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| 11349 | |
| 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. |