Program to check if matrix is lower triangular (original) (raw)

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

// 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

JavaScript

`

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.