C++ Program to Find Inverse of a Graph Matrix

This is a C++ program to Find Inverse of a Graph Matrix. Inverse of a matrix exists only if the matrix is non-singular i.e., determinant should not be 0. Inverse of a matrix can find out in many ways. Here we find out inverse of a graph matrix using adjoint matrix and its determinant. Steps involved in the Example

Begin
   function INV() to get the inverse of the matrix:
   Call function DET().
   Call function ADJ().
   Find the inverse of the matrix using the formula;
   Inverse(matrix) = ADJ(matrix) / DET(matrix)
End.

Example

#include<bits/stdc++.h>
using namespace std;
#define N 5
void getCfactor(int M[N][N], int t[N][N], int p, int q, int n) {
   int i = 0, j = 0;
   for (int r= 0; r< n; r++) {
      for (int c = 0; c< n; c++) //Copy only those elements which are not in given row r and column c: {
         if (r != p && c != q) { t[i][j++] = M[r][c]; //If row is filled increase r index and reset c index
            if (j == n - 1) {
               j = 0; i++;
            }
         }
      }
   }
}
int DET(int M[N][N], int n) //to find determinant {
   int D = 0;
   if (n == 1)
      return M[0][0];
   int t[N][N]; //store cofactors
   int s = 1; //store sign multiplier //
   To Iterate each element of first row
   for (int f = 0; f < n; f++) {
      //For Getting Cofactor of M[0][f] do getCfactor(M, t, 0, f, n); D += s * M[0][f] * DET(t, n - 1);
      s = -s;
   }
   return D;
}
void ADJ(int M[N][N],int adj[N][N])
//to find adjoint matrix {
   if (N == 1) {
      adj[0][0] = 1; return;
   }
   int s = 1,
   t[N][N];
   for (int i=0; i<N; i++) {
      for (int j=0; j<N; j++) {
         //To get cofactor of M[i][j]
         getCfactor(M, t, i, j, N);
         s = ((i+j)%2==0)? 1: -1; //sign of adj[j][i] positive if sum of row and column indexes is even.
         adj[j][i] = (s)*(DET(t, N-1)); //Interchange rows and columns to get the transpose of the cofactor matrix
      }
   }
}
bool INV(int M[N][N], float inv[N][N]) {
   int det = DET(M, N);
   if (det == 0) {
      cout << "can't find its inverse";
      return false;
   }
   int adj[N][N]; ADJ(M, adj);
   for (int i=0; i<N; i++) for (int j=0; j<N; j++) inv[i][j] = adj[i][j]/float(det);
   return true;
}
template<class T> void print(T A[N][N]) //print the matrix. {
   for (int i=0; i<N; i++) { for (int j=0; j<N; j++) cout << A[i][j] << " "; cout << endl; }
}
int main() {
   int M[N][N] = {
      {1, 2, 3, 4,-2}, {-5, 6, 7, 8, 4}, {9, 10, -11, 12, 1}, {13, -14, -15, 0, 9}, {20 , -26 , 16 , -17 , 25}
   };
   float inv[N][N];
   cout << "Input matrix is :\n"; print(M);
   cout << "\nThe Inverse is :\n"; if (INV(M, inv)) print(inv);
   return 0;
}

Output

Input matrix is :
1 2 3 4 -2
-5 6 7 8 4 
9 10 -11 12 1 
13 -14 -15 0 9 
20 -26 16 -17 25
The Inverse is : 
0.0811847 -0.0643008 0.0493814 -0.0247026 0.0237006 
-0.126819 -0.0161738 0.0745377 -0.0713976 0.0151639 
0.0933664 0.0028245 -0.0111876 -0.0220437 0.0154006 
0.143624 0.0582573 -0.0282371 0.0579023 -0.0175466 
-0.15893 0.0724272 0.0259728 -0.00100988 0.0150219