0;
}
double len() {
return sqrt(x * x + y * y);
}
void get() {
scanf("%lf%lf", &x, &y);
}
};

double cross(cpoint o, cpoint p, cpoint q) {
return (p - o) * (q - o);
}

double dot(cpoint o, cpoint p, cpoint q) {
return (p - o) ^ (q - o);
}

double dissqr(cpoint p, cpoint q) {
return sqr(p.x - q.x) + sqr(p.y - q.y);
}

cpoint bp;
int PolarCmp(const cpoint &p1, const cpoint &p2) {
int u = dcmp(cross(bp, p1, p2));
return u > 0 || (u == 0 && dcmp(dissqr(bp,p1)-dissqr(bp,p2))<0);
}

void graham(cpoint pin[], int n, cpoint ch[], int &m) {
int i, j, k, u, v;
memcpy(ch, pin, n * sizeof(cpoint));
for (i = k = 0; i < n; i++) {
u = dcmp(ch[i].x - ch[k].x);
v = dcmp(ch[i].y - ch[k].y);
if (v < 0 || (v == 0 && u < 0)) k = i;
}
bp = ch[k];
sort(ch, ch + n, PolarCmp);
n = unique(ch, ch + n) - ch;
if (n <= 1) {
m = n; return ;
}
if (dcmp(cross(ch[0], ch[1], ch[n-1])) == 0) {
m = 2, ch[1] = ch[n-1]; return ;
}
ch[n++] = ch[0];
for (i = 1, j = 2; j < n; j++){
while (i > 0 && dcmp(cross(ch[i-1], ch[i], ch[j])) <= 0) i--;
ch[++i] = ch[j];
}
m = i;
}

double rotating(cpoint cp[], int n){
int i = 1; double res = 0.0;
cp
= cp[0];
for (int j = 0; j < n; j++){
while (dcmp(fabs(cross(cp[i+1], cp[j], cp[j+1]))-
fabs(cross(cp[i], cp[j], cp[j+1])) ) > 0)
i = (i + 1) % n;
res = max(res, max(dissqr(cp[i], cp[j]),
dissqr(cp[i+1], cp[j+1])));
}
return res;
}
cpoint fp
, ch
;
int main()
{
//freopen("D:/a.txt", "r", stdin);
int n, m;
while (~scanf("%d", &n))
{
for (int i=0; i<n; i++)
fp[i].get();
graham(fp, n, ch, m);
double ans = rotating(ch, m);
printf("%d\n", (int)(ans+0.5));
}
return 0;
}