#define _CRT_SECURE_NO_WARNINGS
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#include <string.h>

double func(double x, double y) {
    return sin(x) - cos(2 * y);
}

double gradientX(double x) {
    return cos(x);
}
double gradientY(double y) {
    return 2 * sin(2 * y);
}

double calcVx(double x) {
    return cos(x) / sin(x);
}

double calcVy(double y) {
    return -0.5 * tan(2 * y);
}

double randOnRange(double min, double max) {
    double f = (double)rand() / RAND_MAX;
    return min + f * (max - min);
};

double distGradient(const double &gradientX, const double &gradientY) {
    return sqrt(pow(gradientX, 2) + pow(gradientY, 2));
}

int main() {
    puts("Really minimum f(x,y) = sin(x)-cos(2y) is -2");
    srand(time(0));
    double arrX[100] = { 0 };
    double arrY[100] = { 0 };
    double eps = 0.01;
    double t = 0;
    double count = 0;
    for (int i = 0; i < 100; i++) {
        arrX[i] = randOnRange(-10, 10);
        arrY[i] = randOnRange(-10, 10);
    }

    for (int i = 0; i < 100; i++) {
        double x = arrX[i];
        double y = arrY[i];
        for (; sqrt(pow(gradientX(x), 2) + pow(gradientY(y), 2) > eps); ) {
            if (gradientX(x) * calcVx(x) + gradientY(y) * calcVy(y) > 0) {
                t = -1;
            }
            else {
                t = 1;
            }
            while (func(x + t * calcVx(x), y + t * calcVy(y)) >= func(x, y) + 3 / 4 * t * (gradientX(x) * calcVx(x) + gradientY(y) * calcVy(y))) {
                t /= 2;
            }
            x = x + t * calcVx(x);
            y = y + t * calcVy(y);
        }
        arrX[i] = x;
        arrY[i] = y;
    }
    for (int i = 0; i < 100; i++) {
        count += func(arrX[i], arrY[i]);
    }
    printf("Average accuracy: %.6lf\n", count / 100);

    return 0;
}