#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include <math.h>

using namespace std;

void mat(double** matice, int N, int M, int res);
void vypis(double** matice,int N, int n, int m);
void PocReseni(double** matice, double* r, int N, int M, int res);
double det(double** matice, int N, int M);

int main(int argc, char** argv){
    int M, N, res, n, m;
    char vstup,vstup2;
    cout << "Vitejte v programu na vypocet Gausovy eliminace a determinantu." << endl;\
    cout << endl << "Nyni vyberte jednu z moznosti:" << endl;
    cout << endl << "a: Zadani matice z klavesnice" << "  b: Zadani matice ze souboru" << endl;
    cin >> vstup;
    if(cin.fail()){
        cout << "Nespravny vstup." << endl;
        return 0;
    }
    switch(vstup){
    case 'a':{
    cout << "Zadejte rozmer matice (pocet radku, poctet sloupcu vcetne prave strany matice):" << endl;
    cin >> N >> M;
    if(cin.fail() || N <= 0 || M <= 0){
        cout << "Nespravny vstup." << endl;
        return 0;
    }
    double **matice = new double*[M];
    for(int i = 0;i < M;i++) {
            matice[i] = new double[N];
        }
   cout << "Zadejte hodnoty matice (po radcich):" << endl;
   for (int i = 0; i < N; i++){
        for (int j = 0; j < M; j++){
            cin >> matice[i][j];
            if(cin.fail()){
                cout << "Nespravny vstup." << endl;
                return 0;
                }
                //if(M == N)
                //matice[i][M+1] = 0;
            }
        }
        if(M == N){ //pokud je matice ctvercova
            M++;
            res = M-2;
            n = N-1;
            m = M-1;
            }
        else{
            res = M;
            n = N;
            m = M;
            }
        cout << endl << "Matice byla uspesne nactena." << endl;
    cout << endl << "Zadana matice:" << endl;
    vypis(matice, N, n, m);
    cout << endl << "Vyberte jakou operaci chcete dal provest:" << endl;
    cout << endl << "a: Gaussovu eliminaci" << "  b: Vypocet determinantu" << endl;
    cin >> vstup2;
    if(cin.fail()){
        cout << "Nespravny vstup." << endl;
        cin.clear();
        delete[] matice;
        return 0;
    }
    switch(vstup2){
    case 'a':
    mat(matice, N, M, res);
    cout << endl;
    cout << "Matice v trojuhelnikovem tvaru:" << endl;
    vypis(matice, N, n, m);
    cin.clear();
    /*for(int i = 0; i < N; i++) {
            delete [] matice[i];
            } */
        break;
    case 'b':
        cout << endl << "Determinant = ";
        det(matice, N, M);
        break;
    default:
        cout << "Nespravny vstup." << endl;
        break;
    }
    delete[] matice;
    break;
    }
    case 'b':
        cout << "Hello world" << endl;
        break;
    default:
        cout << "Nespravny vstup." << endl;
        break;
    }
    return 0;
}
void mat(double** matice, int N, int M, int res){
    int max = 0,pr = 0;
    double pom;
    for(int i = 0; i < N; i++){
            max = i;
    for(int j = i + 1; j < N; j++)
        if(fabs(matice[j][i])>fabs(matice[i][i]))
        max = j;
    for(int k = i; k < M; k++){
        pom = matice[i][k];
        matice[i][k] = matice[max][k];
        matice[max][k]=pom;
    }
    for(int j = i + 1; j < N; j++)
    for(int k = N; k >= i; k--)
        if(matice[i][i] != 0)
        matice[j][k]= matice[j][k] - matice[i][k] * matice[j][i] / matice[i][i];
  }
     double *r = new double[N]; // reseni soustavy
     for(int i = 0; i < N; i++)
        r[i] = matice[i][res];
     if(pr == 0){
        for(int j = N - 1; j >= 0; j--){
                pom = 0;
        for(int k = j + 1; k <= N; k++)
            pom = pom + matice[j][k]*r[k];
        r[j] = (matice[j][N] - pom) / matice[j][j];
        }
   }
   PocReseni(matice, r, N, M, res);
}
void vypis(double** matice, int N, int n, int m)
{
    for(int i = 0; i < N; i++){
            for(int j = 0; j < m; j++)
            {
                cout.setf(ios::fixed);cout.precision(2);
                cout << matice[i][j] << "\t";
        if(j == n - 1)
            cout << "| ";
        if(j == n)
            cout << endl;
            }
        }
}
void PocReseni(double** matice, double* r, int N, int M, int res){
    double *mpr = new double[N];
   for(int i = 0; i < N; i++)
       mpr[i] = matice[i][res]; //prave strany
       int p = 0, pr = 0;
   for(int j = 0; j < res; j++){
        while(p < N){
           if(matice[p][j] == 0){
               if(mpr[p] == 0) //nekonecne reseni
               pr = 1;
               else if(mpr[p] != 0) //zadne reseni
               pr = 2;
               break;
                }
           else{
             pr = 0; //jedno reseni
             p++;
           }
        }
    }
    if(pr == 1)
      cout << endl << "Soustava ma nekonecne mnoho reseni." << endl;
      else if(pr == 2)
      cout << endl << "Soustava nema reseni." << endl;
      else if(pr == 0){
      cout << endl << "Soustava ma jedno reseni:" << endl;
      int k = 1;
      for (int i = 0; i < N; i++){
            cout.setf(ios::fixed);cout.precision(2);
            cout << "k" << k << " = " << r[i] << "\t";
            k++;
      }
      cout << endl;
    }
}
double det(double** matice, int N, int M){
    int subi, subj;
    double d = 0;
    double **mat = new double*[M];
    for(int i = 0;i < M;i++) {
            mat[i] = new double[N-1];
        }
    /*if (N-1 == 2){
        return( (matice[0][0] * matice[1][1]) - (matice[1][0] * matice[0][1]));
    } */
    //else{
        for(int c = 0; c < N-1; c++){
            subi = 0;
    for(int i = 1; i < N-1; i++){
        subj = 0;
    for(int j = 0; j < N-1; j++){
        if (j == c){
            continue;
                }
        mat[subi][subj] = matice[i][j];
        subj++;
            }
        subi++;
            }
        d += (pow(-1 ,c) * matice[0][c] * det(mat, N, M));
        }
    //}
    return d;
}