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,
C++
// 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; } |
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Java
// 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"); } } |
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Python
# Simple Python code for check a matrix is # symmetric or not. # Fills transpose of mat[N][N] in tr[N][N] def transpose(mat, tr, N): for i in range(N): for j in range(N): tr[i][j] = mat[j][i] # Returns true if mat[N][N] is symmetric, else false def isSymmetric(mat, N): tr = [ [0 for j in range(len(mat[0])) ] for i in range(len(mat)) ] transpose(mat, tr, N) for i in range(N): for j in range(N): if (mat[i][j] != tr[i][j]): 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 |
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C#
// Simple C# code for check a matrix is // symmetric or not. using System; 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 bool 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 () { int [,]mat = { { 1, 3, 5 }, { 3, 2, 4 }, { 5, 4, 1 } }; if (isSymmetric(mat, 3)) Console.WriteLine( "Yes"); else Console.WriteLine( "No"); } } // This code is contributed by vt_m. |
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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 ?> |
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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].
C++
// Efficient c++ code for check a matrix is // symmetric or not. #include <iostream> using namespace std; const int MAX = 100; // Returns true if mat[N][N] is symmetric, else false bool isSymmetric(int mat[][MAX], 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 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; } |
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Java
// 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. |
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Python
# 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 |
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C#
// Efficient C# code for check a matrix is // symmetric or no using System; class GFG { //static int MAX = 100; // Returns true if mat[N][N] // is symmetric, else false static bool 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 () { int [,]mat = { { 1, 3, 5 }, { 3, 2, 4 }, { 5, 4, 1 } }; if (isSymmetric(mat, 3)) Console.WriteLine( "Yes"); else Console.WriteLine("NO"); } } // This code is contributed by vt_m. |
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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. ?> |
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Output:
Yes
Time Complexity : O(N x N)
Auxiliary Space : O(1)
This article is contributed by Dharmendra kumar. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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