//Определение номера области, в которую попадает точка с произвольно заданными координатами на плоскости, и площади этой области

#include<iostream>
#include<cmath>
#include <locale>

using namespace std;

float sqr(float x) {
	return pow(x, 2);
}

float M1_top(float x){
	 return sqrt(1 - sqr(x + 1)) + 1;
}

float M1_bottom(float x){
	if (x < -1 - sqrt(3)/2)
		return -sqrt(1 - sqr(x + 1)) + 1;
	else if (x < -0.5)
		return sqrt(1 - sqr(x + 1));
	else
		return sqrt(1 - x*x);
}

float M2_top(float x){
	 return  sqrt(1 - sqr(x - 1)) + 1;
}

float M2_bottom(float x){
	 if (x < 1 + sqrt(3)/2)
		return sqrt(1 - sqr(x - 1));
	else
		return -sqrt(1 - sqr(x - 1)) + 1;
}

float M3_top(float x){
	if (x < 0.5)
		return sqrt(1 - sqr(x - 1));
	else
		return sqrt(1 - x*x);
}

float M3_bottom(float x){
	if (x < 0.5)
		return -sqrt(1 - x*x) + 1;
	else
		return -sqrt(1 - x*x) + 1;
}

float M4_top(float x){
	return -sqrt(1 - x*x);
}

float M4_bottom(float x){
	return -sqrt(1 - sqr(x + 1));
}

float M5_top(float x){
	return sqrt(1 - sqr(x - 1)) - 1;
}

float M5_bottom(float x){
	if (x < 1)
		return sqrt(1 - x*x) - 1;
	else
		return -sqrt(1 - sqr(x - 1));

}

int detect_region(float x, float y){
	if ((sqr(x + 1) + sqr(y - 1) <= 1) && (x*x + y*y >= 1) && (sqr(x + 1) + y*y >= 1))
		return 1;
	else if ((sqr(x - 1) + sqr(y - 1) <= 1) && (sqr(x - 1) + y*y >= 1) && (x >= 1))
		return 2;
	else if ((x*x + y*y <= 1) && (sqr(x - 1) + sqr(y - 1) <= 1) && (x*x + sqr(y - 1) <= 1) && (sqr(x - 1) + y*y <= 1))
        return 3;
    else if ((sqr(x + 1) + y*y <= 1) && (x*x + y*y >= 1) && (x >= -1) && ( y <= 0))
    	return 4;
    else if ((sqr(x - 1) + sqr(y + 1) <= 1) && ( sqr(x - 1) + y*y <= 1) && (x*x + sqr(y + 1) >= 1))
    	return 5;
    else
    	return -1;
}

float caclulate_integral(float (*func)(float), float x_start, float x_stop, float dx){
	float area = 0;
	for(float x = x_start; x <= x_stop; x += dx) {
		area += dx * func(x);
	}
	return area;
}

float get_region_area(int region_number) {
	float x_start, x_stop;
	float inregral_top, inregral_bottom;
	float dx = 0.001;
	switch (region_number){
 		case 1:
 			x_start = -2;
			x_stop = 0;

 			inregral_top = caclulate_integral(M1_top, x_start, x_stop, dx);
 		 	inregral_bottom = caclulate_integral(M1_bottom, x_start, x_stop, dx);
 			return inregral_top - inregral_bottom;
 		case 2:
 			x_start = 1;
			x_stop = 2;

			inregral_top = caclulate_integral(M2_top, x_start, x_stop, dx);
 			inregral_bottom = caclulate_integral(M2_bottom, x_start, x_stop, dx);
 			return inregral_top - inregral_bottom;
 		case 3:
 			x_start = 1 - sqrt(3)/2;
			x_stop = sqrt(3)/2;

			inregral_top = caclulate_integral(M3_top, x_start, x_stop, dx);
 			inregral_bottom = caclulate_integral(M3_bottom, x_start, x_stop, dx);
 			return inregral_top - inregral_bottom;
 		case 4:
 			x_start = -1;
			x_stop = -0.5;

			inregral_top = caclulate_integral(M4_top, x_start, x_stop, dx);
 			inregral_bottom = caclulate_integral(M4_bottom, x_start, x_stop, dx);
 			return inregral_top - inregral_bottom;
 		case 5:
 			x_start = 0.5;
			x_stop = 1 + sqrt(3)/2;

			inregral_top = caclulate_integral(M5_top, x_start, x_stop, dx);
 			inregral_bottom = caclulate_integral(M5_bottom, x_start, x_stop, dx);
 			return inregral_top - inregral_bottom;
 	}
}


int main() {
	float x, y;

	setlocale(LC_ALL,"Russian") ;

	cout << "\nВведите координаты точки: x, y " ;
	cin >> x >> y;

	int region_number = detect_region(x, y);

	if (region_number != -1) {
		float area = get_region_area(region_number);
		cout << "\nТочка в области М" << region_number << ". S = " << area;
	}
	else
		cout << "\nТочка вне выделенных областей";

	cout << "\nПовторить-1, Выход-2: ";

	int choice;
	cin >> choice;
	if (choice == 1) main();
	else return 0;
}