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Bisymmetric matrix in C++?
Here we will see one program that will help to check whether a matrix is bisymmetric or not. The Bisymmetric matrix is one square matrix that are symmetric about both of the major diagonals. The below matrix is an example of bisymmetric matrix.
1 2 3 4 5 2 6 7 8 4 3 7 9 7 3 4 8 7 6 2 5 4 3 2 1
Algorithm
checkBiSymmetric(mat, n)
Begin for i in range 0 to n – 1, do for j in range 0 to i – 1, do if mat[i, j] is not same as mat[j, i], then return false end if done done for i in range 0 to n – 1, do for j in range 0 to n – i, do if mat[i, j] is not same as mat[n – j - 1, n – i - 1], then return false end if done done return true End
Example
#include<iostream> #define N 5 using namespace std; int matrix[N][N] = {{1, 2, 3, 4, 5}, {2, 6, 7, 8, 4}, {3, 7, 9, 7, 3}, {4, 8, 7, 6, 2}, {5, 4, 3, 2, 1}}; bool checkBiSymmetric() { for (int i = 0; i < N; i++) //scan through forward diagonal for (int j = 0; j < i; j++) if (matrix[i][j] != matrix[j][i]) //when corresponding elements are not same, return false return false; for (int i = 0; i < N; i++) //scan through forward diagonal for (int j = 0; j < N - i; j++) if (matrix[i][j] != matrix[N - j - 1][N - i - 1]) //when corresponding elements are not same, return false return false; return true; //otherwise return true } main() { if(checkBiSymmetric()){ cout << "Yes the matrix is bisymmetric"; } else { cout << "No the matrix is not bisymmetric"; } }
Output
Yes the matrix is bisymmetric
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