Check if a given matrix is sparse or not

A matrix is a two dimensional data objects having m rows and n columns, therefore a total of m*n values. If most of the values of a matrix is 0 then we say that the matrix is sparse.
Consider a definition of Sparse where a matrix is considered sparse if number of 0s is more than half of the elements in 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 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.

CPP

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// CPP code to check if a matrix is
// sparse.
#include <iostream>
using namespace std;
  
const int MAX = 100;
  
bool isSparse(int array[][MAX], 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
int main()
{
    int array[][MAX] = { { 1, 0, 3 }, 
                        { 0, 0, 4 }, 
                        { 6, 0, 0 } };
  
    int m = 3,
        n = 3;
    if (isSparse(array, m, n))
        cout << "Yes";
    else
        cout << "No";
}

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Java

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// 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.

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Python3

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# Python 3 code to check
# if a matrix is
# sparse.
  
MAX = 100
   
def isSparse(array,m, n) :
      
    counter = 0
   
    # Count number of zeros
    # in the matrix
    for i in range(0,m) :
        for j in range(0,n) :
            if (array[i][j] == 0) :
                counter = counter + 1
   
    return (counter > 
            ((m * n) // 2))
  
# Driver Function
array = [ [ 1, 0, 3 ],
          [ 0, 0, 4 ],
          [ 6, 0, 0 ] ]
m = 3
n = 3
  
if (isSparse(array, m, n)) :
    print("Yes")
else :
    print("No")
      
      
# this code is contributed by
# Nikita tiwari

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C#

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// C# code to check if a matrix is
// sparse.
using System;
  
class GFG {
      
    static bool 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()
    {
        int [,]array = { { 1, 0, 3 }, 
                         { 0, 0, 4 }, 
                         { 6, 0, 0 } };
      
        int m = 3,
            n = 3;
              
        if (isSparse(array, m, n))
            Console.WriteLine("Yes");
        else
            Console.WriteLine("No");
    }
}
  
// This code is contributed by vt_m.

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PHP

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<?php
// PHP code to check if a matrix is
// sparse.
  
$MAX = 100;
  
function isSparse( $array, $m, $n)
{
    $counter = 0;
  
    // Count number of zeros
    // in the matrix
    for ($i = 0; $i < $m; ++$i)
        for ($j = 0; $j < $n; ++$j)
            if ($array[$i][$j] == 0)
                ++$counter;
  
    return ($counter > (($m * $n) / 2));
}
  
    // Driver Code
    $array = array(array(1, 0, 3), 
                   array(0, 0, 4), 
                   array(6, 0, 0));
  
    $m = 3;
    $n = 3;
    if (isSparse($array, $m, $n))
        echo "Yes";
    else
        echo "No";
  
// This code is contributed by anuj_67.
?>

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Output:

Yes

This article is contributed by Vineet Joshi. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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Improved By : vt_m



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