include iostream include stdio include vector include cmath using name

#include <iostream>
#include <stdio.h>
#include <vector>
#include <cmath>
using namespace std;

//Findine matrix's minors
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;
}

int main()
{


	int N = 0;
	cout << "Enter size matrix: ";
	cin >> N;
	vector <vector<double> > A(N, vector <double>(N));
	vector <double> B(N);

	cout << "Enter coefficients a[i][j]: " << endl;
	for (int i = 0; i < N; ++i)
	{
		for (int j = 0; j < N; ++j)
		{
			cout << "a[" << i + 1 << "][" << j + 1 << "] = ";
			cin >> A[i][j];
		}
		cout << "\n";
	}
	cout << "\n";

	cout << "Enter free coefficients b[i]: " << endl;
	for (int i = 0; i < N; ++i)
	{
		cout << "b[" << i + 1 << "] = ";
		cin >> B[i];
	}
	cout << "\n";

	//CAAAAASE
	int key;
	cout << "Enter key: ";
	cin >> key;

	switch (key)
	{
	case 1:
	{
		cout << "Linear system equation:" << endl;
		for (int i = 0; i < N; ++i)
		{
			for (int j = 0; j < N; ++j)
				cout << A[i][j] << " * X" << j + 1 << "\t";
			cout << " = " << B[i] << "\n";
		}
		cout << endl;
		double det = FindDeterminant(A, N);
		if (det == 0)
		{
			cout << ">>>No roots!<<<" << endl;
		}
		else
		{
			cout << "det_A: " << det << endl;
			cout << "\n";

			for (int i = 0; i < N; ++i)
			{
				cout << "det_" << i << " = " << InsertFreeCoeff(A, B, N, i) << "\n";
			}
			cout << endl;
			cout << "Roots: " << endl;
			for (int i = 0; i < N; ++i)
			{
				cout << "X" << i + 1 << " = " << InsertFreeCoeff(A, B, N, i) / det << "\n";
			}
		}
		break;
	}
	case 2:
	{
		int omega;
		cout << "Enter omega: ";
		cin >> omega;
		cout << endl;
		for (int i = 0; i < N; ++i)
		{
			A[i].push_back(B[i]);
		}


		double eps;
		cout << "Enter epsilon: ";
		cin >> eps;

		//previous values
		vector <double> x_prev(N, 0.0);

		while (true)
		{
			//current values
			vector <double> x_curr(N);
			for (int i = 0; i < N; ++i)
			{
				x_curr[i] = A[i][N]; // N+1?

				for (int j = 0; j < N; ++j)
				{
					if (j < i)
					{
						x_curr[i] = omega*(-A[i][j] * x_curr[j] + x_curr[i]);
					}
					if (j > i)
					{
						x_curr[i] = omega*(-A[i][j] * x_prev[j] + x_prev[i]);
					}
				}
				x_curr[i] /= A[i][i];
			}
			double err = 0.0;
			for (int i = 0; i < N; ++i)
			{
				err += abs(x_curr[i] - x_prev[i]);
			}

			if (err < eps)
			{
				break;
			}
			x_prev = x_curr;
		}
		for (int i = 0; i < N; ++i)
		{
			cout << x_prev[i];
		}
	}
	}

	cout << "\n";




	system("pause");
}