Check if a given matrix is sparse or not

Last Updated : 20 Jul, 2022

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

Implementation:

C++

// 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";
}

Java

// 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.

Python3

# 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

// 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.

PHP

<?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.
?>

JavaScript

<script>
    // Javascript code to check 
    // if a matrix is
    // sparse.
    
    let MAX = 100;
       
    function isSparse(array, m, n)
    {
        let counter = 0;
       
        // Count number of zeros in the matrix
        for (let i = 0; i < m; ++i)
            for (let j = 0; j < n; ++j)
                if (array[i][j] == 0)
                    ++counter;
       
        return (counter > parseInt((m * n) / 2), 10);
    }
    
    let array = [ [ 1, 0, 3 ], 
                   [ 0, 0, 4 ], 
                   [ 6, 0, 0 ] ];
       
    let m = 3,
    n = 3;
    if (isSparse(array, m, n))
      document.write("Yes");
    else
      document.write("No");
    
</script>

Output

Yes

Time Complexity: O(m*n)
Auxiliary Space: O(1)

Check if a given matrix is Hankel or not

Aarti_Rathi and Vineet Joshi

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Check if a given matrix is sparse or not

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