#include <iostream>
#include <cstdlib>
#include <cmath>
using namespace std;

const int n = 4;
class opt
{
private:
	long double a[n + 1][n + 1];
	long double x[n + 1];
	long double b[n + 1];
	long double v[n + 1];
public:
	opt()
	{
		int i, j;
		for (i = 1; i <= n; i++)
		{
			for (j = 1; j <= n; j++)
			{
				a[i][j] = rand() % 5 + 1;
				/*cout << "a[" << i << "][" << j << "] = ";
				 cin >> a[i][j];*/
			}
			b[i] = rand() % 5 + 1;
		}
	}

	void printMatrix()
	{
		int i, j;
		cout << "Matrix A: \n";
		for (i = 1; i <= n; i++)
		{
			for (j = 1; j <= n; j++)
			{
				cout.precision(2);
				cout.width(5);
				cout << a[i][j] << "  ";
			}
			cout << endl;
		}
	}

	void printVectorB()
	{
		int i;
		cout << "Vector B: \n";
		for (i = 1; i <= n; i++)
		{
			cout.precision(2);
			cout.width(5);
			cout << b[i] << " ";
		}
		cout << endl;
	}
	void printVectorX()
	{
		int i;
		cout << "Vector X: \n";
		for (i = 1; i <= n; i++)
		{
			cout.precision(2);
			cout.width(5);
			cout << x[i] << " ";
		}
		cout << endl;
	}

	void calcX()
	{
		int i;
		for (i = 1; i <= n; i++)
		{
			x[i] = b[i] / a[i][i];
		}
	}

	void getFineMatrix()
	{
		int  j, k, aMax, h, t, temp;
		for (k = 2; k <= n; k++)
		{
			aMax = a[k][k];
			h = k;
			for (t = k + 1; t <= n; t++)
			{
				if (abs(a[t][k]) > aMax)
				{
					aMax = abs(a[t][k]);
					h = t;
				}
				if (h != k)
				{
					for (j = k; j <= n; j++)
					{
						temp = a[k][j];
						a[k][j] = a[h][j];
						a[h][j] = temp;
					}
					temp = b[k];
					b[k] = b[h];
					b[h] = temp;
				}
			}
		}
	}
	void calcOpt()
	{
		int i, j, k, g, q, aMax, h, t, temp;
		long double r;
		for (k = 2; k <= n; k++)
		{
			aMax = a[k][k];
			h = k;
			for (t = k + 1; t <= n; t++)
			{
				if (abs(a[t][k]) > aMax)
				{
					aMax = abs(a[t][k]);
					h = t;
				}
				if (h != k)
				{
					for (j = k; j <= n; j++)
					{
						temp = a[k][j];
						a[k][j] = a[h][j];
						a[h][j] = temp;
					}
					temp = b[k];
					b[k] = b[h];
					b[h] = temp;
				}
			}
			for (i = 1; i <= k - 1; i++)
			{
				r = a[k][i] / a[i][i];
				for (j = i; j <= n; j++)
				{
					a[k][j] = a[k][j] - r * a[i][j];
				}
				b[i] = b[i] - r * b[k];
			}
			for (g = 1; g <= k - 1; g++)
			{
				r = a[g][k] / a[k][k];
				for (q = k; q <= n; q++)
				{
					a[g][q] = a[g][q] - r * a[k][q];
				}
				b[q] = b[q] - r * b[g];
			}
		}
	}
	void vectorDeviations()
	{
		int i;
		cout << "Vector deviations " << endl;
		for (i = 1; i <= n; i++)
		{
			v[i] = a[i][i] * x[i] - b[i];
			cout.precision(2);
			cout.width(5);
			cout << v[i] << " ";
		}
	}
};
int main()
{
	opt lab;
	lab.printMatrix();
	lab.printVectorB();
	cout << "--------Fine----------------\n";
	lab.getFineMatrix();
	lab.printMatrix();
	lab.printVectorB();
	cout << "------------------------------\n";
	lab.calcOpt();
	lab.printMatrix();
	lab.printVectorB();
	lab.calcX();
	lab.printVectorX();
	lab.vectorDeviations();
	cin.get();
	return 0;
}