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

C++Server Side ProgrammingProgramming

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 −

 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

To check whether the matrix is Hankel Matrix or not, we have to check whether mat[i, j] = ai+j or not. ai+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])
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