LightOJ 1043 - Triangle Partitioning

/**
@author - Rumman BUET CSE'15

problem - 1043 - Triangle Partitioning

link - http://www.lightoj.com/volume_showproblem.php?problem=1043

concept -

Binary search / Bisection.
It is a easy problem of bisection.
You can understand it without explanation.
Whatever ,
    Take length - 0.000000001 as hi
    and  0 + 0.000000001 as lo
    otherwise , AD will be '0' or full AB which is not acceptable.
    because , then ABC will be not a triangle or r will  be infinity.

*/

#include<bits/stdc++.h>
using namespace std ;
#define ll long long
#define d 0.00000001

int main()
{
    double AB, AC, BC, r ;
    ll T, t = 0 ;

    scanf("%lld",&T);

    while(T--)
    {
        t++ ;

        /**
            for scanning double data ,
                you have to use
                %lf.
                not %f .
            Be careful in these issues.

        */
        scanf("%lf %lf %lf %lf",&AB, &AC, &BC,&r );

//        cout << AB << " " << AC << " " << BC << " " << r << endl ;
        double s, ADE, ABC ;
        s = 0.5 * (AB + AC + BC);
        ABC = sqrt(1.0 * s*(s-AB)*(s-AC)*(s-BC));

        double  hi , lo , mid , AD , DE , AE , trap , R ;

        hi = AB - d ;
        lo = d ;
        ll k = 0 ;
        while(hi - lo > d)
        {
            AD = (hi+lo)/2.0 ; /// mid == AD
            DE = AD * 1.0 *BC /AB ;
            AE = AD * 1.0 *AC /AB ;
            s = 0.5 * (AD + DE + AE);
            ADE = sqrt(1.0 * s*(s-AD)*(s-DE)*(s-AE));
            trap = ABC - ADE ;
            R = ADE *1.0 / trap ;

            if(R > r)
            {
                hi =  AD ;
//                cout << "hi " << hi << endl  ;
            }
            else
            {
                lo = AD ;
//                cout << "lo " << lo << endl ;
            }
        }
        /**
            for precision issue in double, you have to use %.8f -
            that means 'f' ;
            not 'lf' .
        */
        printf("Case %lld: %.11f\n",t , AD);

    }

    return 0 ;

}