#pragma once

#include <vector>
#include <array>

using namespace std;

template <typename T, size_t M>
class Polygon
{
public:
	double perimeter();
	void add_vertex(const array<T, M> &point);
	double min_square();
	double min_surround_area();

private:
	vector<array<T, M>> coordinates_;
};

template <typename T, size_t M>
void Polygon<T, M>::add_vertex(const array<T, M> &point)
{
	coordinates_.push_back(point);
}

template <typename T, size_t M>
double Polygon<T, M>::perimeter()
{
	double p = 0; //хранение результата
	double len; //длина текущего отрезка
	double sum; //текущая координата
				//a_len = sqrt((x ^ 2) + (y ^ 2))

	for (size_t i = 0; i < coordinates_.back() - 1; i++) //по точкам
	{
		sum = 0;

		for (size_t j = 0; j < M; j++) //по координатам
			sum += (abs(coordinates_[i][j] - coordinates_[i + 1][j]))
			* (abs(coordinates_[i][j] - coordinates_[i + 1][j]));


		len = sqrt(sum);
		p += len;
	}

	for (size_t j = 0; j < M; j++)
		sum += (abs(coordinates_[0][j] - coordinates_[coordinates_.back()][j]))
		* (abs(coordinates_[0][j] - coordinates_[coordinates_.back()][j]));

	len = sqrt(sum);
	p += len;

	return p;
}

template <typename T, size_t M>
double Polygon<T, M>::min_square()
{
	double s = 0;
	T min_x, min_y, max_x, max_y;

	min_x = coordinates_[0][0];
	max_x = coordinates_[0][0];
	min_y = coordinates_[0][1];
	max_y = coordinates_[0][1];

	for (size_t i = 0; i < coordinates_.back() - 1; i++) //по точкам
	{
			if (coordinates_[i][0] > max_x) max_x = coordinates_[i][0];
			if (coordinates_[i][0] < min_x) min_x = coordinates_[i][0];

			if (coordinates_[i][1] > max_y) max_y = coordinates_[i][1];
			if (coordinates_[i][1] > min_y) min_y = coordinates_[i][1];
	}

	s = (max_x - min_x) * (max_y - min_y);

	return s;
}

template<typename T, size_t M>
double Polygon<T, M>::min_surround_area()
{
	static_assert(M == 2, "Реализовано только для случая M = 2");
	double s = min_square();

	return s;
}