A matrix is a two-dimensional data object having m rows and n columns, therefore a total of m*n values. If most of the values of a matrix are 0 then we say that the matrix is sparse.
Consider a definition of Sparse where a matrix is considered sparse if the number of 0s is more than half of the elements in the matrix,
Examples:
Input : 1 0 3
0 0 4
6 0 0
Output : Yes
There are 5 zeros. This count
is more than half of matrix
size.
Input : 1 2 3
0 7 8
5 0 7
Output: No
To check whether a matrix is a sparse matrix, we only need to check the total number of elements that are equal to zero. If this count is more than (m * n)/2, we return true.
C++
// CPP code to check if a matrix is// sparse.#include <iostream>using namespace std;const int MAX = 100;bool isSparse(int array[][MAX], int m, int n){ int counter = 0; // Count number of zeros in the matrix for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) if (array[i][j] == 0) ++counter; return (counter > ((m * n) / 2));}// Driver Functionint main(){ int array[][MAX] = { { 1, 0, 3 }, { 0, 0, 4 }, { 6, 0, 0 } }; int m = 3, n = 3; if (isSparse(array, m, n)) cout << "Yes"; else cout << "No";} |
Output:
Yes
Time complexity: O(m*n) where m and n are rows and columns respectively of a given matrix
Auxiliary Space: O(1)
Please refer complete article on Check if a given matrix is sparse or not for more details!
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