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; } |
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; } |
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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