Java Program To Determine If a Given Matrix is a Sparse Matrix

What is a Sparse Matrix?

A matrix is said to be a sparse matrix if most of the elements of that matrix are 0. It means that the number of non-zero elements has a lesser count than the number of zero elements.

Let's say we have a matrix of size 3*3, which means it has 9 elements. If 5 or more of those elements are 0, then we can say that the matrix is sparse.

A = [ 0 2 0 ]
    [ 0 5 4 ]
    [ 0 0 0 ]

In this case, we have 6 elements that are 0, hence it is a sparse matrix.

Algorithm

To determine if a given matrix is a sparse matrix or not, we can follow these steps:

• Declare an integer matrix, namely input_matrix
• Define the values.
• Iterate over each element of the matrix using two for-loops, and count the number of elements that have the value 0.
• If the zero elements is greater than half the total elements, it's a sparse matrix, else it's not.

Java Program to Determine whether a Matrix is Sparse

Here, is the code to determine if a given matrix is a sparse matrix or not. We are taking more than half of the elements as 0 to make it a sparse matrix.

public class SparseMatrixOrNot{  
   public static void main(String[] args){
      int[][] arr = {
         {9,0,0},
         {0,0,5},
         {0,0,0}
      };
      int cnt0 = 0;
      int totalEl = arr.length * arr[0].length;
      System.out.println("The matrix is defined as:");
      for(int i = 0; i < arr.length; i++){
         for(int j = 0; j < arr[i].length; j++){
            System.out.print(arr[i][j] + " ");
            if(arr[i][j] == 0){
               cnt0++;
            }
         }
         System.out.println();
      }
      if(cnt0 > totalEl / 2){
         System.out.println("\nYes, the matrix is a sparse matrix");
      } else {
         System.out.println("\nNo, the matrix is not a sparse matrix");
      }
   }
}

Output

Following is the output of the above code:

The matrix is defined as:
4 0 6
0 0 9
6 0 0

Yes, the matrix is a sparse matrix

Example 2

Now, take a matrix with more non-zero elements than zero elements and check if it is a sparse matrix or not.

public class SparseMatrixOrNot{  
   public static void main(String[] args){
      int[][] arr = {
         {1,0,3},
         {0,5,0},
         {7,8,9}
      };
      int cnt0 = 0;
      int totalEl = arr.length * arr[0].length;
      System.out.println("The matrix is defined as:");
      for(int i = 0; i < arr.length; i++){
         for(int j = 0; j < arr[i].length; j++){
            System.out.print(arr[i][j] + " ");
            if(arr[i][j] == 0){
               cnt0++;
            }
         }
         System.out.println();
      }
      if(cnt0 > totalEl / 2){
         System.out.println("\nYes, the matrix is a sparse matrix");
      } else{
         System.out.println("\nNo, the matrix is not a sparse matrix, contains more non-zero elements than zero elements.");
      }
   }
}

Output

Following is the output of the above code:

The matrix is defined as:
1 0 3
0 5 0
7 8 9
No, the matrix is not a sparse matrix, it contains more non-zero elements than zero elements.