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Null Matrix

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Description

A matrix is said to be a null matrix if all the elements of a matrix is 0. If any one of the matrix elements is not zero then it will not be called a null matrix.

For example:

Algorithm

INPUT: A matrix
OUTPUT: Whether it is an upper triangular matrix or nor

PROCESS:
Step 1: [taking the input]
	Read m, n [the rows and columns of the matrix]
	For i=0 to m-1 repeat
		For j=0 to n-1 repeat
			Read a[i][j]
		[End of ‘for’ loop]
	[End of ‘for’ loop]
Step 2: [Checking and printing]
	for i = 0 to m-1 repeat
        		for j = 0 to n-1 repeat
            			if a[i][j] ≠ 0 then
                			Set f <- 1
			[End of ‘if’]
		[End of ‘for’ loop]
	[End of ‘for’ loop]
   	if f = 0 then
        		print "Null matrix"
    	else
        		print "Not a null Matrix"
[End of ‘if’]
Step 3: Stop.

Code

TIME COMPLEXITY:

for (i = 0; i < m; i++)------------------ O(m)

for (j = 0; j < n; j++)------------- O(n)

{

if (a[i][j] != 0)------------------ O(c1)

f = 1;

}

if (f == 0)--------------------- O(c2)

printf("\nNull matrix");

else---------------------------- O(c3)

printf("\nNot a null Matrix");

the time complexity is O(m*n). if the number of rows and columns are same then the time complexity will be O( $n^{2}$ ).

Contributed by

Souvick Das

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