Solution UVA: 438 The Circumference of the Circle

Problem	Verdict	Lang	Time	Best	Rank	Submit Time
| discuss438 - The Circumference of the Circle	Accepted	C++11	0.000	0.000	2662	3 mins ago

 

#include <bits/stdc++.h>

using namespace std;

double sqr(double x){

    return x*x;

}

double sqrt(double x){

    return pow(x, 1.0/2);

}

int main() {

    double xa, ya, xb, yb, xc, yc;

   

    while(cin >> xa >> ya >> xb >> yb >> xc >> yc){

        double ab = sqrt(sqr(xb-xa)+sqr(yb-ya));

        double bc = sqrt(sqr(xc-xb)+sqr(yc-yb));

        double ac = sqrt(sqr(xc-xa)+sqr(yc-ya));

        double p = (ab + bc + ac) / 2;

        double s = sqrt(p*(p-ab)*(p-bc)*(p-ac));

        double r = ab*bc*ac / (4*s);

        cout<<fixed<<setprecision(2)<<3.141592653589793*2*r<<"\n";

    }

   

}

1. Function Definitions:

   • double sqr(double x): Defines a function to compute the square of a given double value.
   • double sqrt(double x): Defines a function to compute the square root of a given double value using the pow function.

2. Main Function:

   • Declares six variables xa, ya, xb, yb, xc, yc to store the coordinates of three points.

3. While Loop:

   • Uses a while loop that reads input for the coordinates of three points until it reaches the end of the input.
   • Inside the loop, it calculates the distances ab, bc, and ac between the points using the distance formula.

4. Circumference Calculation:

   • Calculates the semi-perimeter p using the formula: $�=\frac{��+��+��}{2}$.
   • Calculates the area s of the triangle using Heron's formula: $�=\sqrt{�\cdot (�-��)\cdot (�-��)\cdot (�-��)}$.
   • Computes the radius r of the circumcircle using the formula: $�=\frac{��\cdot ��\cdot ��}{4\cdot �}$.
   • Finally, calculates the circumference of the circumcircle and outputs it with fixed precision.