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.
Java
// Java code to check// if a matrix is// sparse.import java.io.*;class GFG { static int MAX = 100; static boolean isSparse(int array[][], 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 Function public static void main(String args[]) { int array[][] = { { 1, 0, 3 }, { 0, 0, 4 }, { 6, 0, 0 } }; int m = 3, n = 3; if (isSparse(array, m, n)) System.out.println("Yes"); else System.out.println("No"); }}// This code is contributed by// Nikita Tiwari. |
Output:
Yes
Time complexity: O(m*n) where m is no of rows and n is no of columns of 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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