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## Discussion of Problem 1768. Circular Strings

Posted by Tigran92[RAU_902] 19 Nov 2010 20:07
Who can tell me what is wrong?

// Geometry.cpp : Defines the entry point for the console application.
//

#include "stdafx.h"

#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <stack>
#include <queue>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <string>
#include <cstring>
#include <ctime>

using namespace std;

#define sz(a)    (a.size())
#define all(a)   (a.begin(),a.end())
#define Sort(a)  (sort(all(a)))
#define pb       (push_back)
#define dump(x)    cerr<<#x<<" = "<<(x)<<endl;
#define debug(x)  cerr<<#x<<" = "<<(x)<<" (L"<< __LINE__ <<")"<<" "<< __FILE__ <<endl;
#define eps 1e-7
int sign (double x)  { return ((x)>eps?1:((x)<-eps?2:0));}

const double PI=acos(-1.0);
const int INF=2100000000;
struct point {
double x;
double y;
};
struct line {
point a;
point b;
};
double mult(point p1,point p2,point p0){
return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);
}
double sqrdist(point a,point b){
return ((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
int is_convex(int n,point *p){
int i,s[3]={1,1,1};
for(i=0;i<n && s[1]|s[2];i++){
double x=(mult(p[(i+1)%n],p[(i+2)%n],p[i]));
s[sign(x)]=0;
}
return s[1]|s[2];
}
bool dist(int n,point *p){
double dis=sqrdist(p[0],p[1]);
int i;
for(i=0;i<n;i++){
if(fabs(dis-sqrdist(p[i],p[(i+1)%n]))>=eps){
return (false);
}
}
return (true);
}
double distance1(point a,point b){
return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
double getangle(point a,point b,point c){
double sq=((a.x-b.x)*(a.y-c.y)-(a.x-c.x)*(a.y-b.y));
double ab=distance1(a,b);
double bc=distance1(b,c);
double sinphi=(ab*bc)/sq;
return asin(sinphi);
}
bool isangles(int n,point *p){
double sinphi=getangle(p[0],p[1],p[2]);
int i;
for(i=0;i<n;i++){
if(fabs(sinphi-getangle(p[i],p[(i+1)%n],p[(i+2)%n]))>eps){
return (false);
}
}
return (true);
}
bool isRight(int n,point *p){
if(dist(n,p) && is_convex(n,p) && isangles(n,p)){
return (true);
}
return (false);
}
int main(){
int n;
int i;
cin>>n;
point *p=new point [n];
for(i=0;i<n;i++){
cin>>p[i].x;
cin>>p[i].y;
}
(isRight(n,p))?(puts("YES")):(puts("NO"));
return (0);
}