# Program to Determine Whether a Given Matrix is a Sparse Matrix

Program to Determine Whether a Given Matrix is an Sparse Matrix on fibonacci, factorial, prime, armstrong, swap, reverse, search, sort, stack, queue, array, linkedlist, tree, graph etc.

## Program to determine whether a given matrix is a sparse matrix

### Explanation

In this program, we need to check whether the given matrix is the sparse matrix.

### Sparse Matrix

A matrix is said to be sparse matrix if most of the elements of that matrix are 0. It implies that it contains very less non-zero elements.

To check whether the given matrix is the sparse matrix or not, we first count the number of zero elements present in the matrix. Then calculate the size of the matrix. For the matrix to be sparse, count of zero elements present in an array must be greater than size/2.

Number of zeroes present in above matrix is 6 and size of the matrix is 3 * 3 = 9. Since, 6 > 4.5 that means, most elements of given array are zero. Hence, the above matrix is a sparse matrix.

### Algorithm

1. Declare and initialize a two-dimensional array a.
2. Calculate the number of rows and columns present in the given array and store it in variables rows and cols respectively.
3. Loop through the array and count the number of zeroes present in the given array and store in the variable count.
4. Calculate the size of the array by multiplying the number of rows with many columns of the array.
5. If the count is greater than size/2, given matrix is the sparse matrix. That means, most of the elements of the array are zeroes.
6. Else, the matrix is not a sparse matrix.

### Python

```#Initialize matrix a
a = [
[4, 0, 0],
[0, 5, 0],
[0, 0, 6]
];

count = 0;

#Calculates number of rows and columns present in given matrix
rows = len(a);
cols = len(a[0]);

#Calculates the size of the array

size = rows * cols;

#Count all zero element present in matrix
for i in range(0, rows):
for j in range(0, cols):
if(a[i][j] == 0):
count = count + 1;

if(count > (size/2)):
print("Given matrix is a sparse matrix");
else:
print("Given matrix is not a sparse matrix");
```

Output:

```Given matrix is a sparse matrix
```

### C

```#include <stdio.h>

int main()
{
int rows, cols, size, count = 0;

//Initialize matrix a
int a[][3] = {
{4, 0, 0},
{0, 5, 0},
{0, 0, 6}
};

//Calculates number of rows and columns present in given matrix
rows = (sizeof(a)/sizeof(a[0]));
cols = (sizeof(a)/sizeof(a[0][0]))/rows;

//Calculates the size of array
size = rows * cols;

//Count all zero element present in matrix
for(int i = 0; i < rows; i++){
for(int j = 0; j < cols; j++){
if(a[i][j] == 0)
count++;
}
}

if(count > (size/2))
printf("Given matrix is a sparse matrix");
else
printf("Given matrix is not a sparse matrix");

return 0;
}
```

Output:

```Given matrix is a sparse matrix
```

### JAVA

```public class SparseMatrix
{
public static void main(String[] args) {
int rows, cols, size, count = 0;

//Initialize matrix a
int a[][] = {
{4, 0, 0},
{0, 5, 0},
{0, 0, 6}
};

//Calculates number of rows and columns present in given matrix
rows = a.length;
cols = a[0].length;

//Calculates the size of array
size = rows * cols;

//Count all zero element present in matrix
for(int i = 0; i < rows; i++){
for(int j = 0; j < cols; j++){
if(a[i][j] == 0)
count++;
}
}

if(count > (size/2))
System.out.println("Given matrix is a sparse matrix");
else
System.out.println("Given matrix is not a sparse matrix");
}
}
```

Output:

```Given matrix is a sparse matrix
```

### C#

```using System;

public class SparseMatrix
{
public static void Main()
{
int rows, cols, size, count = 0;

//Initialize matrix a
int[,] a = {
{4, 0, 0},
{0, 5, 0},
{0, 0, 6}
};

//Calculates number of rows and columns present in given matrix
rows = a.GetLength(0);
cols = a.GetLength(1);

//Calculates the size of array
size = rows * cols;

//Count all zero element present in matrix
for(int i = 0; i < rows; i++){
for(int j = 0; j < cols; j++){
if(a[i,j] == 0)
count++;
}
}

if(count > (size/2))
Console.WriteLine("Given matrix is a sparse matrix");
else
Console.WriteLine("Given matrix is not a sparse matrix");
}
}
```

Output:

```Given matrix is a sparse matrix
```

### PHP

```<!DOCTYPE html>
<html>
<body>
<?php
//Initialize matrix a
\$a = array(
array(4, 0, 0),
array(0, 5, 0),
array(0, 0, 6)
);

\$count = 0;

//Calculates number of rows and columns present in given matrix
\$rows = count(\$a);
\$cols = count(\$a[0]);

//Calculates the size of array
\$size = \$rows * \$cols;

//Count all zero element present in matrix
for(\$i = 0; \$i < \$rows; \$i++){
for(\$j = 0; \$j < \$cols; \$j++){
if(\$a[\$i][\$j] == 0)
\$count++;
}
}

if(\$count > (\$size/2))
print("Given matrix is a sparse matrix");
else
print("Given matrix is not a sparse matrix");
?>
</body>
</html>
```

Output:

```Given matrix is a sparse matrix
```

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