This is the java program to find out a given matrix is sparse matrix or not. Sparse matrix contains zero elements above a certain threshold. This threshold is given by (n*m)/2, where n and m are the rows and columns in matrix. Hence, if a matrix contains more than nm/2 mumber of zeros it is sparse matrix otherwise not.

Here is the source code of the Java Program to Check if it is a Sparse Matrix. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

`//This is a sample program to check whether the matrix is sparse matrix or not`

`//The complexity of the code is O(n^2)`

import java.util.Scanner;

public class Sparsity_Matrix

`{`

public static void main(String args[])

`{`

Scanner sc = new Scanner(System.in);

System.out.println("Enter the dimensions of the matrix: ");

int m = sc.nextInt();

int n = sc.nextInt();

double[][] mat = new double[m][n];

int zeros = 0;

System.out.println("Enter the elements of the matrix: ");

for(int i=0; i<m; i++)

`{`

for(int j=0; j<n; j++)

`{`

mat[i][j] = sc.nextDouble();

if(mat[i][j] == 0)

`{`

`zeros++;`

`}`

`}`

`}`

if(zeros > (m*n)/2)

`{`

System.out.println("The matrix is a sparse matrix");

`}`

`else`

`{`

System.out.println("The matrix is not a sparse matrix");

`}`

sc.close();

`}`

`}`

Output:

$ javac Sparsity_matrix.java $ java Sparsity_matrix Enter the dimensions of the matrix: 2 3 Enter the elements of the matrix: 1 0 0 2 1 1 The matrix is not a sparse matrix $ javac Sparsity_matrix.java $ java Sparsity_matrix Enter the dimensions of the matrix: 3 4 Enter the elements of the matrix: 1 0 0 0 0 1 0 0 0 0 1 1 The matrix is a sparse matrix

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