1043 - Triangle Partitioning

#include <bits/stdc++.h>
using namespace std;

double a, b, c, A, B, C;
double Ratio = 0;

double binarySearch(double low, double high) {
    double result = 0;
    int count = 70;
    double mid;
    while (count--) {
        mid = (low + high) / 2.00;
        a = mid;
        b = (a / A) * B;
        c = (a / A) * C;
        double ADE = ((a + b + c) / 2.0);
        double ABC = ((A + B + C) / 2.0);
        double areaOne = sqrt(ADE * (ADE - a) * (ADE - b) * (ADE - c));
        double areaTwo = sqrt(ABC * (ABC - A) * (ABC - B) * (ABC - C));
        double BDEC = areaTwo - areaOne;
        result = areaOne / BDEC;
        if (result > Ratio) {
            high = mid;
        } else {
            low = mid;
        }
    }
    return mid;
}

int main() {
    int testCase;
    cin >> testCase;
    for (int i = 0; i < testCase; i++) {
        cin >> A >> B >> C >> Ratio;
        printf("Case %d: %.10lf\n", i + 1, binarySearch(0, A));
    }

    return 0;
}