C++ Program to Check If a Matrix Is a Lower Triangular Matrix

C++ program to check if a given matrix is a lower triangular has been shown here. A square matrix is considered a lower triangular matrix if all the elements above the main diagonal are Zero. The elements in the main diagonal may or may not be 0.

Examples:

In the given examples, (i), (ii), (iv) and (v) are lower triangular matrices as every element above the principal diagonal is 0 in each of these matrices. The matrix shown in (iii) is not a lower triangular matrix as one element above the principal diagonal is non-zero. The dotted lines have been drawn over the principal diagonals.

Page content(s):

1. Algorithm

2. Pseudocode

3. Time Complexity

4. Program & Output

1. Algorithm to Check If a Matrix Is a Lower Triangular Matrix

1. Take a matrix $A_{m\times n}$ as input

2. Check if $m=n$

3. If step [2] is false then display "Input matrix is not a square matrix!" and exit program

4. If step [2] is true, then

5. Check if $A_{i,j} \neq 0$ for each $i < j$ and $i \in [1, m]$ and $j \in [1, n]$

6. If step [5] is true for atleast one $A_{i,j}$ then display "The matrix is not a lower triangular matrix" and exit program.

7. If step [5] is false then display "The matrix is a lower triangular matrix" and exit program.

2. Pseudocode to Check If a Matrix Is a Lower Triangular Matrix

Input: A matrix $A_{m\times n}$

Output: A is lower triangular or not

1. Procedure lowerTriangularMatrix($A_{m\times n}$):

2. If $m == n$:

3. Repeat for each $i < j$ where $i \in [1, m]$ and $j \in [1, n]$

4. If $A_{i,j} \neq 0$:

5. Return Not a lower triangular matrix

6. Return A lower triangular matrix

7. Else:

8. Return It should be a square matrix

9. End Procedure

3. Time Complexity to Check If a Matrix Is a Lower Triangular Matrix

Time Complexity: O($mn$)

Where $m$ is the number of rows and $n$ is the number of columns in the matrices.

4. C++ Program to Check If a Matrix Is a Lower Triangular Matrix

Code has been copied

/**********************************
        alphabetacoder.com
  C++ Program to check if a matrix 
   is a lower triangular matrix
***********************************/
#include <iostream>

using namespace std;

int main() {
    // declare variables
    int m, n, i, j, flag = 0;
    int A[10][10] = {0};

    //take input of the order of the matrix
    cout << "Enter the number of rows and columns of matrix = ";
    cin >> m >> n;

    //take input of the first matrix
    cout << "Enter the elements of matrix of order " << m << " x " << n << " = " << endl;
    for (i = 0; i < m; i++)
        for (j = 0; j < n; j++)
            cin >> A[i][j];

    // check if the matrix is a square matrix or not
    // if it is square matrix, check if it is lower triangular or not
    if (m != n)
        cout << "\nInput matrix is not a square matrix!" << endl;
    else {
        // check if A is lower triangular or not by
        // finding an non-zero element above main diagonal 
        for (i = 0; i < m; i++) {
            for (j = i + 1; j < n; j++) {
                if (A[i][j] != 0) {
                    // non-zero element found
                    flag = 1;
                    break;
                }
            }
            // break the loop as non-zero element 
            // above main diagonal has been detected
            if (flag == 1)
                break;
        }

        // display the result
        if (flag == 0)
            cout << "\nIt is a lower triangular matrix!";
        else
            cout << "\nIt is not a lower triangular matrix!";
    }

    return 0;
}

Output

Case 1:

Enter the number of rows and columns of matrix = 4 4

Enter the elements of matrix of order 4 x 4 =

4 0 0 0

3 7 0 0

1 0 0 0

6 3 1 1

It is a lower triangular matrix!

Case 2:

Enter the number of rows and columns of matrix = 3 3

Enter the elements of matrix of order 3 x 3 =

0 0 6

8 5 0

2 1 0

It is not a lower triangular matrix!