Program to check if matrix is lower triangular
Last Updated :
20 Feb, 2023
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 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 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# 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 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.
?>
<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>
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.