ZeroJudge E513: Symmetric Matrix

UVa 11349 – Symmetric Matrix

You're given a square matrix M.
The elements of matrix M are denoted as M[i][j]: {0 < i < N, 0 < j < N}.
In this problem, you must determine whether the given matrix is symmetric.

Definition: A symmetric matrix has all non-negative elements and is symmetric concerning the center of the matrix.
Any other matrix is considered non-symmetric.

What you need to do is determine whether this matrix is symmetric.
The elements within the matrix range from −2^32 to 2^32, and 0 < N ≤ 100.

Sample Inputs/Outputs

Sample Input(s)Sample Output(s)
The first line of input contains a number T (T ≤ 300), indicating the number of test cases.
The first line of each test case contains an integer N, indicating the dimension of the square matrix.
The next N lines contain the elements of the matrix.
Each of the N lines contains N numbers, where the j-th number on the i-th line represents M[i][j].		For each test case, output a line in the format "Test #t: S", where t is the test case number and S is the answer string.
If the input matrix is symmetric, S= "Symmetric".
If the input matrix is not symmetric, S= "Non-symmetric".
2
N = 3
5 1 3
2 0 2
3 1 5
N = 3
5 1 3
2 0 2
0 1 5		Test #1: Symmetric.
Test #2: Non-symmetric.

Thought Process

In this question, Long Long Int should be used to store the data in the matrix. When receiving the data, if a number less than 0 is encountered, you can set a boolean value to true, and then there's no need to perform further checks.

You can collect the data from the matrix into a one-dimensional array and then check if this one-dimensional array is a palindrome. This way, you can determine if the matrix is symmetric.

Sample Code－ZeroJudge E513: Symmetric Matrix

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

int main() {
    cin.sync_with_stdio(0);
    cin.tie(0);
    int N;
    cin >> N;
    for (int i = 0; i<N; i++)
    {
        char a, b;
        int M;
        cin >> a >> b >> M;
        vector<long long int>num;
        bool negative = false;
        for (int j = 0; j<M; j++)
        {
            for (int k = 0; k<M; k++)
            {
                long long int tmp;
                cin >> tmp;
                num.push_back(tmp);
                if (tmp < 0) negative = true;
            }
        }
        if (!negative)
        {
            vector<long long int>tmp = num;
            reverse(tmp.begin(), tmp.end());
            if (tmp == num) cout << "Test #" << i+1 << ": Symmetric.\n";
            else cout << "Test #" << i+1 << ": Non-symmetric.\n";
        }
        else cout << "Test #" << i+1 << ": Non-symmetric.\n";
    }
}

//ZeroJudge E513
//Dr. SeanXD
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