Given a matrix of size n x n. The task is to check whether the given matrix is a Centrosymmetric Matrix or not.
In mathematics, a centrosymmetric matrix is a matrix that 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
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 implementation of the above approach:
C++
// CPP Program to check whether given// matrix is centrosymmetric or not.#include <bits/stdc++.h>using namespace std;#define N 3bool 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 Programint 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 Coden = 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
<?php// PHP Program to check whether given// matrix is centrosymmetric or not.//$N = 3;function checkCentrosymmetricted( $n, $m){ $mid_row; // Finding the middle row // of the matrix if ($n & 1) $mid_row = $n / 2 + 1; else $mid_row = $n / 2; // for each row upto middle row. for($i = 0; $i < $mid_row; $i++) { // If each element and // its corresponding // element is not equal // then return false. for($j = 0; $j < $n; $j++) { if ($m[$i][$j] != $m[$n - $i - 1] [$n - $j - 1]) return false; } } return true;} // Driver Code $n = 3; $m = array(array(1, 3, 5 ), array( 6, 8, 6 ), array( 5, 3, 1 )); if(checkCentrosymmetricted($n, $m) ) echo "Yes" ; else echo "No"; // This code is contributed by anuj_67.?> |
Javascript
<script>// Javascript Program to check whether given// matrix is centrosymmetric or not.let N = 3function checkCentrosymmetricted( n, m){ let mid_row; // Finding the middle row of the matrix if (n & 1) mid_row = Math.floor(n / 2) + 1; else mid_row = n / 2; // for each row upto middle row. for (let i = 0; i < mid_row; i++) { // If each element and its corresponding // element is not equal then return false. for (let j = 0; j < n; j++) { if (m[i][j] != m[n - i - 1][n - j - 1]) return false; } } return true;}// Driver Codelet n = 3;let m = [ [ 1, 3, 5 ], [ 6, 8, 6 ], [ 5, 3, 1 ] ];(checkCentrosymmetricted(n, m) ? (document.write("Yes")) : document.write("No"));// This code is contributed by jana_sayanta.</script> |
Output
Yes
Time Complexity: O(N2)
Auxiliary Space: O(1)
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