#include <iostream>
#include <fstream>
#include <cmath>

using namespace std;

typedef long double real;

real m_cos(real k, real a, real b) {
    real result = k*(a - b) + cos(k*a);

    if (result <= -1) {
        return -1;
    }

    return result;
}

real M_cos(real k, real a, real b) {
    real result = k*(b - a) + cos(k*b);

    if (result >= 1) {
        return 1;
    }

    return result;
}

real m_sin(real k, real a, real b) {
    real result = k*(a - b) + sin(k*a);

    if (result <= -1) {
        return -1;
    }

    return result;
}

real M_sin(real k, real a, real b) {
    real result = k*(b - a) + sin(k*b);

    if (result >= 1) {
        return 1;
    }

    return result;
}

real m_f(real a, real b) {
    return m_cos(314, a, b) - M_cos(650, a, b) - 1;
}

real M_f(real a, real b) {
    return M_cos(314, a, b) - m_cos(650, a, b) - 1;
}

real m_fp(real a, real b) {
    return m_sin(650, a, b) - M_sin(314, a, b);
}

real M_fp(real a, real b) {
    return M_cos(650, a, b) - m_cos(314, a, b);
}

real f(real x) {
    return cos(314*x) - cos(650*x);
}

ofstream out("results.txt");

real eps = 10;

void update_eps(real x) {
    x = abs(x);

    if (eps > x) {
        eps = x;
    }
}

int sgn(real x) {
    return (x > 0) - (x < 0);
}

real binary_search(real a, real b) {
    if (a > b) {
        throw("The empty segment error");
    }

    while (true) {
        if (a == b) {
            return a;
        }

        real c = (a + b)/2;

        if (c < a || c > b) {
            if (abs(f(a)) < abs(f(b))) {
                return a;
            } else {
                return b;
            }
        }

        real f_a = f(a);
        real f_b = f(b);

        if (f_a == 0 && f_b == 0) {
            return c;
        }

        if (f_a == 0) {
            return a;
        }

        if (f_b == 0) {
            return b;
        }

        if (c == a || c == b) {
            return c;
        }

        real f_c = f(c);

        if (f_c == 0 || sgn(f_a) == sgn(f_b)) {
            return c;
        }

        if (sgn(f_a) == sgn(f_c)) {
            a = c;
         } else {
            b = c;
         }
    }
}

void search(real a, real b) {
    if (a > b) {
        return;
    }

    if (m_f(a, b) > 0 || M_f(a, b) < 0) {
        return;
    }

    update_eps(m_f(a, b));
    update_eps(M_f(a, b));

    if (m_fp(a, b) >= 0 || M_fp(a, b) <= 0) {

        out << "There is the unique solution " << binary_search(a, b) << " in the interval " << (f(a) == 0 ? '[' : '(') << a << "," << b << (f(b) == 0 ? ']' : ')') << "\n";

        return;
    }

    update_eps(m_fp(a, b));
    update_eps(M_fp(a, b));

    real c = (a + b)*0.5;

    if (c <= a || c >= b) {
        cout << "The solutions in the segment [" << a << "," << b << "] are possible\n";
        out << "The solutions in the segment [" << a << "," << b << "] are possible\n";

        return;
    }

    search(a, c);
    search(c, b);
}

int main() {
    search(0, M_PI);
    cout << "Epsilon = " << eps << endl;

    return 0;
}