Question

1. Write a recursive program in C++ to compute the determinant of an NxN matrix, A. Your program should ask the user to enter the value of N, followed by the path of a file where the entries of the matrix could be found. It should then read the file, compute the determinant and return its value. Compile and run your program.

Answer 1

#include <fstream>
#include <string>
#include <vector>
#include <iostream>
#include <sstream>

using namespace std;

int ReadNumbers( const string & s, vector <double> & v );
void import_matrix_from_txt_file(const char* filename_X, vector <double>& v, int& rows, int& cols);

int main(){
vector <double> v;
int rows=0;
int cols=0;

import_matrix_from_txt_file("x.txt",v,rows,cols);
}

int ReadNumbers( const string & s, vector <double> & v ) {
istringstream is( s );
double n;
while( is >> n ) {
v.push_back( n );
}
return v.size();
}

void import_matrix_from_txt_file(const char* filename_X, vector <double>& v, int& rows, int& cols){
  
ifstream file_X;
string line;
  
file_X.open(filename_X);
if (file_X.is_open())
{
int i=0;
getline(file_X, line);
  
  
cols =ReadNumbers( line, v );
cout << "cols:" << cols << endl;
  
  
for ( i=1;i<32767;i++){
if ( getline(file_X, line) == 0 ) break;
ReadNumbers( line, v );
  
}
  
rows=i;
cout << "rows :" << rows << endl;
if(rows >32766) cout<< "N must be smaller than MAX_INT";
  
file_X.close();
}
else{
cout << "file open failed";
}
  
cout << "v:" << endl;
for (int i=0;i<rows;i++){
for (int j=0;j<cols;j++){
cout << v[i*cols+j] << "\t" ;
}
cout << endl;
}
}

// Finding Determinant

int determinantOfMatrix(int mat[N][N], int n)

{

    int D = 0; // Initialize result

  

    // Base case : if matrix contains single element

    if (n == 1)

        return mat[0][0];

  

    int temp[N][N]; // To store cofactors

  

    int sign = 1; // To store sign multiplier

  

     // Iterate for each element of first row

    for (int f = 0; f < n; f++)

    {

        // Getting Cofactor of mat[0][f]

        getCofactor(mat, temp, 0, f, n);

        D += sign * mat[0][f] * determinantOfMatrix(temp, n - 1);

  

        // terms are to be added with alternate sign

        sign = -sign;

    }

  

    return D;

}