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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