Soj-1, 11512

11512. Big circle Constraints

Time Limit: 2 secs, memory limit: 256 MB

Description

 

On the opening ceremony of World Cup there was a part where contains kids from around the world was trying to make a big circle on the field which symbolized tolerance and multicultural friendship.

They succeed in making a perfect circle, but as they didn't practice very much, kids weren't uniformly distributed on circle. you spotted that very quickly, and you want to know what is the minimum distance between some two kids.

 

Input

 

First line of the input contains number N (2 <= n <= 10 ^ 5) representing number of kids. each of next n lines contains two real numbers rounded on two decimal places-coordinates of the each kid. all coordinates will be in interval [-10 ^ 6, 10 ^ 6]. it is guaranteed that all points will be on circle.

 

 

Output

 

First and only line of output shoshould contain one real number (rounded on two decimal places)-Euclidian Distance between two nearest kids. euclidian Distance between points (x1, Y1) and (X2, Y2) is SQRT (x1-x2) ^ 2 + (y1-y2) ^ 2 ).

 

Sample Input

51.00 4.00-0.50 -1.604.00 1.003.12 3.12-1.60 -0.50

Sample output

1.56

Hint

 

In the sample, kids at points (−0.50, −1.60) and (−1.60, −0.50) are nearest and distance between them is 1.56.

 

Problem Source

2014/jboi 2014

 

Question: Find the shortest String Length formed by several points on the circle.

Idea: first select three points to determine the center of the center (the vertical line intersection of the two strings), and then translate the entire circle to make the center and the coordinate origin coincide, in this way, we can sort each point counterclockwise from the positive and half axes of the X axis, and then find the length of the string formed by the adjacent two points. The minimum value is the answer.

 

 1 // Problem#: 11512 2 // Submission#: 3027891 3 // The source code is licensed under Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License 4 // URI: http://creativecommons.org/licenses/by-nc-sa/3.0/ 5 // All Copyright reserved by Informatic Lab of Sun Yat-sen University 6 #include<bits/stdc++.h> 7 using namespace std; 8 typedef long long ll; 9 struct P{10     double x,y;11 };12 vector<P>v;13 int n;14 double X,Y;15 inline double d2(P a,P b)16 {17     return (a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y);18 }19 int F(P p)20 {21     if(p.y == 0)return p.x > 0 ? 0 : 4;22     if(p.x == 0)return p.y > 0 ? 2 : 6;23     if(p.x > 0 && p.y > 0)return 1;24     if(p.x < 0 && p.y > 0)return 3;25     if(p.x < 0 && p.y < 0)return 5;26     if(p.x > 0 && p.y < 0)return 7;27 }28 bool cmp(const P& a,const P& b)29 {30     int fa = F(a),fb = F(b);31     if(fa != fb)return fa < fb;32     else return a.y * b.x < a.x * b.y;33 }34 int main()35 {36     int i;37     while(~scanf("%d",&n))38     {39         v.clear();40         for(i=0;i<n;i++)41         {42             P p;43             scanf("%lf%lf",&p.x,&p.y);44             v.push_back(p);45         }46         if(n==2)47         {48             printf("%.2f\n",sqrt(d2(v[0],v[1])));49             continue;50         }51         double xm01=(v[0].x+v[1].x)/2.0,ym01=(v[0].y+v[1].y)/2.0;52         double xm12=(v[1].x+v[2].x)/2.0,ym12=(v[1].y+v[2].y)/2.0;53         double dym01m12 = ym12 - ym01;54         double dx01=v[1].x-v[0].x,dy01=v[1].y-v[0].y;55         double dx12=v[2].x-v[1].x,dy12=v[2].y-v[1].y;56         X = (dym01m12 * dy12 * dy01 - xm01 * dx01 * dy12 + xm12 * dx12 * dy01) / (dx12 * dy01 - dx01 * dy12);57         if(dy01)58         Y = ym01 - (X - xm01) * dx01 / dy01;59         else//dy12 != 060         Y = ym12 - (X - xm12) * dx12 / dy12;61         for(i=0;i<n;i++)62         {63             v[i].x-=X;64             v[i].y-=Y;65         }66         sort(v.begin(),v.end(),cmp);67         double ans=d2(v[0],v[1]);68         double d;69         for(i=1;i<n;i++)ans = min(ans,d=d2(v[i-1],v[i]));70         ans = min(ans,d2(v[n-1],v[0]));71         printf("%.2f\n",sqrt(ans));72     }73     return 0;74 }75 /*76 377 0.71 0.7178 0.71 -0.7179 -1.00 0.0080 */                                 

 

PS: The data of the original question seems to be not strong enough. The above group of data cannot be accessed even if 70th lines of code are removed.

Soj-1, 11512