学步园

题目链接：Beauty Contest

题意：给n个点，求两个点的最远距离。

题解：最长的边肯定是凸多边形的对角线，所以求出凸包后遍历对角线，求出最大距离。

代码：

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <iostream>
#include <algorithm>
#include <queue>
#include <stack>
#include <vector>
#include <deque>
#include <set>
#include <map>
#include <string>
using namespace std;
#define For(i,a) for(i=0;i<a;i++)
#define Foru(i,a,b) for(i=a;i<=b;i++)
#define Ford(i,a,b) for(i=a;i>=b;i--)
#define clr(ar,vel) memset(ar,vel,sizeof(ar))
#define PB push_back
typedef long long ll;
const int maxint = 0x7fffffff;
const ll maxll = 1LL<<60;
const double EPS = 1e-10; 
typedef pair <int,int> pii;
//  二维向量类
double add( double a, double b){
	if( abs(a+b) < EPS * ( abs(a) + abs(b))) return 0;
	return a+b;
}
struct P{
	double x, y;
	P() {}
	P(double x, double y) : x(x), y(y) {}
	P operator + (P p){ return P(add(x, p.x), add(y, p.y));}
	P operator - (P p){ return P(add(x, -p.x), add(y, -p.y));}
	P operator * (double d){ return P(x*d, y*d);}
	bool operator < (const P& a) const {
		if( x != a.x) return x < a.x;
		else return y < a.y;
	}
	double dot(P p){ return add(x*p.x, y*p.y);}
	double det(P p) { return add( x*p.y, -y*p.x);}
};
P p[50010];
int n;
bool cmp_x(P a, P b){
	if( a.x != b.x) return a.x < b.x;
	return a.y < b.y;
}
vector<P> convex_hull(P *ps, int n){
	sort(p, p+n, cmp_x);
	int k = 0;
	vector<P> qs(n*2);
	// down
	for(int i = 0; i < n; i ++){
		while( k > 1 && (qs[k-1] - qs[k-2]).det(ps[i] - qs[k-1]) <= 0) k--;
		qs[k++] = ps[i];
	}
	// up
	for(int i = n-2, t = k; i >= 0; i --){
		while( k > t && (qs[k-1] - qs[k-2]).det(ps[i] - qs[k-1]) <= 0) k--;
		qs[k++] = ps[i];
	}
	qs.resize(k-1);
	return qs;
}
double dist(P p, P q){
	return (p-q).dot(p-q);
}
void solve(){
	int x, y;
	for(int i = 0; i < n; i ++){
		scanf("%d%d",&x,&y);
//			cin >> p[i].x >> p[i].y;
		p[i].x = x; p[i].y = y;
	}
	vector<P> qs = convex_hull(p, n);
	double res = 0;
	for(int i = 0; i < qs.size(); i ++){
		for(int j = 0; j < i; j ++){
			res = max( res, dist(qs[i], qs[j]));
		}
	}
	printf("%.0f\n",res);
}
	 
int main(){
	while(~scanf("%d",&n)) solve();
	return 0;
}