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POJ 2187 Beauty Contest(凸包)

題意:題目的意思就是說給你N個點,然後讓你求出最遠的兩個點的距離的平方(注意:是平方);

分析:對於50000個點暴力肯定是不行的,那麼我們可以聯絡到凸包,因為最遠的點肯定是在凸包上,那麼要求最遠的
距離,我們就可以先對這些點求一次凸包(複習凸包的寫法)。然後對於凸包上面的點可以列舉,因為這時候要列舉的
點的數目已經減少很多了,這時候,就是普通的暴搞了。主要是前面的凸包的寫法。

#include<iostream>
#include<algorithm>
#include<cmath>
#include<vector>
#include<cstdio>
#define N 50005
using namespace std;

struct node{
	int x, y;
	bool friend operator < (const node &a, const node &b){
		if(a.y == b.y)
			return a.x < b.x;
		return a.y < b.y;
	}
}point[N];

double calcurateDis(node a, node b){
	return (a.x - b.x)*(a.x - b.x) + (a.y - b.y)*(a.y - b.y);
}

bool judge(node a, node b, node c){
	return (a.x - c.x)*(b.y - c.y) >= (b.x - c.x)*(a.y - c.y);
}

double solve(int n){
	vector<node> tempPoint(n*2);
	sort(point, point + n);
	if(n == 1){
		return 0;
	}
	if(n == 2){
		return calcurateDis(point[0], point[1]);
	}
	tempPoint[0] = point[0];
	tempPoint[1] = point[1];
	tempPoint[2] = point[2];
	int top = 1;
	for(int i = 2; i < n; i++){
		while(top != 0 && judge(point[i], tempPoint[top], tempPoint[top - 1]))	top--;
		tempPoint[++top] = point[i];
	}
	int len = top;
	tempPoint[++top] = point[n - 2];
	for(int i = n - 3; i >= 0; i--){
		while(top != len && judge(point[i], tempPoint[top], tempPoint[top - 1]))	top--;
		tempPoint[++top] = point[i];
	}
	double result = 0.0;
	for(int i = 0; i < top; ++i)
		for(int j = i + 1; j < top; ++j)
			result = max(result, calcurateDis(tempPoint[i], tempPoint[j]));
	return result;
}

int main(){
	int n;
	while(~scanf("%d", &n)){
		for(int i = 0; i < n; i++)
			scanf("%d %d", &point[i].x, &point[i].y);

		printf("%.0lf\n", solve(n));
	}
	return 0;
}