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# Circle of death CodeChef Solution

## Circle of death CodeChef Solution in C++14

``````#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <sstream>
#include <queue>
#include <deque>
#include <bitset>
#include <iterator>
#include <list>
#include <stack>
#include <map>
#include <set>
#include <functional>
#include <numeric>
#include <utility>
#include <limits>
#include <time.h>
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <unordered_map>
#include <unordered_set>

using namespace std;
#ifdef ONLINE_JUDGE
#define endl "\n"
#endif

#define gcd(a,b) __gcd(a,b)
#define all(cont) conbegin(), conend()
#define rall(cont) conend(), conbegin()
#define rsort(x) sort(x,[](auto a, auto b){rtn a > b;});
#define forr(i,v) for (int i = 0; i < v; i++)
#define each(x,v) for (auto x: v)
#define forrr(i,j,v,w) for (int i = 0; i < v; i++) for (int j = 0; j < w; j++)
#define ni(x) int x; cin >> x;
#define nii(x,y) int x,y; cin >> x >> y;
#define niii(x,y,z) int x,y,z; cin >> x >> y >> z;
#define niiii(w,x,y,z) int w,x,y,z; cin >> w >> x >> y >> z;
#define nl(x) ll x; cin >> x;
#define nll(x,y) ll x,y; cin >> x >> y;
#define nlll(x,y,z) ll x,y,z; cin >> x >> y >> z;
#define nllll(w,x,y,z) ll w,x,y,z; cin >> w >> x >> y >> z;
#define get(v) vi v;forr (i,n){ni(x);v.pb(x);}
#define amax(a,b) a = max(a,b);
#define amin(a,b) a = min(a,b);
#define mp make_pair
#define pb push_back
#define ff first
#define ss second
#define rz resize
#define sz size()
#define cnt continue
#define brk break
#define rtn return
#define W() int T; cin >> T; while(T--)
#define trace(x) cerr<<#x<<": "<<x<<endl;
#define output()
#define ff first
#define float double
typedef long int int32;
typedef unsigned long int uint32;
typedef long long int int64;
typedef unsigned long long int  uint64;
typedef long long ll;
typedef string str;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<bool> vb;
typedef vector<ll> vl;
typedef vector<int> vi;
typedef vector<str> vs;
typedef vector<pii> vpii;
typedef vector<vpii> vppii;
typedef vector<vi> vii;
typedef unordered_map<int,int> mpii;
typedef set<int> seti;
typedef set<pair<int,int>> spii;
typedef vector<set<int>> vseti;

const ll linf = 1e18+10;
const int inf = 1e9+10;
const double eps = 1e-9;
const double pi = 3.1415926535897932384626433832795;
const int mod = 1000000007;
const int base = 31;

ll max(ll a, ll b){
return a > b ? a : b;
}

ll min(ll a, ll b){
return a < b ? a : b;
}

void out(vl v){
for (int i:v){
cerr << i << " ";
}
cerr << endl;
}

void out(vi v){
for (int i:v){
cerr << i << " ";
}
cerr << endl;
}

void out(vb v){
for (int i:v){
cerr << i << " ";
}
cerr << endl;
}

void out(vii v){
for (vi i:v){
out(i);
}
cerr << endl;
}

void out(pii i){
cerr << "<" << i.ff << "," << i.ss << ">  ";
}

void out(vpii v){
for (pii i:v){
out(i);
}
cerr << endl;
}

void out(mpii v){
for (pii i:v){
out(i);
}
cerr << endl;
}

void out(int v[], int n){
forr (i,n){
cerr << v[i] << " ";
}
cerr << endl;
}

void out(map<int,int> v){
for (pii i:v){
out(i);
}
cerr << endl;
}

int add(int a, int b){
int res = (a+b) % mod;
if (res < 0)
res += mod;
rtn res;
}

int mul(int a, int b){
int res = (a * 1LL * b) % mod;
if (res < 0)
res += mod;
rtn res;
}

int power(int a, int b){
int res = 1;
while(b){
if (b % 2)
res = mul(res,a);
a = mul(a,a);
b /= 2;

}
rtn res;
}

int inv(int x){
rtn x == 1 ? 1 : power(x,mod-2);
}

void ans (str x){
cout << x << endl;
}

void ans (const char* x){
cout << x << endl;
}

template<typename T>
void ans (T x){
ans(to_string(x));
}

bool isPrime(int x)
{
int primes[168] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997};
int j = 0;
while (primes[j] < floor(sqrt(x)) + 1)
{
if (x % primes[j] == 0)
{
return false;
}
j++;
}
return true;
}

void sieve(int n=1000005){
bool p[1000005];
memset(p,1,sizeof(p));
p[0] = p[1] = 0;
for (int i = 2; i * i < n; i++){
if (p[i]){
for (int j = 2 * i; j < n; j += i){
p[j] = 0;
}
}
}
}

vi range(int n){
vi v(n);
for (int i = 1;i < n; i++){
v[i] = i;
}
rtn v;
}

#define x ff
#define y ss
typedef pair<double,double> pdd;

double cross(pii a, pii b){
rtn a.x * 1.0 * b.y - a.y * 1.0 * b.x;
}

double area(pii a, pii b, pii c){
rtn abs(cross({b.x - a.x,b.y - a.y},{c.x - b.x,c.y - b.y})/2.0);
}

double radius(pii a, pii b, pii c){
auto d = area(a,b,c);
if (d == 0) rtn 0.0;
rtn hypot(a.x - b.x, a.y - b.y) * hypot(c.x - b.x, c.y - b.y) * hypot(a.x - c.x, a.y - c.y) / (4.0 * d);
}

double dist(pii a, pii b){
rtn hypot(a.x - b.x,a.y - b.y);
}

pdd centre(pii a, pii b, pii c)
{
rtn {a.x - ((((b.y-a.y)*dist(c,a)*dist(c,a)) -  ((c.y-a.y)*dist(b,a)*dist(b,a)))/(2.0*((b.x-a.x)*(c.y-a.y)  - (c.x-a.x)*(b.y-a.y))))
,a.y + (((b.x-a.x)*(dist(c,a)*dist(c,a)) - (c.x-a.x)*(dist(b,a)*dist(b,a)))/(2.0* (((b.x-a.x)*(c.y-a.y))-((c.x-a.x)*(b.y-a.y)))))};
}

void pre(){

}

void solve(){
ni(n);
vpii v;
forr (i,n){
nii(x,y);
v.pb({x,y});
}
int t = 0, b = 0;
forr (i,n){
forr (j,i){
forr (k,j){
pdd c;
auto r = radius(v[i],v[j],v[k]);
if (r < eps){
c = {0,0};
} else {
c = centre(v[i],v[j],v[k]);
}
// cerr << c.ff << " " << c.ss << " " << r << endl;
forr (m,n){
if (m == i || m == j || m == k) cnt;
b ++;
if (r == 0){
cnt;
}
t += hypot(c.x-v[m].x,c.y-v[m].y) <= (r + eps);
if (0 && hypot(c.x-v[m].x,c.y-v[m].y) <= (r + eps)){
out(v[i]);
out(v[j]);
out(v[k]);
cerr << "<" << c.ff << "," << c.ss << ">  ";
out(v[m]);
cerr << endl;
}
}
}
}
}
ans(t * 1.0 / b);
}

int32_t main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);cout.tie(NULL);cerr.tie(NULL);

#ifndef ONLINE_JUDGE
freopen("../../input.txt","r",stdin);
freopen("../../output.txt","w",stdout);
freopen("../../error.txt","w",stderr);
#endif
clock_t tStart = clock();

pre();
W(){
solve();
}

double t =  (double)(clock() - tStart)/CLOCKS_PER_SEC;
cerr << endl << "Time: " << t;
rtn 0;
}

/*

*/``````

## Circle of death CodeChef Solution in PYTH 3

``````# cook your dish here
# cook your dish here

from itertools import combinations
T = int(input())
while T != 0:
N = int(input())
points = []
for i in range(N):
x,y = map(int,input().strip().split())
points.append([x,y])
kill = 0
total = (N*(N-1)*(N-2)*(N-3))/6
comb = combinations(points,3)
for x in list(comb):
[x1,y1] = x[0]
[x2,y2] = x[1]
[x3,y3] = x[2]
area = (x1 - x2)*(y2 - y3) - (y1 - y2)*(x2 - x3)
if area == 0:
continue
x12 = x1 - x2
x13 = x1 - x3
y12 = y1 - y2
y13 = y1 - y3
y31 = y3 - y1
y21 = y2 - y1
x31 = x3 - x1
x21 = x2 - x1
sx13 = pow(x1, 2) - pow(x3, 2)
sy13 = pow(y1, 2) - pow(y3, 2)
sx21 = pow(x2, 2) - pow(x1, 2)
sy21 = pow(y2, 2) - pow(y1, 2)
f = (((sx13) * (x12) + (sy13) * (x12) + (sx21) * (x13) + (sy21) * (x13)) / (2 * ((y31) * (x12) - (y21) * (x13))))
g = (((sx13) * (y12) + (sy13) * (y12) + (sx21) * (y13) + (sy21) * (y13)) / (2 * ((x31) * (y12) - (x21) * (y13))))
c = (-pow(x1, 2) - pow(y1, 2) - 2 * g * x1 - 2 * f * y1)
for i in points:
if i in x:
continue
else:
if (pow(i[0],2) + pow(i[1],2) + 2*g*i[0] + 2*f*i[1] + c) <= 0.000001:
kill = kill+1
prob = kill/total
print(prob)
T = T-1``````

## Circle of death CodeChef Solution in C

``````#include<stdio.h>
#include<math.h>
#define MAX  31
struct point
{
int x;
int y;
};
int det(int a1,int a2,int a3,int b1,int b2,int b3,int c1,int c2,int c3)
{
return a1*(b2*c3-b3*c2)-a2*(b1*c3-b3*c1)+a3*(b1*c2-b2*c1);
}
main()
{
int test,area=0,n,count,com,i,j,k,l,c1,c2,c3,c4,d;
struct point a[MAX];
scanf("%d",&test);
while(test--)
{
scanf("%d",&n);
count=0;com=0,area=0;
for(i=0;i<n;i++)
{
scanf("%d %d",&a[i].x,&a[i].y);
}

for(i=0;i<n;i++)
{
for(j=i+1;j<n;j++)
{
for(k=j+1;k<n;k++)
{
com+=(n-3);

area=det(a[i].x,a[i].y,1,a[j].x,a[j].y,1,a[k].x,a[k].y,1);
if(area==0)
{

//printf("Line ");
continue;
}
else
{
c1=area;
c2=det(pow(a[i].x,2)+pow(a[i].y,2),a[i].y,1,
pow(a[j].x,2)+pow(a[j].y,2),a[j].y,1,
pow(a[k].x,2)+pow(a[k].y,2),a[k].y,1);
c3=det(pow(a[i].x,2)+pow(a[i].y,2),a[i].x,1,
pow(a[j].x,2)+pow(a[j].y,2),a[j].x,1,
pow(a[k].x,2)+pow(a[k].y,2),a[k].x,1);
c4=det(pow(a[i].x,2)+pow(a[i].y,2),a[i].x,a[i].y,
pow(a[j].x,2)+pow(a[j].y,2),a[j].x,a[j].y,
pow(a[k].x,2)+pow(a[k].y,2),a[k].x,a[k].y);
//printf("\n equ is %d %d %d %d",c1,c2,c3,c4);
for(l=0;l<n;l++)
{
if(l==i || l==j || l==k)
continue;

d=c1*(pow(a[l].x,2)+pow(a[l].y,2))-c2*a[l].x+c3*a[l].y-c4;
if(area>0 && d<=0)
count++;
else if(area<0 && d>=0)
count++;
}

}

}
}
}
//printf("%d is com and %d is count",com,count);
printf("%.6lf\n",(double)count/(double)com);
}
}``````

## Circle of death CodeChef Solution in JAVA

``````/* package codechef; // don't place package name! */

import java.io.BufferedOutputStream;
import java.io.IOException;

public class Main {

public class Point {
int x ;
int y ;
public Point(int xx , int yy) {
x = xx;
y = yy;
}
}

static Main main;

public static void main(String [] args ) {
main = new Main();
try{
String str;
BufferedOutputStream bos = new BufferedOutputStream(System.out);
String eol = System.getProperty("line.separator");
byte [] eolb = eol.getBytes();
int t = Integer.parseInt(str);
for(int i = 0 ; i < t ; i++) {
int n = Integer.parseInt(str);
Point [] points = new Point[n];
for(int j = 0 ; j < n ; j++) {
int blank = str.indexOf( " ");
int x = Integer.parseInt(str.substring(0,blank));
int y = Integer.parseInt(str.substring(blank+1));
points[j] = main.new Point(x,y);
}
int count = 0;
int countT = 0;
for(int p = 0 ; p < n ; p++) {
for(int q = p+1 ; q < n ; q++) {
for(int r = q+1 ; r < n ; r++) {
countT+=(n-3);
if(!collinear(points[p],points[q],points[r])) {
for(int s = 0 ; s < n ; s++) {
if((s!=p)&&(s!=q)&&(s!=r)) {
// find circumradius and circumcentre;
long x = points[s].x;
long y = points[s].y;
long x1 = points[p].x;
long y1 = points[p].y;
long x2 = points[q].x;
long y2 = points[q].y;
long x3 = points[r].x;
long y3 = points[r].y;
long a = (x1*(y2-y3)-y1*(x2-x3)+x2*y3-x3*y2) ;
long bx = ((x1*x1+y1*y1)*(y2-y3)-y1*(x2*x2+y2*y2-x3*x3-y3*y3)+(x2*x2+y2*y2)*y3-(x3*x3+y3*y3)*y2);
bx *= -1;
long by = ( (x1*x1+y1*y1)*(x2-x3) - x1*(x2*x2+y2*y2-x3*x3-y3*y3) + (x2*x2+y2*y2)*x3 - (x3*x3+y3*y3)*x2);
long c = (x1*x1+y1*y1)*(x2*y3-x3*y2) - x1*((x2*x2+y2*y2)*y3-(x3*x3+y3*y3)*y2) + y1 *((x2*x2+y2*y2)*x3-(x3*x3+y3*y3)*x2) ;
c*=-1;
long x0 = 2 * a * x + bx ;
long y0 = 2 * a * y + by ;
x0*=x0;
y0*=y0;
long r0 = bx*bx+by*by-4*a*c;
if((x0+y0)<=r0) {
count++;
}
}
}
}
}
}
}
double prob = ((double)count)/((double)(countT));
bos.write(new Double(prob).toString().getBytes());
bos.write(eolb);
}
bos.flush();
} catch(IOException ioe) {
ioe.printStackTrace();
}
}
public static boolean collinear(Point p1 , Point p2 , Point p3 ) {
int x1 = p1.x;
int y1 = p1.y;
int x2 = p2.x;
int y2 = p2.y;
int x3 = p3.x;
int y3 = p3.y;
if(((y2-y1)*(x3-x1))==((y3-y1)*(x2-x1)) ) {
return true;
}
return false;
}
}``````

## Circle of death CodeChef Solution in PYTH

``````import math

x,y =[],[]

def ss(i):
return x[i] * x[i] + y[i] * y[i]
def check(a,b,c):
s2 = [ss(a),ss(b),ss(c)]
D =  (x[a] * (y[b]-y[c]) + x[b] * ( y[c]-y[a]) + x[c] *(y[a]-y[b]))
if D == 0:return [0,0,-1]
sx = (ss(a)* (y[b]-y[c]) + ss(b) * ( y[c]-y[a]) + ss(c)*(y[a]-y[b]))*0.5 / D
sy = (ss(a)* (x[b]-x[c]) + ss(b) * ( x[c]-x[a]) + ss(c)*(x[a]-x[b]))*-0.5/ D
r  = math.hypot(x[a]-sx,y[a]-sy)
return [sx,sy,r]
def solve():
global x,y
n = int(raw_input())
x ,y= [0] * n ,[0] *n
num,den = 0,0
for i in xrange(n):
x[i],y[i] = map(int,raw_input().split())
for a in xrange(n):
for b in xrange(a+1,n):
for c in xrange(b+1,n):
sx,sy,r= check(a,b,c)
#print [(x[a],y[a]),(x[b],y[b]),(x[c],y[c])],r,(sx,sy)
for i in xrange(n):
if a!=i and b!=i and c!=i:
if math.hypot(x[i]-sx,y[i]-sy) < r + 1e-9:
num+=1
den +=1
print num * 1. / den

for i in xrange(int(raw_input())):
solve()``````

## Circle of death CodeChef Solution in C#

``````#define ONLINE_JUDGE

using System;
using System.Collections.Generic;
using System.Text;
using System.IO;

class Program
{

static int tests = 1;

#if (ONLINE_JUDGE)
static TextReader r = Console.In;
static TextWriter w = Console.Out;
#else
static string path = @"C:\Y\Prog\CodeChef\2013-06-Circle-of-death\";
static string resultFile = "0{0}Result.txt";
static string sourceFile = "0{0}Source.txt";

static TextWriter w;
#endif

static void Main(string[] args)
{

//Point p = Line.getCenter(new Point(98,100), new Point(100, 102), new Point(102,100));
//Console.WriteLine("Point {0} {1}", p.x, p.y);
//return;

for (int i = 1; i <= tests; i++)
{
#if (!ONLINE_JUDGE)
r = new StreamReader(string.Format(path + sourceFile, i));
w = new StreamWriter(string.Format(path + resultFile, i), false);
#endif
int cases = Convert.ToInt32(r.ReadLine());
for (int j = 0; j < cases; j++)
solve();
#if (!ONLINE_JUDGE)
w.Flush(); w.Close();
Console.WriteLine("CASE: {0}", i);
string result = File.ReadAllText(string.Format(path + resultFile, i));
if (answer != result)
{
Console.WriteLine("FAIL:");
Console.WriteLine("Result" + Environment.NewLine + result);
}
else
Console.WriteLine("OK");
#endif
}
}

public static void solve()
{
int n = Convert.ToInt32(r.ReadLine());
Point[] points = new Point[n];
for (int i = 0; i < n; i++)
{
string[] buff = r.ReadLine().Split(' ');
points[i] = new Point(Convert.ToInt32(buff[0]), Convert.ToInt32(buff[1]));
}

int totalKilled = 0;
int cases = 0;
//Console.WriteLine("begin");
for (int i1 = 0; i1 < points.Length; i1++)
for (int i2 = i1+1; i2 < points.Length; i2++)
for (int i3 = i2+1; i3 < points.Length; i3++)
{
if (i1 == i2 || i1 == i3 || i2 == i3) continue;
cases++;
Point p = Line.getCenter(points[i1], points[i2], points[i3]);
if (p.x == double.NaN) continue;
double r1 = p.dist(points[i1]);

//if (i1 == 0 && i2 == 1 && i3 == 4)
//{
//    Console.Write("A ");
//}
for (int i4 = 0; i4 < points.Length; i4++)
{
if (i4 == i1 || i4 == i2 || i4 == i3) continue;
double r2 = p.dist(points[i4]);
if (r2 < (r1 + 1e-06))
{
totalKilled++;
//Console.Write("Killed ");
//Console.WriteLine("p1 {0} p2 {1} p3 {2} p4 {3} r2 {4} r1 {5}", i1, i2, i3, i4, r2, r1);
}
else
{
//Console.Write("Fail ");
//Console.WriteLine("p1 {0} p2 {1} p3 {2} p4 {3} r2 {4} r1 {5}", i1, i2, i3, i4, r2, r1);
}
}
}
w.WriteLine((totalKilled / (double) cases) / (points.Length - 3.0));
}

public static void getLineIntersection()
{

}

}

public class Line
{
// ax + by = c

public double a;
public double b;
public double c;
public Line(Point p1, Point p2)
{
a = p2.y - p1.y;
b = p1.x - p2.x;
c = a * p1.x - b * p1.y;
}

public Line(double a, double b, double c) { this.a = a; this.b = b; this.c = c; }

public static Point getIntersection(Line l1, Line l2)
{
Point p = new Point(double.NaN, double.NaN);
double det = l1.a * l2.b - l2.a * l1.b;
if (Math.Abs(det) < 1e-09) return p;
p.x = (l2.b * l1.c - l1.b * l2.c) / det;
p.y = (l1.a * l2.c - l2.a * l1.c) / det;
return p;
}

public static Line getPerp(Point p1, Point p2)
{
Line l = new Line(p1, p2);
Point center = new Point((p1.x + p2.x) / 2, (p1.y + p2.y) / 2);
double a = -l.b;
double b = l.a;
double c = a * center.x + b * center.y;
return new Line(a, b, c);
}

public static Point getCenter(Point p1, Point p2, Point p3)
{
return getIntersection(getPerp(p1, p2), getPerp(p2, p3));
}

}

public class Point
{
public double x, y;
public Point(double x, double y) { this.x = x; this.y = y; }
public double dist(Point p) { return Math.Sqrt( (p.x - x) * (p.x - x) + (p.y - y) * (p.y - y)); }
}
``````

## Circle of death CodeChef Solution in GO

``````package main

import (
"fmt"
)

func IntAbs(x int) int {
if x < 0 {
return -x
}
return x
}

func one_case() {
//fmt.Println("case investigation started")
pn := 0
fmt.Scan(&pn)
arx, ary := make([]int, pn), make([]int, pn)
for p := 0; p < pn; p++ {
fmt.Scan(&arx[p], &ary[p])
}

var num, denum float64 //probability
for p := 0; p < pn; p++ {
for q := p+1; q < pn; q++ {
for r := q+1; r < pn; r++ {
x1, y1 := arx[p], ary[p]
x2, y2 := arx[q], ary[q]
x3, y3 := arx[r], ary[r]

denxy := 2 * ((y3-y2)*(x2-x1) - (x3-x2)*(y2-y1))

numx := (x2*x2 - x1*x1 + y2*y2 - y1*y1) * (y3-y2) -
(x3*x3 - x2*x2 + y3*y3 - y2*y2) * (y2-y1)

numy := (x2-x1) * (x3*x3 - x2*x2 + y3*y3 - y2*y2) -
(x3-x2) * (x2*x2 - x1*x1 + y2*y2 - y1*y1)

if denxy < 0 {
denxy, numx, numy = -denxy, -numx, -numy
}

//fmt.Println("\tp1 = ", x1, ",", y1)
//fmt.Println("\tp2 = ", x2, ",", y2)
//fmt.Println("\tp3 = ", x3, ",", y3)
//if denxy == 0 {
//	fmt.Println("\tno circle")
//} else {
//	fmt.Println("\t circle center = ", float64(numx) / float64(denxy),
//		float64(numy) / float64(denxy))
//}

for s:=0; s < pn; s++ {
if s != p && s != q && s != r {
x,y := arx[s], ary[s]
//fmt.Print("\t\tcand = ", x, ",", y)
if denxy!=0 &&
(x-x1)*((x+x1)*denxy - 2*numx) +
(y-y1)*((y+y1)*denxy - 2*numy) <= 0 {
//fmt.Println(" accepted")
num++
}// else {
//	fmt.Println(" declined")
//}
denum++
}
}
//fmt.Println()
}
}
}
fmt.Println(num/denum)
}

func main() {
tk := 0
fmt.Scan(&tk)
for t := 0; t < tk; t++ {
one_case()
}
}``````
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