#include <iostream>
#include <cmath>
#include <iomanip>
#include <vector>

using namespace std;

void GetMinor(vector <vector<double>> A, vector <vector<double>> &B, int x, int y, int size)
{
	int _x = 0;
	int _y;

	for (int i = 0; i < size; ++i)
	{
		if (i != x)
		{
			_y = 0;
			for (int j = 0; j < size; ++j)
			{
				if (j != y)
				{
					B[_x][_y] = A[i][j];
					_y++;
				}
			}
			_x++;
		}
	}
}

//Finding determinant of matrix (size x size)
double FindDeterminant(vector <vector<double>> A, int size)
{
	if (size == 1)
	{
		return A[0][0];
	}
	else
	{
		double det = 0;
		vector <vector<double>> Minor(size - 1, vector <double>(size - 1));
		for (int i = 0; i < size; ++i)
		{
			GetMinor(A, Minor, 0, i, size);
			det += pow(-1, i) * A[0][i] * FindDeterminant(Minor, size - 1);
		}
		return det;
	}
}

double InsertFreeCoeff(vector <vector<double>> A, vector<double> B, int size, int j)
{
	for (int i = 0; i < size; ++i)
	{
		A[i][j] = B[i];
	}
	double det = FindDeterminant(A, size);
	return det;
}

void display()
{
	setlocale(LC_ALL, "rus");
	double *a = NULL, *b = NULL, **sum = NULL;
	const int N = 5;

	double  x[N] = { -3, -1, 0, 1, 3 },
		y[N] = { -4, -0.8, 1.6, 2.3, 1.5};
	int K, i, j, k, m;
	double z, c;
	cout << "Порядок k= ";
	cin >> K;
	cin.get();
	b = new double[K + 1];
	a = new double[K + 1];
	sum = new double *[K + 1];
	for (int i = 0; i<K + 1; i++)
		sum[i] = new double[K + 1];


	for (i = 0; i<K + 1; i++)
	{
		for (j = 0; j<K + 1; j++)
		{
			sum[i][j] = 0;
			for (k = 0; k<N; k++)
			{
				sum[i][j] += pow(x[k], i + j);
			}
		}
	}
	for (i = 0; i<K + 1; i++)
	{
		b[i] = 0;
		for (k = 0; k<N; k++)
		{
			b[i] += pow(x[k], i) * y[k];
		}
	}
	for (int i = 0; i<K + 1; i++)
	{
		for (int j = 0; j<K + 1; j++)
			cout << sum[i][j] << "\t";
		cout << "|" << b[i] << "|\t";
		cout << endl;
	}

	for (int i = 0; i<K + 1; i++)
		
	cout << endl;

	vector <vector<double> > A(K + 1, vector <double>(K + 1));
	vector <double> B(K + 1);
	for (int i = 0; i < K + 1; i++)
	{
		for (int j = 0; j < K + 1; j++)
		{
			A[i][j] = sum[i][j];
		}
		B[i] = b[i];
	}

	//решаем методом Крамера
	double det = FindDeterminant(A, K + 1);
	if (det == 0)
	{
		cout << ">>>No roots!<<<" << endl;
	}
	else
	{
		cout << "det_A: " << det << endl;
		cout << "\n";

		for (int i = 0; i < K + 1; ++i)
		{
			cout << "det_" << i << " = " << InsertFreeCoeff(A, B, K + 1, i) << "\n";
		}
		cout << endl;
		cout << "Roots: " << endl;
		for (int i = 0; i < K + 1; ++i)
		{
			cout << "X" << i + 1 << " = " << InsertFreeCoeff(A, B, K + 1, i) / det << "\n";
		}
	}

	system("Pause");
}