C++ Program to Check if a given matrix is sparse or not
Last Updated :
11 Jul, 2022
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++
#include <iostream>
using namespace std;
const int MAX = 100;
bool isSparse( int array[][MAX], int m, int n)
{
int counter = 0;
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));
}
int 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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