# Centrosymmetric Matrix

Given a matrix of size n x n. The task is to check whether the given matrix is Centrosymmetric Matrix or not.

In mathematics, a centrosymmetric matrix is a matrix which is symmetric about its center. Examples:

```Input : n = 3,
m[][] = { { 1, 3, 5 },
{ 6, 8, 6 },
{ 5, 3, 1 } };
Output : Yes

Input : n = 3,
m[][] = { { 1, 3, 5 },
{ 6, 8, 6 },
{ 5, 3, 0 } };
Output : No
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

The idea is to check for each element whether m[i][j] is equal to m[n – i – 1][n – j – 1]. If any element does not satisfy the above condition, then print “No”, otherwise print “Yes”.

Below is the implemantation of the above approach:

## C++

 `// CPP Program to check whether given ` `// matrix is centrosymmetric or not. ` `#include ` `using` `namespace` `std; ` `#define N 3 ` ` `  `bool` `checkCentrosymmetricted(``int` `n, ``int` `m[N][N]) ` `{ ` `    ``int` `mid_row; ` ` `  `    ``// Finding the middle row of the matrix ` `    ``if` `(n & 1) ` `        ``mid_row = n / 2 + 1; ` `    ``else` `        ``mid_row = n / 2; ` ` `  `    ``// for each row upto middle row. ` `    ``for` `(``int` `i = 0; i < mid_row; i++) { ` ` `  `        ``// If each element and its corresponding ` `        ``// element is not equal then return false. ` `        ``for` `(``int` `j = 0; j < n; j++) { ` `            ``if` `(m[i][j] != m[n - i - 1][n - j - 1]) ` `                ``return` `false``; ` `        ``} ` `    ``} ` ` `  `    ``return` `true``; ` `} ` ` `  `// Driven Program ` `int` `main() ` `{ ` `    ``int` `n = 3; ` `    ``int` `m[N][N] = { { 1, 3, 5 }, ` `                    ``{ 6, 8, 6 }, ` `                    ``{ 5, 3, 1 } }; ` ` `  `    ``(checkCentrosymmetricted(n, m) ?  ` `              ``(cout << ``"Yes"``) : (cout << ``"No"``)); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java Program to check whether given ` `// matrix is centrosymmetric or not. ` `import` `java.io.*; ` ` `  `class` `GFG { ` `         `  `    ``static` `int` `N = ``3``; ` `     `  `    ``static` `boolean` `checkCentrosymmetricted( ` `                           ``int` `n, ``int` `m[][]) ` `    ``{ ` `        ``int` `mid_row; ` `     `  `        ``// Finding the middle row of the ` `        ``// matrix ` `        ``if` `((n & ``1``)>``0``) ` `            ``mid_row = n / ``2` `+ ``1``; ` `        ``else` `            ``mid_row = n / ``2``; ` `     `  `        ``// for each row upto middle row. ` `        ``for` `(``int` `i = ``0``; i < mid_row; i++) ` `        ``{ ` `     `  `            ``// If each element and its  ` `            ``// corresponding element is ` `            ``// not equal then return false. ` `            ``for` `(``int` `j = ``0``; j < n; j++) ` `            ``{ ` `                ``if` `(m[i][j] != ` `                  ``m[n - i - ``1``][n - j - ``1``]) ` `                    ``return` `false``; ` `            ``} ` `        ``} ` `     `  `        ``return` `true``; ` `    ``} ` `     `  `    ``// Driven Program ` `    ``public` `static` `void` `main (String[] args) ` `    ``{ ` `        ``int` `n = ``3``; ` `        ``int` `m[][] = { { ``1``, ``3``, ``5` `}, ` `                      ``{ ``6``, ``8``, ``6` `}, ` `                      ``{ ``5``, ``3``, ``1` `} }; ` ` `  `    ``if``(checkCentrosymmetricted(n, m)) ` `        ``System.out.println( ``"Yes"``); ` `    ``else` `        ``System.out.println( ``"No"``); ` `    ``} ` `} ` ` `  `// This code is contributed by anuj_67. `

## Python3

 `# Python3 Program to check whether given ` `# matrix is centrosymmetric or not. ` ` `  `def` `checkCentrosymmetricted( n, m): ` ` `  `    ``mid_row ``=` `0``; ` ` `  `    ``# Finding the middle row  ` `    ``# of the matrix ` `    ``if` `((n & ``1``) > ``0``): ` `        ``mid_row ``=` `n ``/` `2` `+` `1``; ` `    ``else``: ` `        ``mid_row ``=` `n ``/` `2``; ` ` `  `    ``# for each row upto middle row. ` `    ``for` `i ``in` `range``(``int``(mid_row)):  ` ` `  `        ``# If each element and  ` `        ``# its corresponding ` `        ``# element is not equal  ` `        ``# then return false. ` `        ``for` `j ``in` `range``(n): ` `            ``if` `(m[i][j] !``=` `m[n ``-` `i ``-` `1``][n ``-` `j ``-` `1``]): ` `                ``return` `False``; ` ` `  `    ``return` `True``; ` `     `  `# Driver Code ` `n ``=` `3``; ` `m ``=` `[[``1``, ``3``, ``5` `], ` `     ``[ ``6``, ``8``, ``6` `], ` `     ``[ ``5``, ``3``, ``1` `]]; ` ` `  `if``(checkCentrosymmetricted(n, m)): ` `    ``print``(``"Yes"``); ` `else``: ` `    ``print``(``"No"``); ` `         `  `# This code is contributed by mits `

## C#

 `// C# Program to check whether given ` `// matrix is centrosymmetric or not. ` `using` `System; ` ` `  `class` `GFG { ` `         `  `    ``///static int N = 3; ` `     `  `    ``static` `bool` `checkCentrosymmetricted( ` `                        ``int` `n, ``int` `[,]m) ` `    ``{ ` `        ``int` `mid_row; ` `     `  `        ``// Finding the middle row of the ` `        ``// matrix ` `        ``if` `((n & 1)>0) ` `            ``mid_row = n / 2 + 1; ` `        ``else` `            ``mid_row = n / 2; ` `     `  `        ``// for each row upto middle row. ` `        ``for` `(``int` `i = 0; i < mid_row; i++) ` `        ``{ ` `     `  `            ``// If each element and its  ` `            ``// corresponding element is ` `            ``// not equal then return false. ` `            ``for` `(``int` `j = 0; j < n; j++) ` `            ``{ ` `                ``if` `(m[i,j] != ` `                ``m[n - i - 1,n - j - 1]) ` `                    ``return` `false``; ` `            ``} ` `        ``} ` `     `  `        ``return` `true``; ` `    ``} ` `     `  `    ``// Driven Program ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `n = 3; ` `        ``int` `[,]m = { { 1, 3, 5 }, ` `                    ``{ 6, 8, 6 }, ` `                    ``{ 5, 3, 1 } }; ` ` `  `        ``if``(checkCentrosymmetricted(n, m)) ` `            ``Console.WriteLine( ``"Yes"``); ` `        ``else` `            ``Console.WriteLine( ``"No"``); ` `    ``} ` `} ` ` `  `// This code is contributed by anuj_67. `

## PHP

 ` `

Output
`Yes`

Complexity : O(N2)

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