HDU 3007 【隨機增量法】

題目大意：給定平面上 n 個點，求最小圓覆蓋

我就是抄了個板而已…

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Q:爲什麼是 O(n) 的
A:（搖頭搖頭搖頭
Q:三角形外心怎麼求
A:不知道…
Q:學這個有什麼用
A:（一臉懵逼
Q:怎麼什麼都不知道→→
A:窩弱嘛TAT

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怎麼覺得自己又抽了=。=

三角形外心 (我知道泥萌都會。。。
因爲到各點距離相等，有

(x1−x)2−(y1−y)2=(x2−x)2+(y2−y)2(x2−x)2+(y2−y)2=(x3−x)2+(y3−y)2

化簡得到

2(x2−x1)x+2(y2−y1)y=x22+y22−x21−y21   /   A1x+B1y=C12(x3−x2)x+2(y3−y2)y=x23+y23−x22−y22   /   A2x+B2y=C2

有

⎧⎩⎨x=C1B2−C2B1A1B2−A2B1y=A1C2−A2C1A1B2−A2B1

#include<iostream>
#include<cstdio>
#include<cmath>
#include<algorithm>
#define D double
#define N 505
#define pf(x) (x * x)
using namespace std;

int n;D r;
struct point{D x,y;}e[N],ans;

D dis(point a,point b)
{
    return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
}

point center(point a,point b,point c)
{
    D A1 = (b.x - a.x) * 2,B1 = (b.y - a.y) * 2,C1 = pf(b.x) + pf(b.y) - pf(a.x) - pf(a.y);
    D A2 = (c.x - b.x) * 2,B2 = (c.y - b.y) * 2,C2 = pf(c.x) + pf(c.y) - pf(b.x) - pf(b.y);
    return (point){(C1 * B2 - C2 * B1) / (A1 * B2 - A2 * B1),
                   (A1 * C2 - A2 * C1) / (A1 * B2 - A2 * B1)};
}

void mcc()
{
    random_shuffle(e + 1,e + n + 1);
    ans = e[1],r = 0;
    for (int i = 2;i <= n;i ++)
        if (dis(ans,e[i]) > r)
        {
            ans = e[i],r = 0;
            for (int j = 1;j < i;j ++)
                if (dis(ans,e[j]) > r)
                {
                    ans.x = (e[i].x + e[j].x) / 2.;
                    ans.y = (e[i].y + e[j].y) / 2.;
                    r = dis(ans,e[j]);
                    for (int k = 1;k < j;k ++)
                        if (dis(ans,e[k]) > r)
                        {
                            ans = center(e[i],e[j],e[k]);
                            r = dis(ans,e[i]);
                        }
                }

        }
}

int main()
{
    while (scanf("%d",&n) && n)
    {
        for (int i = 1;i <= n;i ++)
            scanf("%lf%lf",&e[i].x,&e[i].y);
        mcc();
        printf("%.2f %.2f %.2f\n",ans.x,ans.y,r);
    }

    return 0;
}