FAI - PROGRAM2

#include <iostream>
#include <fstream>
#include <iomanip>
#include <string>
using namespace std;

ofstream fout("matriceOUT.txt");

string solutie;
int nrPasi;

struct frecventa
{
    int coordLinie = 0, coordColoana = 0;
    string necPP;
}frc1[10];


void citireMatrice(float mat[][10], int& nrL, int& nrC)
{
    ifstream fin("matriceIN.txt");
    fin >> nrL >> nrC;
    for (int i = 0; i < nrL; i++)
        for (int j = 0; j < nrC; j++)
            fin >> mat[i][j];
}
void afisareMatrice(float mat[][10], int nrL, int nrC)
{
    for (int i = 0; i < nrL; i++)
    {
        for (int j = 0; j < nrC; j++)
        {
            if (mat[i][j] == -0)    mat[i][j] = 0;
            fout << setw(10) << mat[i][j] << ' ';
        }
        fout << "\n";
    }
    fout << "\n";
}

void interschimbareLinii(float mat[][10], int nrC, int linie1, int linie2) //S_ij sau L_i <-> L_j
{
    for (int i = 0; i < nrC; i++)
        swap(mat[linie1][i], mat[linie2][i]);
}

void multiplicareLinie(float mat[][10], int nrC, int linie, float a) // M_i(a) sau L_i -> a*L_i
{
    for (int i = 0; i < nrC; i++)
        mat[linie][i] = mat[linie][i] * a;
}

void operatieLinii(float mat[][10], int nrC, int linie1, int linie2, float a) //T_i(a*L_j) sau L_i -> aL_j + L_i

{
    for (int j = 0; j < nrC; j++)
        if ((float)(mat[linie1][j] - a * mat[linie2][j]) < (float)0.001 && (float)(mat[linie1][j] - a * mat[linie2][j]) > (float)-0.001)
            mat[linie1][j] = 0;
        else
            mat[linie1][j] = mat[linie1][j] - a * mat[linie2][j];
}

int liberColoana(float mat[][10], int nrL, int linie, int coloana)
{
    for (int i = linie; i < nrL; i++)
        if (mat[i][coloana] != 0)
            return i;
    return -1;
}

bool liberLinie(float mat[][10], int nrC, int linie, int coloana)
{
    for (int i = coloana; i < nrC; i++)
        if (mat[linie][i] != 0)
            return false;
    return true;
}

//3. Solutia sistemului
void Determinat(float mat[][10], int nrL, int nrC)
{
    for (int i = 0; i < nrL; i++)
        if (liberLinie(mat, nrC - 1, i, 0) == false)
        {
            solutie += to_string(mat[i][nrC - 1]);
            if (i + 1 < nrL && liberLinie(mat, nrC - 1, i + 1, 0) == false)
                solutie += ",   ";
        }
    solutie += ")}. ";
}

void Nedeterminat(float mat[][10], int nrL, int nrC, int frv, string text)
{
    int suma = 0, colNedet1, colNedet2 = 0;
    if (text == "beta")
    {
        for (int i = 0; i < frv; i++)
        {
            for (int j = 0; j < nrC - 1; j++)
                if (j != frc1[i].coordColoana)
                    colNedet2 = j;
        }
    }

    for (int i = 0; i < frv; i++)
        suma += frc1[i].coordColoana;
    colNedet1 = (nrC - 2) * (nrC - 1) / 2 - (suma + colNedet2);

    if (text == "alfa")
    {
        cout << "Indicele coloanei care da necunoscuta secundara: " << colNedet1 + 1 << "\n\n";
        colNedet2 = -1;
    }
    else
        cout << "Indicii coloanelor care dau necunoscutele secundare: " << colNedet1 + 1 << ' ' << colNedet2 + 1 << "\n\n";

    for (int i = 0; i < frv; i++)
    {
        if (mat[frc1[i].coordLinie][nrC - 1] != 0)
        {
            frc1[i].necPP += to_string(mat[frc1[i].coordLinie][nrC - 1]);
            if (liberLinie(mat, nrC - 1, i, frc1[i].coordColoana + 1) == false && frc1[i].coordColoana + 1 < nrC - 1)
                frc1[i].necPP += " + ";
        }
        else
        {
            if (liberLinie(mat, nrC - 1, i, frc1[i].coordColoana + 1) == true)
                frc1[i].necPP += "0";
        }
        for (int j = 0; j < nrC - 1; j++)
            if (j != frc1[i].coordColoana)
            {
                if (mat[i][j] != 0)
                {
                    if (j != colNedet1 && j != colNedet2)
                        frc1[i].necPP += to_string(-mat[i][j]);
                    else
                    {
                        if (j == colNedet1)
                            frc1[i].necPP += "(" + to_string(-mat[i][j]) + ")*alfa";

                        if (j == colNedet2 && text == "beta")
                            frc1[i].necPP += "(" + to_string(-mat[i][j]) + ")*beta";
                    }

                    if (liberLinie(mat, nrC - 1, i, j + 1) == false && j + 1 < nrC - 1)
                        frc1[i].necPP += " + ";
                }
            }
    }

    int i = 0, parcurgCol = 0, okAlfa = 0;
    while (parcurgCol < nrC - 1 && i < frv)
    {
        if (parcurgCol == frc1[i].coordColoana)
        {
            solutie += frc1[i].necPP;
            i++;
        }
        else
        {
            if (okAlfa == 0)
            {
                solutie += "alfa";
                okAlfa = 1;
            }
            else
                solutie += "beta";
        }
        if (parcurgCol + 1 < nrC - 1)
            solutie += ",   ";
        parcurgCol++;
    }

    if (parcurgCol + 1 < nrC - 1)
        solutie += "alfa,   ";

    if (parcurgCol < nrC - 1)
    {
        if (text == "beta")
            solutie += text;
        else
            solutie += "alfa";
    }
}

//2. Tipul sistemului
void tipSistem(float mat[][10], int nrL, int nrC, int frv)
{

    for (int i = 0; i < nrL; i++)
        if (liberLinie(mat, nrC - 1, i, 0) == true && mat[i][nrC - 1] != 0)
        {
            fout << "incompatibil. \n";
            fout << "3) Nu avem solutie. ";
            return;
        }

    solutie += "3) S = {(";
    if (frv == nrC - 1)
    {
        fout << "compatibil determinat. \n";
        Determinat(mat, nrL, nrC);
    }
    else
        if (frv == (nrC - 1) - 1)
        {
            fout << "compatibil simplu nedeterminat. \n";
            Nedeterminat(mat, nrL, nrC, frv, "alfa");
            solutie += ") | alfa apartine numerelor reale}. ";
        }
        else
            if (frv == (nrC - 1) - 2)
            {
                fout << "compatibil dublu nedeterminat. \n";
                Nedeterminat(mat, nrL, nrC, frv, "beta");
                solutie += ") | alfa si beta apartin numerelor reale}. ";
            }
            else
            {
                fout << "compatibil - nedeterminat. ";
                solutie = "";
                return;
            }
    fout << solutie;
}

//1. Pasii intermediari
void parcurgereMatrice(float mat[][10], int nrL, int nrC, int& frv)
{
    int contorLinie = 0, contorColoana = 0;
    while (contorLinie < nrL && contorColoana < nrC - 1)
    {
        if (mat[contorLinie][contorColoana] == 0)
        {
            int indiceLinie = liberColoana(mat, nrL, contorLinie, contorColoana);
            if (indiceLinie != -1)
            {
                if (nrPasi == 0) fout << "\n\n";
                fout << "L_" << contorLinie + 1 << " <-> L_" << indiceLinie + 1 << ", matricea devine: \n\n";
                interschimbareLinii(mat, nrC, contorLinie, indiceLinie);
                afisareMatrice(mat, nrL, nrC);
                nrPasi++;
            }
            else
                contorColoana++;
        }
        else
            if (mat[contorLinie][contorColoana] != 1 && mat[contorLinie][contorColoana] != 0)
            {
                if (nrPasi == 0) fout << "\n\n";
                fout << "L_" << contorLinie + 1 << " -> " << "(1/" << mat[contorLinie][contorColoana] << ")*L_" << contorLinie + 1 << ", matricea devine: \n\n";
                multiplicareLinie(mat, nrC, contorLinie, 1 / mat[contorLinie][contorColoana]);
                afisareMatrice(mat, nrL, nrC);
                nrPasi++;
            }
            else
                if (mat[contorLinie][contorColoana] == 1)
                {
                    for (int i = 0; i < nrL; i++)
                    {
                        if (i != contorLinie && mat[i][contorColoana] != 0)
                        {
                            if (nrPasi == 0) fout << "\n\n";
                            fout << "L_" << i + 1 << " -> " << "(" << -mat[i][contorColoana] << ")*L_" << contorLinie + 1 << " + L_" << i + 1 << ", matricea devine: \n\n";
                            operatieLinii(mat, nrC, i, contorLinie, mat[i][contorColoana]);
                            afisareMatrice(mat, nrL, nrC);
                            nrPasi++;
                        }
                    }
                    frc1[frv].coordLinie = contorLinie++;
                    frc1[frv++].coordColoana = contorColoana++;
                }
    }
    if (contorLinie == nrL || contorColoana == nrC - 1)
    {
        if (nrPasi == 0)
            fout << "nu s-au efectuat schimbari in matricea initiala. \n";

        fout << "2) Tipul sistemului: sistemul este ";
        tipSistem(mat, nrL, nrC, frv);
    }
}


int main()
{
    float mat[10][10];
    int nrL, nrC, frv = 0;

    citireMatrice(mat, nrL, nrC);

    fout << "Matricea extinsa a sistemului: \n\n";
    afisareMatrice(mat, nrL, nrC);
    fout << "1) Pasi intermediari: ";
    parcurgereMatrice(mat, nrL, nrC, frv);

    cout << "Indicii coloanelor care dau necunoscutele principale: \n";
    for (int i = 0; i < frv; i++)
        cout << frc1[i].coordLinie + 1 << ' ' << frc1[i].coordColoana + 1 << endl;
    return 0;
}