[18 Feb 2020] Program to check if a matrix is symmetric

Program to check if a matrix is symmetric
A square matrix is said to be symmetric matrix if the transpose of the matrix is same as the given matrix. Symmetric matrix can be obtain by changing row to column and column to row.

Examples:

Input : 1 2 3
        2 1 4
        3 4 3
Output : Yes

Input : 3 5 8
        3 4 7
        8 5 3
Output : No

// Simple c++ code for check a matrix is

// symmetric or not.

#include <iostream>

using namespace std;

  

const int MAX = 100;

  

// Fills transpose of mat[N][N] in tr[N][N]

void transpose(int mat[][MAX], int tr[][MAX], int N)

{

    for (int i = 0; i < N; i++)

        for (int j = 0; j < N; j++)

            tr[i][j] = mat[j][i];

}

  

// Returns true if mat[N][N] is symmetric, else false

bool isSymmetric(int mat[][MAX], int N)

{

    int tr[N][MAX];

    transpose(mat, tr, N);

    for (int i = 0; i < N; i++)

        for (int j = 0; j < N; j++)

            if (mat[i][j] != tr[i][j])

                return false;

    return true;

}

  

// Driver code

int main()

{

    int mat[][MAX] = { { 1, 3, 5 },

                       { 3, 2, 4 },

                       { 5, 4, 1 } };

  

    if (isSymmetric(mat, 3))

        cout << "Yes";

    else

        cout << "No";

    return 0;

}




// Simple java code for check a matrix is // symmetric or not.    import java.io.*;    class GFG {               static int  MAX = 100;    // Fills transpose of mat[N][N] in tr[N][N]  static void transpose(int mat[][], int tr[][], int N) {     for (int i = 0; i < N; i++)         for (int j = 0; j < N; j++)             tr[i][j] = mat[j][i]; }    // Returns true if mat[N][N] is symmetric, else false  static boolean isSymmetric(int mat[][], int N) {     int tr[][] = new int[N][MAX];     transpose(mat, tr, N);     for (int i = 0; i < N; i++)         for (int j = 0; j < N; j++)             if (mat[i][j] != tr[i][j])                 return false;     return true; }    // Driver code     public static void main (String[] args)  {                    int mat[][] = { { 1, 3, 5 },                     { 3, 2, 4 },                     { 5, 4, 1 } };        if (isSymmetric(mat, 3))         System.out.println( "Yes");     else         System.out.println ( "No");            } }


Output :

 Yes

Time Complexity : O(N x N)
Auxiliary Space : O(N x N)




// Efficient Java code for check a matrix is // symmetric or no    import java.io.*;    class GFG {          static int MAX = 100;    // Returns true if mat[N][N] // is symmetric, else false  static boolean isSymmetric(int mat[][], int N) {     for (int i = 0; i < N; i++)         for (int j = 0; j < N; j++)             if (mat[i][j] != mat[j][i])                 return false;     return true; }    // Driver code            public static void main (String[] args)  {             int mat[][] = { { 1, 3, 5 },                     { 3, 2, 4 },                     { 5, 4, 1 } };        if (isSymmetric(mat, 3))         System.out.println(  "Yes");     else                    System.out.println("NO");                } } // This article is contributed by vt_m.


Output:

Yes










# Efficient Python code for check a matrix is # symmetric or not.    # Returns true if mat[N][N] is symmetric, else false def isSymmetric(mat, N):     for i in range(N):         for j in range(N):             if (mat[i][j] != mat[j][i]):                 return False     return True     # Driver code mat = [ [ 1, 3, 5 ], [ 3, 2, 4 ], [ 5, 4, 1 ] ] if (isSymmetric(mat, 3)):     print "Yes" else:     print "No"    # This code is contributed by Sachin Bisht


Output:

Yes

Time Complexity : O(N x N)
Auxiliary Space : O(1)