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Symmetric Matrix
You‘re given a square matrix M. Elements of this matrix are Mij : {0 < i < n, 0 < j < n}. In this
problem you’ll have to find out whether the given matrix is symmetric or not.
Definition: Symmetric matrix is such a matrix that all elements of it are non-negative and symmetric
with relation to the center of this matrix. Any other matrix is considered to be non-symmetric. For
example:
M =
5
1
3
2
0
2
3
1
5
is symmetric
M =
5
1
3
2
0
2
0
1
5
is not symmetric, because 3 ̸= 0
All you have to do is to find whether the matrix is symmetric or not. Elements of a matrix given
in the input are −232 ≤Mij ≤232 and 0 < n ≤100.
Input
First line of input contains number of test cases T ≤300. Then T test cases follow each described in
the following way. The first line of each test case contains n – the dimension of square matrix. Then
n lines follow each of then containing row i. Row contains exactly n elements separated by a space
character. j-th number in row i is the element Mij of matrix you have to process.
Output
For each test case output one line ‘Test #t: S’. Where t is the test number starting from 1. Line S is
equal to ‘Symmetric’ if matrix is symmetric and ‘Non-symmetric’ in any other case.
Sample Input
2
N = 3
5 1 3
2 0 2
3 1 5
N = 3
5 1 3
2 0 2
0 1 5
Sample Output
Test #1: Symmetric.
Test #2: Non-symmetric. |