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
A Simple solution is to do following.
1) Create transpose of given matrix.
2) Check if transpose and given matrices are same or not.
PHP
<?php // Simple PHP code for check a matrix is // symmetric or not. // Returns true if mat[N][N] is // symmetric, else false function isSymmetric($mat, $N) { $tr = array(array()); for ($i = 0; $i < $N; $i++) for ($j = 0; $j < $N; $j++) $tr[$i][$j] = $mat[$j][$i]; // Fills transpose of // mat[N][N] in tr[N][N] for ($i = 0; $i < $N; $i++) for ($j = 0; $j < $N; $j++) if ($mat[$i][$j] != $tr[$i][$j]) return false; return true; } // Driver code $mat= array(array(1, 3, 5), array(3, 2, 4), array(5, 4, 1)); if (isSymmetric($mat, 3)) echo "Yes"; else echo "No"; // This code is contributed by Sam007 ?> |
Output :
Yes
Time Complexity : O(N x N)
Auxiliary Space : O(N x N)
An Efficient solution to check a matrix is symmetric or not is to compare matrix elements without creating a transpose. We basically need to compare mat[i][j] with mat[j][i].
PHP
<?php // Efficient PHP code for // check a matrix is // symmetric or not. $MAX = 100; // Returns true if mat[N][N] // is symmetric, else false function isSymmetric($mat, $N) { for ($i = 0; $i < $N; $i++) for ($j = 0; $j < $N; $j++) if ($mat[$i][$j] != $mat[$j][$i]) return false; return true; } // Driver code $mat = array(array(1, 3, 5), array(3, 2, 4), array(5, 4, 1)); if (isSymmetric($mat, 3)) echo("Yes"); else echo("No"); // This code is contributed by Ajit. ?> |
Output:
Yes
Time Complexity : O(N x N)
Auxiliary Space : O(1)
Please refer complete article on Program to check if a matrix is symmetric for more details!
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