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.
C++
#include <bits/stdc++.h>
#define N 4
using namespace std;
bool isLowerTriangularMatrix( int mat[N][N])
{
for ( int i = 0; i < N; i++)
for ( int j = i + 1; j < N; j++)
if (mat[i][j] != 0)
return false ;
return true ;
}
int main()
{
int mat[N][N] = { { 1, 0, 0, 0 },
{ 1, 4, 0, 0 },
{ 4, 6, 2, 0 },
{ 0, 4, 7, 6 } };
if (isLowerTriangularMatrix(mat))
cout << "Yes" ;
else
cout << "No" ;
return 0;
}
|
Java
import java.io.*;
class Lower_triangular
{
int N = 4 ;
boolean 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 ;
}
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 } };
if (ob.isLowerTriangularMatrix(mat))
System.out.println( "Yes" );
else
System.out.println( "No" );
}
}
|
Python3
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
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" )
|
C#
using System;
class Lower_triangular
{
int N = 4;
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 ;
}
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 } };
if (ob.isLowerTriangularMatrix(mat))
Console.WriteLine( "Yes" );
else
Console.WriteLine( "No" );
}
}
|
PHP
<?php
$N = 4;
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;
}
$mat = array ( array ( 1, 0, 0, 0 ),
array ( 1, 4, 0, 0 ),
array ( 4, 6, 2, 0 ),
array ( 0, 4, 7, 6 ));
if (isLowerTriangularMatrix( $mat ))
echo ( "Yes" );
else
echo ( "No" );
?>
|
Output:
Yes
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