Check if a given matrix is Hankel or not in C++

Suppose we have a square matrix, our task is to check whether the matrix is Hankel matrix or not. The Hankel matrix is a square matrix, in which each ascending skew-diagonal elements from left to right is constant. Suppose a matrix is like below −

To check whether the matrix is Hankel Matrix or not, we have to check whether mat[i, j] = a_i+j or not. a_i+j can be defined as −

$$a_{i+j}=\begin{cases}mat[i+j,0]< n\mat[i+j-n+1,n-1]otherwise\end{cases}$$

Example

 Live Demo

#include <iostream>
#define N 5
using namespace std;
bool isHankelMat(int mat[N][N], int n) {
   for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
         if (i + j < n) {
            if (mat[i][j] != mat[i + j][0])
            return false;
         } else {
            if (mat[i][j] != mat[i + j - n + 1][n - 1])
            return false;
         }
      }
   }
   return true;
}
int main() {
   int n = 5;
   int mat[N][N] = {
      { 1, 2, 3, 4, 5},
      { 2, 3, 4, 5, 6},
      { 3, 4, 5, 6, 7},
      { 4, 5, 6, 7, 8},
      { 5, 6, 7, 8, 9}
   };
   if(isHankelMat(mat, n))
      cout << "This is Hankel Matrix";
   else
      cout << "This is not Hankel Matrix";
}

Output

This is Hankel Matrix