Solution UVA: 190 - Circle Through Three Points (rare method)

Popular method: 

 Once you have the center of the circle (h,k) and the radius r from the previous step, you can calculate c, d, and e as follows (simple expanding and regrouping):

c = -2h

d = -2k

e = h^2 + k^2 - r^2

My method:

1/ I use three point A, B, C for x^2 + y^2 + cx + dy − e = 0 

So I get c, d, e

2/ I see h = c/2 and k = c/2

So I get h, k

3/ I use point A and h, k for  (x − h)^2 + (y − k)^2 = r^2

So I get r

4/ You had h, k, c, d, e but in a few case maybe will nan 

So I swap point A, B, C by permutation and It's was accepted

Successful people always have their own way :))

Code use my method

#include<bits/stdc++.h>

using namespace std;

string s;

double sqr(double x){

    return x*x;

}

struct equation{

    double x, y, z;

};

struct point{

    double x, y;

};

void f(point A, point B, point C){

    equation e1;

    e1.z = sqr(A.x) + sqr(A.y);

    e1.x = A.x;

    e1.y= A.y;

   

    equation e2;

    e2.z = sqr(B.x) + sqr(B.y);

    e2.x = B.x;

    e2.y= B.y;

   

    equation e3;

    e3.z = sqr(C.x) + sqr(C.y);

    e3.x = C.x;

    e3.y= C.y;

     

    equation e12;

    e12.x = e1.x - e2.x;

    e12.y = e1.y - e2.y;

    e12.z = e1.z - e2.z;

   

    equation e13;

    e13.x = e1.x - e3.x;

    e13.y = e1.y - e3.y;

    e13.z = e1.z - e3.z;

   

    double t1, t2, t3, t4, c, d, e;

    t1 = e12.z / e12.x;

    t2 = - (e12.y / e12.x);

    t3 = e13.x * t1;

    t4 = e13.x * t2 + e13.y;

    d = (e13.z - t3) / t4;

    c = (e13.z - e13.y*d) / e13.x;

    d = -d;

    c = -c;

    e = sqr(A.x) + sqr(A.y) + c*A.x + d*A.y;

    e = -e;

   

    double h, k, r;

    h = c/2;

    k = d/2;

    r = sqrt(sqr(A.x + h) + sqr(A.y + k));

   

     if (isnan(h) || isnan(k) || isnan(c) || isnan(d) || isnan(e)) {

        throw std::runtime_error("One or more variables are NaN.");

    }

   

   

//  cout<<fsp(3)<<"(x "<<f(h)<<" "<<abs(h)<<")^2 + (y "<<f(k)<<" "<<abs(k)<<")^2 = "<<r<<"^2\n";

//  cout<<fsp(3)<<"x^2 + y^2 "<<f(c)<<" "<<abs(c)<<"x "<<f(d)<<" "<<abs(d)<<"y "<<f(e)<<" "<<abs(e)<<" = 0\n\n";

    cout << fixed << setprecision(3);

    cout << "(x " << (h < 0 ? "-" : "+") << " " << abs(h) << ")^2 + ";

    cout << "(y " << (k < 0 ? "-" : "+") << " " << abs(k) << ")^2 = ";

    cout << r << "^2" << endl;

    cout << "x^2 + y^2 ";

    cout << (c < 0 ? "-" : "+") << " " << abs(c) << "x ";

    cout << (d < 0 ? "-" : "+") << " " << abs(d) << "y ";

    cout << (e < 0 ? "-" : "+") << " " << abs(e) << " = 0" << endl << endl;

}

int main(){

    while(getline(cin, s)){

        stringstream ss(s);

       

        point A, B, C;

        ss >> A.x; ss >> A.y;

        ss >> B.x; ss >> B.y;

        ss >> C.x; ss >> C.y;

       

        try{f(A, B, C);}catch(...){

            try{f(A, C, B);}catch(...){

                try{f(B, A, C);}catch(...){

                    try{f(B, C, A);}catch(...){

                        try{f(C, A, B);}catch(...){

                            try{f(C, B, A);}catch(...){

   

            }

               

            }  

               

            }  

               

            }  

               

            }

           

        }

    }

}