#define _CRT_SECURE_NO_WARNINGS
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#include <string.h>
// f(x, y) = 16x ^ 2 + 3y ^ 2, c = 13

const int SIZE = 100;


double func(double a, double b, double x, double y) {
    return a * pow(x, 2) + b * pow(y, 2);
}

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

double calculateX(double x, double L, const double& gradientX) {
    return x -  gradientX/L;
};

double calculateY(double y, double L, const double& gradientY) {
    return y - gradientY/L;
};

double gradientX(double a, double x) {
    return 2 * a * x;
}
double gradientY(double b, double y) {
    return 2 * b * y;
}

double max(double a, double b) {
    if (2 * a > 2 * b) {
        return 2 * a;
    }
    else return 2 * b;
}

int maxN(const double& func, double accuracy, double L) {
    double N = ((2 * L) / (pow(accuracy, 2))) * func;
    floor(N);
    return N;
}

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

void firstTest()  {
    puts("test 1:");
    double a = 16;
    double b = 3;
    double c = 13;
    double accuracy = 0.01;
    double arrCoords[SIZE][2] = { 0 };
    long double count = 0;
    double L = max(a, b);
    int maxIter = 0;
    for (int i = 0; i < SIZE; i++) {
        arrCoords[i][0] = randOnRange(-sqrt(c / a), sqrt(c / a));
        arrCoords[i][1] = sqrt((c - a * pow(arrCoords[i][0], 2)) / b);
        //printf("[%.3lf;%.3lf]\t", arrCoords[i][0], arrCoords[i][1]);
    }
    for (int i = 0; i<SIZE;i++){
        maxIter += maxN(func(a, b, arrCoords[i][0], arrCoords[i][1]), accuracy, L);
        int k = 0;
        for (; distGradient(gradientX(a,arrCoords[i][0]),gradientY(b, arrCoords[i][1]))>=accuracy; k++) {
            double x = arrCoords[i][0];
            double y = arrCoords[i][1];
            arrCoords[i][0] = calculateX(x, L, gradientX(a, x));
            arrCoords[i][1] = calculateY(y, L, gradientY(b, y));

        }
        count += k;
        //printf("%d ", k);
        //printf("%d", maxIter);
        //printf("\n");
    }

    printf("average max iteration  = %d\naverage real iteration = %.2lf\n", maxIter / SIZE, ceil(count / SIZE));
}

void secondTest() {
    puts("test 2:");
    double a = 16;
    double b = 3;
    double c = 13;
    double accuracy = 0.01;
    double arrCoords[SIZE][2] = { 0 };
    long double count = 0;
    double L = max(a, b);
    int maxIter = 0;
    for (int i = 0; i < SIZE; i++) {
        arrCoords[i][0] = randOnRange(-0.5, 0.5);
        arrCoords[i][1] = sqrt((c - a * pow(arrCoords[i][0], 2)) / b);
        //printf("[%.3lf;%.3lf]\t", arrCoords[i][0], arrCoords[i][1]);
    }
    for (int i = 0; i < SIZE; i++) {
        maxIter += maxN(func(a, b, arrCoords[i][0], arrCoords[i][1]), accuracy, L);
        int k = 0;
        for (; distGradient(gradientX(a, arrCoords[i][0]), gradientY(b, arrCoords[i][1])) >= accuracy; k++) {
            double x = arrCoords[i][0];
            double y = arrCoords[i][1];
            arrCoords[i][0] = calculateX(x, L, gradientX(a, x));
            arrCoords[i][1] = calculateY(y, L, gradientY(b, y));

        }
        count += k;
        /*printf("%d ", k);
        printf("%d", maxIter);
        printf("\n");*/
    }

    printf("average max iteration  = %d\naverage real iteration = %.2lf\n", maxIter / SIZE, ceil(count / SIZE));
}

void thirdTest() {
    puts("test 3:");
    double a = 16;
    double b = 3;
    double c = 13;
    double accuracy = 0.01;
    double arrCoords[SIZE][2] = { 0 };
    double count = 0;
    double L = max(a, b);
    int maxIter = 0;
    for (int i = 0; i < SIZE; i++) {
        arrCoords[i][0] = randOnRange(-sqrt(c / a), -sqrt(c / a) + 0.1);
        arrCoords[i][1] = sqrt((c - a * pow(arrCoords[i][0], 2)) / b);
        //printf("[%.3lf;%.3lf]\t", arrCoords[i][0], arrCoords[i][1]);
    }
    for (int i = 0; i < SIZE; i++) {
        maxIter += maxN(func(a, b, arrCoords[i][0], arrCoords[i][1]), accuracy, L);
        int k = 0;
        for (; distGradient(gradientX(a, arrCoords[i][0]), gradientY(b, arrCoords[i][1])) >= accuracy; k++) {
            double x = arrCoords[i][0];
            double y = arrCoords[i][1];
            arrCoords[i][0] = calculateX(x, L, gradientX(a, x));
            arrCoords[i][1] = calculateY(y, L, gradientY(b, y));

        }
        count += k;
        /*printf("%d ", k);
        printf("%d", maxIter);
        printf("\n");*/
    }
    printf("average max iteration  = %d\naverage real iteration = %.2lf\n", maxIter / SIZE, ceil(count / SIZE));
}

int main() {
    srand(time(0));
    firstTest();
    secondTest();
    thirdTest();
    return 0;
}