### What is a sparse matrix ?

A sparse matrix is a matrix in which most of the values are zero. Similarly a matrix with maximum non-zero values is known as dense matrix. In this tutorial, we will learn how to check if a matrix is sparse or not in java.

### Sparsity of a matrix :

The proportion of zero elements to non-zero elements of a matrix is called sparsity. If a matrix contains 9 zero values and 3 non-zero values, the sparsity will be 9/3 = 3 .

### Checking a matrix sparse or not programatically :

To check if a matrix is sparse-matrix or not, we will count the number of zeros in the matrix. If the count is more than half of the numbers, it will be a sparse-matrix and otherwise a Dense matrix. For a matrix with ‘r’ no of rows and ‘c’ no of columns, the total number of elements will be ‘r * c’ .

Let’s take a look into the java program to find if a matrix is sparse or Dense :

import java.util.Scanner; public class Main { public static void main(String[] args){ int row = 0; int col = 0; int count = 0; //number of zero counts Scanner sc = new Scanner(System.in); System.out.println("Please enter the row numbers for the matrix : "); row = sc.nextInt(); System.out.println("Please enter the column numbers for the matrix : "); col = sc.nextInt(); int[][] matrix = new int[row][col]; for (int i = 0; i < row ; i++){ System.out.println("Please enter row no : "+(i+1)); for (int j = 0; j < col ; j++){ matrix[i][j] = sc.nextInt(); if(matrix[i][j] == 0){ count ++; } } } if(count > (row*col)/2){ System.out.println("The above matrix is a Sparse matrix "); }else{ System.out.println("The above matrix is a Dense matrix"); } } }

### Sample Output :

Please enter the row numbers for the matrix : 3 Please enter the column numbers for the matrix : 3 Please enter row no : 1 1 0 0 Please enter row no : 2 2 0 0 Please enter row no : 3 0 0 3 The above matrix is a Sparse matrix

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