How to correctly use pointers in code

Question

For the following code, how can I find [A^-1] using pointers(equation for [A^-1]= 1/ det (A)? I am not sure whether pointers are used in the arithmetic or if they are used to call a value. Explaining what a pointer would be nice as I'm not exactly sure what they even do. I have most of the code written, except for this one part, so any help is much appreciated. Thanks in advance.

#include <iostream>
#include <cmath>
#include <string>
#include <fstream>
#include <ctime>
#include <cstdlib>
#include <bits/stdc++.h>
#define N 3

using namespace std;
template<class T>

void display(T A[N][N])
{
for (int i=0; i<N; i++)
{

for (int j=0; j<N; j++)     
cout << A[i][j] << "\t\t";
cout << endl;
}
}

template<class T>

void display(T A[N])

{

for (int i=0; i<N; i++)

{
cout << A[i]<< "\n";
}
}

void getCofactor(int A[N][N], int temp[N][N], int p, int q, int n)

{

int i = 0, j = 0;

for (int row = 0; row < n; row++)

{

for (int col = 0; col < n; col++)

{
if (row != p && col != q)

{

temp[i][j++] = A[row][col];

if (j == n - 1)
{

j = 0;

i++;

}

}

}

}

}

int determinant(int A[N][N], int n)
{

int D = 0; 

if (n == 1)

return A[0][0];

int temp[N][N]; 

int sign = 1; 

for (int f = 0; f < n; f++)

{
getCofactor(A, temp, 0, f, n);

D += sign * A[0][f] * determinant(temp, n - 1);
sign = -sign;
}

return D;
}

void adjoint(int A[N][N],int adj[N][N])
{
if (N == 1)
{

adj[0][0] = 1;

return;
}

int sign = 1, temp[N][N];

for (int i=0; i<N; i++)
{

for (int j=0; j<N; j++)
{
getCofactor(A, temp, i, j, N);
sign = ((i+j)%2==0)? 1: -1;
    adj[j][i] = (sign)*(determinant(temp, N-1));
}
}
}

bool inverse(int A[N][N]){

int det = determinant(A, N);

if (det == 0){

cout << "Singular matrix, can't find its inverse";

return false;
}

return true;
}

void computeInverse(int A[N][N], float inverse[N][N]){

int det = determinant(A, N);

int adj[N][N];

adjoint(A, adj);

for (int i=0; i<N; i++)

for (int j=0; j<N; j++)

inverse[i][j] = adj[i][j]/float(det);

cout<<"\nThe Inverse of the Matrix A is:"<<endl;

display(inverse);

}
int main()
{
system("cls");

int A[N][N] = {{-1, 4, -2}, {-3, -2, +1}, {+2, -5, +3}};

char X[N];

int B[N];

float inv[N][N];

cout<<"\nEnter a 3*3 Matrix A"<<endl;

for(int i=0;i<N;i++){

for(int j=0;j<N;j++){

cin>>A[i][j];

}

}

cout<<"\nEnter variables x, y, z for Matrix X"<<endl;

for(int i=0;i<N;i++){

cin>>X[i];

 }

 if (X[0] == 'x' && X[1] == 'y' && X[2] == 'z')

 cout<<"\nMatrix X is Valid"<<endl;

else{

cout<<"\nMatrix X is Invalid"<<endl;

return -1;

}

cout<<"\nEnter values for Matrix B"<<endl;

for(int i=0; i<N; i++)

cin>>B[i];

cout<<"\nMatrix A is:------->\n";

display(A);

cout<<"\nMatrix X is:------->\n";

display(X);

cout<<"\nMatrix B is:------->\n";

display(B);

bool isInverseExist = inverse(A);

if (isInverseExist)

computeInverse(A, inv);

return 0;
}

Answer 1

Okay, Here is a simple pointer example using a char array. This can work with other data types as well. Don't remember where I read it; Think of a pointer as an empty bottle.

lets break this down in English first then I'll share a simple example that can be compiled. Imagine that you have 10 m&m's sitting in front of you on a table. These m&m's represent a character array that we will call char mm[10]; Assume that this array is filled with chars that represent the color of all 10 of the m&m's

Now, we don't want to leave our candy's on the table all day so we will store all ten of the m&m's in a special jar specifically made for the m&m's. this jar will be called char* mm_ptr;

So now we are left with a table of m&m's and a jar sitting next to the pile. The next step is to fill the jar with the m&m's and you do it like this: mm_ptr = mm;

You now have a "jar full of m&m's". This allows you to access the m&m's directly from the jar!

Here is a Working example of of putting m&m's into a jar:

#include <iostream>
//using namespace std;


int main(){//The main function is our table

        char mm[10];    //Our pile of m&m's

        for(int i=0; i<10; i++){
                if(i < 5){
                        mm[i] = 'b';    //Lets say that half of the m&m's are blue
                }else{
                        mm[i] = 'r';    //and that the other half is red
                }
        }

        char* mm_ptr;           //This is our bottle that we will 
                                //use to store our m&m's

        mm_ptr = mm;    //this is us storing the m&m's in the jar!

        for(int i=0; i<10; i++){//Lets dump those candies back onto the table!
                std::cout<<mm_ptr[i]<<std::endl;

        }
        return 0;
}

A correctly initialized pointer will work almost exactly like a normal array