poj 3301

题目：http://poj.org/problem?id=3301

题意：给出一些点的坐标，求一个最小的正方形来覆盖所有的点

用三分枚举转角即可，坐标转换公式： x’ = x * cosa - y * sina;     y’ = y * cosa + x * sina;

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
using namespace std;

#define N 60
#define inf 100000000
#define eps 1e-8
double const pi=acos(-1.0);
struct node
{
    double x,y;
}p[N],tp[N];
int n;
node cal(node a,double key)
{
    node temp;
    temp.x = a.x * cos(key) - a.y * sin(key);
    temp.y = a.y * cos(key) + a.x * sin(key);
    return temp;
}
double ca(double key)
{
    double minx,miny,maxx,maxy;
    minx = miny = inf;
    maxx = maxy = -inf;
    for(int i = 0; i < n; i++)
    {
        tp[i] = cal(p[i],key);
        minx = min(minx,tp[i].x);
        miny = min(miny,tp[i].y);
        maxx = max(maxx,tp[i].x);
        maxy = max(maxy,tp[i].y);
    }
    double tx = maxx - minx;
    double ty = maxy - miny;
    return max(tx * tx,ty * ty);
}
int main()
{
    int cas;
    //freopen("data.txt","r",stdin);
    scanf("%d",&cas);
    while(cas--)
    {
        scanf("%d",&n);
        for(int i=0; i<n; i++)
        {
            scanf("%lf%lf",&p[i].x,&p[i].y);
        }
        double l = 0.0;
        double r = pi;
        double lmid,rmid;
        while(fabs(r - l) > eps)
        {
            lmid = (l * 2.0 + r) / 3.0;
            rmid = (l + r * 2.0) / 3.0;
            if(ca(lmid) > ca(rmid))  l = lmid;
            else r = rmid;
        }
        printf("%.2lf\n",ca(l));
    }
    return 0;
}