BZOJ 2823 AHOI 2012 信号塔 凸包+最小圆覆盖

标签：bzoj   计算几何   ahoi 2012   最小圆覆盖   

题目大意：给出平面上n个点，求最小圆覆盖。

思路：圆覆盖问题只与所有点中凸包上的点有关，因此先求一下凸包，然后数据范围骤减。大概是只剩下logn左右个点。这样就可以随便浪了。

先找所有三个点组成的圆，然后找两个点为直径所组成的圆。

还有就是三角形的外心公式，简直不是人推的，然后我就机制的百度了，结果如下：

不要模拟退火。。。

样例很坑，当你算出2.49 2.86的时候，不要认为你被卡精了，其实是你写挂了。。。

CODE：

#include <cmath>
#include <cstdio>
#include <iomanip>
#include <cstring>
#include <iostream>
#include <algorithm>
#define MAX 1000010
#define INF 1e15
using namespace std;
#define sqr(a) ((a) * (a))
 
struct Point{
    double x,y,alpha;
     
    Point(double _,double __):x(_),y(__) {}
    Point() {}
    bool operator <(const Point &a)const {
        return alpha < a.alpha;
    }
    Point operator -(const Point &a)const {
        return Point(x - a.x,y - a.y);
    }
    void Read() {
        scanf("%lf%lf",&x,&y);
    }
    void Calc(const Point &p) {
        alpha = atan2(y - p.y,x - p.x);
    }
}point[MAX];
 
int cnt;
double min_x = INF,min_y = INF;
 
Point stack[MAX];
int top;
 
double Cross(const Point &p,const Point &q)
{
    return p.x * q.y - p.y * q.x;
}
 
double Calc(const Point &a,const Point &b)
{
    return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
}

double CalcX(const Point &p1,const Point &p2,const Point &p3)
{
	double up = sqr(p1.x) * (p2.y - p3.y) + sqr(p2.x) * (p3.y - p1.y) + sqr(p3.x) * (p1.y - p2.y);
	up -= (p1.y - p2.y) * (p2.y - p3.y) * (p3.y - p1.y);
	double down = p1.x * (p2.y - p3.y) + p2.x * (p3.y - p1.y) + p3.x * (p1.y - p2.y);
	return up / (2 * down);
}

double CalcY(const Point &p1,const Point &p2,const Point &p3)
{
	double up = -(sqr(p1.y) * (p2.x - p3.x) + sqr(p2.y) * (p3.x - p1.x) + sqr(p3.y) * (p1.x - p2.x));
	up += (p1.x - p2.x) * (p2.x - p3.x) * (p3.x - p1.x);
	double down = p1.x * (p2.y - p3.y) + p2.x * (p3.y - p1.y) + p3.x * (p1.y - p2.y);
	return up / (2 * down);
}

inline double Judge(double x,double y)
{
	double re = .0;
	for(int i = 0; i <= top; ++i)
		re = max(re,Calc(Point(x,y),stack[i]));
	return re;
}

int main()
{
    cin >> cnt;
    for(int i = 1; i <= cnt; ++i)
        point[i].Read();
    int p;
    for(int i = 1; i <= cnt; ++i)
        if(point[i].y < min_y) {
            min_y = point[i].y;
            min_x = point[i].x;
            p = i;
        }
        else if(point[i].y == min_y && point[i].x < min_x) {
            min_x = point[i].x;
            p = i;
        }
    for(int i = 1; i <= cnt; ++i)
        if(i != p)
            point[i].Calc(point[p]);
    sort(point + 1,point + cnt + 1);
    stack[top] = point[1];
    stack[++top] = point[2];
    stack[++top] = point[3];
    for(int i = 4; i <= cnt; ++i) {
        while(top >= 2 && Cross(stack[top] - stack[top - 1],point[i] - stack[top - 1]) <= 0)
            --top;
        stack[++top] = point[i];
    }
    double ans = INF;
    double X,Y,x,y,r;
    for(int i = 0; i <= top; ++i)
    	for(int j = i + 1; j <= top; ++j)
    		for(int k = j + 1; k <= top; ++k) {
    			x = CalcX(stack[i],stack[j],stack[k]);
    			y = CalcY(stack[i],stack[j],stack[k]);
    			r = Judge(x,y);
    			if(r < ans) {
    				ans = r;
    				X = x,Y = y;
    			}
    		}
   	for(int i = 0; i <= top; ++i)
   		for(int j = 0; j <= top; ++j) {
			r = Judge((stack[i].x + stack[j].x) / 2,(stack[i].y + stack[j].y) / 2);
			if(r < ans) {
				ans = r;
				X = (stack[i].x + stack[j].x) / 2;
				Y = (stack[i].y + stack[j].y) / 2;
			}
		}
    printf("%.2lf %.2lf %.2lf\n",X,Y,ans);
    return 0;
}

BZOJ 2823 AHOI 2012 信号塔 凸包+最小圆覆盖

标签：bzoj   计算几何   ahoi 2012   最小圆覆盖   

原文地址：http://blog.csdn.net/jiangyuze831/article/details/42174135