import java.util.Scanner;
public class Main {
public static void main(String[] arg) {
Scanner scanner = new Scanner(System.in);
// todo
}
}
NC20534. [AHOI2012]信号塔
描述
输入描述
共N+1行,第一行为正整数N(1 ≤ N ≤ 1000000),表示队员个数。
接下来N行,每行两个实数用空格分开,分别是第i个队员的坐标X
输出描述
一行,共三个实数(中间用空格隔开),分别是信号塔的坐标,和信号塔覆盖的半径。(注:队员是否在边界上的判断应符合他到圆心的距离与信号塔接收半径之差的绝对值小于10^-6)
示例1
输入:
5 1.200 1.200 2.400 2.400 3.800 4.500 2.500 3.100 3.900 1.300
输出:
2.50 2.85 2.10
C++14(g++5.4) 解法, 执行用时: 275ms, 内存消耗: 8100K, 提交时间: 2020-10-05 19:19:16
#include<bits/stdc++.h>#define eps 1e-6using namespace std;const int maxn=1e6+10;struct node{double x,y;}p[maxn],o;double dis(node x,node y){return sqrt((x.x-y.x)*(x.x-y.x)+(x.y-y.y)*(x.y-y.y));}node circle(node a,node b,node c)//三点共圆圆心公式{double X=( (a.x*a.x-b.x*b.x+a.y*a.y-b.y*b.y)*(a.y-c.y)-(a.x*a.x-c.x*c.x+a.y*a.y-c.y*c.y)*(a.y-b.y) ) / (2*(a.y-c.y)*(a.x-b.x)-2*(a.y-b.y)*(a.x-c.x));double Y=( (a.x*a.x-b.x*b.x+a.y*a.y-b.y*b.y)*(a.x-c.x)-(a.x*a.x-c.x*c.x+a.y*a.y-c.y*c.y)*(a.x-b.x) ) / (2*(a.y-b.y)*(a.x-c.x)-2*(a.y-c.y)*(a.x-b.x));double R=sqrt((X-a.x)*(X-a.x)+(Y-a.y)*(Y-a.y));return (node){X,Y};}double r=0;void minicircle(int n){o=p[0],r=0;for(int i=0;i<n;i++){if(dis(p[i],o)-r>eps){o=p[i];r=0;for(int j=0;j<i;j++){if(dis(p[j],o)-r>eps){o={(p[i].x+p[j].x)/2.0,(p[i].y+p[j].y)/2.0};r=dis(p[i],p[j])/2.0;for(int k=0;k<j;k++){if(dis(p[k],o)-r>eps){o=circle(p[i],p[j],p[k]);r=dis(p[i],o);}}}}}}}int main(){int n;scanf("%d",&n);for(int i=0;i<n;i++) scanf("%lf%lf",&p[i].x,&p[i].y);srand((unsigned long)time(NULL));random_shuffle(p,p+n);minicircle(n);printf("%.2f %.2f %.2f\n",o.x,o.y,r);return 0;}
C++11(clang++ 3.9) 解法, 执行用时: 257ms, 内存消耗: 8132K, 提交时间: 2020-10-16 20:07:20
#include<algorithm>#include<iostream>#include<cstdio>#include<cstring>#include<cmath>using namespace std;#define ll long long#define f(i,a,b) for(int i=a;i<=b;i++)#define inf 0x7f7f7f7f;const double eps=1e-5;struct dot{double x,y;}p[1000010],ans;ll n;double ar;double dis(dot a,dot b){return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));}dot Ce(dot p1,dot p2,dot p3){double a,b,c,d,e,f;a=p2.y-p1.y;b=p3.y-p1.y;c=p2.x-p1.x;d=p3.x-p1.x;f=p3.x*p3.x+p3.y*p3.y-p1.x*p1.x-p1.y*p1.y;e=p2.x*p2.x+p2.y*p2.y-p1.x*p1.x-p1.y*p1.y;return (dot){(a*f-b*e)/(2*a*d-2*b*c),(d*e-c*f)/(2*a*d-2*b*c)};}int main(){scanf("%lld",&n);f(i,1,n)scanf("%lf%lf",&p[i].x,&p[i].y);//cout<<Ce(p[1],p[2],p[3]).x;//random_shuffle(p+1,p+n+1);ar=dis(p[1],p[2])/2.0,ans=(dot){(p[1].x+p[2].x)/2.0,(p[1].y+p[2].y)/2.0};f(i,2,n)if(dis(p[i],ans)>ar+eps){ans=p[i],ar=0;f(j,1,i-1)if(dis(p[j],ans)>ar+eps){ans=(dot){(p[i].x+p[j].x)/2.0,(p[i].y+p[j].y)/2.0};ar=dis(ans,p[i]);f(k,1,j-1)if(dis(p[k],ans)>ar+eps)ans=Ce(p[i],p[j],p[k]),ar=dis(ans,p[i]);}}printf("%.2lf %.2lf %.2lf",ans.x,ans.y,ar);return 0;}