Program to check if matrix is lower triangular

Given a square matrix and the task is to check the matrix is in lower triangular form or not. A square matrix is called lower triangular if all the entries above the main diagonal are zero. 

Examples: 

Input : mat[4][4] = {{1, 0, 0, 0},
                     {1, 4, 0, 0},
                     {4, 6, 2, 0},
                     {0, 4, 7, 6}};
Output : Matrix is in lower triangular form.

Input : mat[4][4] = {{1, 0, 0, 0},
                     {4, 3, 0, 1},
                     {7, 9, 2, 0},
                     {8, 5, 3, 6}};
Output : Matrix is not in lower triangular form.

Implementation:

C++

// Program to check lower
// triangular matrix.
#include <bits/stdc++.h>
#define N 4
using namespace std;

// Function to check matrix is in
// lower triangular form or not.
bool isLowerTriangularMatrix(int mat[N][N])
{
    for (int i = 0; i < N-1; i++)
        for (int j = i + 1; j < N; j++)
            if (mat[i][j] != 0)
                return false;
    return true;
}

// Driver function.
int main()
{
    int mat[N][N] = { { 1, 0, 0, 0 },
                      { 1, 4, 0, 0 },
                      { 4, 6, 2, 0 },
                      { 0, 4, 7, 6 } };

    // Function call
    if (isLowerTriangularMatrix(mat))
        cout << "Yes";
    else
        cout << "No";
    return 0;
}

Java

// Java Program to check for
// a lower triangular matrix.
import java.io.*;

class Lower_triangular
{
    int N = 4;

    // Function to check matrix is
    // in lower triangular form or not.
    boolean isLowerTriangularMatrix(int mat[][])
    {
        for (int i = 0; i < N-1; i++)
            for (int j = i + 1; j < N; j++)
                if (mat[i][j] != 0)
                    return false;

        return true;
    }

    // Driver function.
    public static void main(String args[])
    {
        Lower_triangular ob = new Lower_triangular();
        int mat[][] = { { 1, 0, 0, 0 },
                        { 1, 4, 0, 0 },
                        { 4, 6, 2, 0 },
                        { 0, 4, 7, 6 } };

        // Function call
        if (ob.isLowerTriangularMatrix(mat))
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}

// This code is contributed by Anshika Goyal.

Python3

# Python3 Program to check
# lower triangular matrix.

# Function to check matrix
# is in lower triangular
def islowertriangular(M):
    for i in range(0, len(M)):
        for j in range(i + 1, len(M)):
            if(M[i][j] != 0):
                    return False
    return True

# Driver function.
M = [[1,0,0,0],
     [1,4,0,0],
     [4,6,2,0],
     [0,4,7,6]]

if islowertriangular(M):
    print ("Yes")
else:
    print ("No")

# This code is contributed by Anurag Rawat

C#

// C# program to check for
// a lower triangular matrix.
using System;

class Lower_triangular
{
    int N = 4;

    // Function to check matrix is
    // in lower triangular form or not.
    bool isLowerTriangularMatrix(int[, ] mat)
    {
        for (int i = 0; i < N; i++)
            for (int j = i + 1; j < N; j++)
                if (mat[i, j] != 0)
                    return false;

        return true;
    }

    // Driver function.
    public static void Main()
    {
        Lower_triangular ob = new Lower_triangular();
        int[, ] mat = { { 1, 0, 0, 0 },
                        { 1, 4, 0, 0 },
                        { 4, 6, 2, 0 },
                        { 0, 4, 7, 6 } };

        // Function call
        if (ob.isLowerTriangularMatrix(mat))
            Console.WriteLine("Yes");
        else
            Console.WriteLine("No");
    }
}

// This code is contributed by vt_m.

PHP

<?php
// PHP Program to check lower
// triangular matrix.
$N = 4;

// Function to check matrix is in
// lower triangular form or not.
function isLowerTriangularMatrix($mat)
{
    global $N;
    for ($i = 0; $i < $N; $i++)
        for ($j = $i + 1; $j < $N; $j++)
            if ($mat[$i][$j] != 0)
                return false;
    return true;
}

// Driver Code
$mat = array(array( 1, 0, 0, 0 ),
             array( 1, 4, 0, 0 ),
             array( 4, 6, 2, 0 ),
             array( 0, 4, 7, 6 ));


// Function call
if (isLowerTriangularMatrix($mat))
    echo("Yes");
else
    echo("No");

// This code is contributed by Ajit.
?>

Javascript

<script>
// Java  script Program to check for
// a lower triangular matrix.

    let N = 4;

    // Function to check matrix is
    // in lower triangular form or not.
    function isLowerTriangularMatrix(mat)
    {
        for (let i = 0; i < N-1; i++)
            for (let j = i + 1; j < N; j++)
                if (mat[i][j] != 0)
                    return false;

        return true;
    }

    // Driver function.


        let mat = [[ 1, 0, 0, 0 ],
                        [ 1, 4, 0, 0 ],
                        [ 4, 6, 2, 0 ],
                        [ 0, 4, 7, 6 ]];

        // Function call
        if (isLowerTriangularMatrix(mat))
            document.write("Yes");
        else
            document.write("No");


// contributed by sravan kumar
</script>

Output

Yes

Time Complexity: O(n²), where n represents the number of rows and columns of the matrix.
Auxiliary Space: O(1), no extra space is required, so it is a constant.