# C++ determinant calculator - follow-up

After following some suggestions you can find here, I'd like to show you the result:

#include <iostream>
#include <string>
#include <vector>

double getDeterminant(std::vector<std::vector<double>> vect, int dimension);

int main() {

//First, the user has to enter the dimension of the matrix
int dimension;
std::cout << "Please enter dimension of Matrix: ";
std::cin >> dimension;
std::cout << std::endl;

if(dimension < 0) {
std::cout << "ERROR: Dimension cannot be < 0." << std::endl;
return -1;
}

//Now, the user has to enter the matrix line by line, seperated by commas
std::vector<std::vector<double>> vect(dimension, std::vector<double> (dimension));
std::string str;
for(int i = 1; i <= dimension; i++) {
std::cout << "Enter line " << i << " only seperated by commas: ";
std::cin >> str;
std::cout << std::endl;
str = str + ',';
std::string number;
int count = 0;
for(int k = 0; k < str.length(); k++) {
if(str[k] != ',') {
number = number + str[k];
}
else if(count < dimension) {
if(number.find_first_not_of("0123456789.-") != std::string::npos) {
std::cout << "ERROR: Not only numbers entered." << std::endl;
return -1;
}
vect[i - 1][count] = std::stod(number);
number = "";
count++;
}
else {
std::cout << "ERROR: Too many numbers entered." << std::endl;
return -1;
}
}
}

//Output
for(int i = 0; i < dimension; i++) {
for(int j = 0; j < dimension; j++) {
std::cout << vect[i][j] << " ";
}
std::cout << std::endl;
}

std::cout << "Determinant of the matrix is : " << getDeterminant(vect, dimension) << std::endl;
return 0;
}

double getDeterminant(std::vector<std::vector<double>> vect, int dimension) {

if(dimension == 0) {
return 0;
}

if(dimension == 1) {
return vect;
}

//Formula for 2x2-matrix
if(dimension == 2) {
return vect * vect - vect * vect;
}

double result = 0;
int sign = 1;
for(int i = 0; i < dimension; i++) {

//Submatrix
std::vector<std::vector<double>> subVect(dimension - 1, std::vector<double> (dimension - 1));
for(int m = 1; m < dimension; m++) {
int z = 0;
for(int n = 0; n < dimension; n++) {
if(n != i) {
subVect[m-1][z] = vect[m][n];
z++;
}
}
}

//recursive call
result = result + sign * vect[i] * getDeterminant(subVect, dimension - 1);
sign = -sign;
}

return result;
}


Do you have any more suggestions to improve the code?

You can find the follow-up question here.

double getDeterminant(std::vector<std::vector<double>> vect, int dimension);


This will create a copy of the std::vector. For small std::vector this is not a problem, but it's good to make it a habit to pass complex data structures as const&, so the copy will not be created:

double getDeterminant(const std::vector<std::vector<double>>& vect, int dimension);


To make your code more readable, you can use an alias for the long vector name:

using Matrix = std::vector<std::vector<double>>;
double getDeterminant(const Matrix& vect, int dimension);


Lastly it is not necessary to pass the dimension, as it is accessible from the vector class:

double getDeterminant(const Matrix& vect);


std::endl will flush the output buffer. Only use it, if you want the buffer to be flushed. Writing to the screen takes a fair amount of time (compared to other instructions). Instead just use \n, it is cross-platform compatible

std::cin >> dimension;
std::cout << '\n';


This terminates the program. A better way of handling the erroneous input would be to allow the user to repeat the line

if(number.find_first_not_of("0123456789.-") != std::string::npos) {
std::cout << "ERROR: Not only numbers entered." << std::endl;
return -1;
}


Furthermore, this still allows for invalid numbers, I could input something like .-.-.-. for example.

This

number = number + str[k];


Can be replaced by the shorter version

number += str[k];

if(dimension == 0) {
return 0;
}


Mathematically, that is not correct. The determinant of an empty (i.e. zero-dimensional) matrix is one, see for example What is the determinant of []? on Mathematics Stack Exchange.

With respect to efficiency: Your program computes the determinant recursively using the Laplace formula, which requires $$\ O(n!) \$$ arithmetic operations, and the creation of many temporary “submatrices”.

A better method (at least for larger matrices) is Gaussian elimination which requires $$\ O(n^3) \$$ arithmetic operations, and can operate on a single copy of the original matrix.

A vector of vectors can be an inefficient representation, because the storage may be scattered across many pages of memory. We can keep the data close together by using a single vector, and linearising the rows within it, perhaps like this:

#include <cstddef>
#include <vector>

class Matrix
{
std::size_t width;
std::size_t height;
std::vector<double> content;

public:
Matrix(std::size_t width, std::size_t height)
: width{width},
height{height},
content(width * height)
{}

double& operator()(std::size_t row, std::size_t col) {
return content[row * width + col];
}

double const& operator()(std::size_t row, std::size_t col) const {
return content[row * width + col];
}
};


Repeating from the original review:

• always check the result of stream input operations
• avoid comparing signed and unsigned types; or better, avoid the comparison by using range-based for.
• You should add a mechanism to initialize the Matrix. Right now the official way is to assign the elements one by one. Feb 11 '20 at 9:30
• Left as an excercise; it's not hard to add a std::initializer_list<double> to the arguments. That's a distraction from the main point, which is to linearise the array of elements. Feb 11 '20 at 11:08

Though there is already an accepted answer, I would add that usually, you would want to only return values between 0 and 127 in main -- just replace return -1; with return 1;, following the convention that non-zero exit codes represent errors or exceptions. (https://stackoverflow.com/a/8083027/9870592)