FOR FREE YEAR SOLVED

Lower Triangular Matrix Checking

Back to Programming

Description

A matrix is said to be a lower triangular matrix if the elements above the principal diagonal is 0. The matrix should be a square matrix.

For example

 

This is an example of a lower triangular matrix as all the elements above the principal diagonal are 0.

Algorithm

INPUT: A matrix
OUTPUT: Whether it is a lower triangular matrix or nor

PROCESS:
Step 1: [taking the input]
	Read n [order of the square matrix]
	For i=0 to n-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 n-1 repeat
        		for j = i+1 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 "Lower triangular matrix"
    	else
        		print "Not a Lower Triangular Matrix"
	[End of ‘if’]
Step 3: Stop.

Code

TIME COMPLEXITY:

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

        for (j = i+1; j < n; j++)------ O(n-i-1)

        {

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

                f = 1;

                                }

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

        printf("\nLower triangular matrix");

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

        printf("\nNot a Lower Triangular Matrix");

c1,c2 and c3 is constant here so, the time complexity is O(n2).

Contributed by