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
// 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 = 3n = 3 if (isSparse(array, m, n)) : print("Yes") else : print("No") # this code is contributed by # Nikita tiwari |
C#
// 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. ?> |
Output:
Yes
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