Program to check if matrix is upper triangular

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

Examples: 

Input : mat[4][4] = {{1, 3, 5, 3},
                     {0, 4, 6, 2},
                     {0, 0, 2, 5},
                     {0, 0, 0, 6}};
Output : Matrix is in Upper Triangular form.

Input : mat[4][4] = {{5, 6, 3, 6},
                     {0, 4, 6, 6},
                     {1, 0, 8, 5},
                     {0, 1, 0, 6}};
Output : Matrix is not in Upper Triangular form.

Implementation:

C++

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

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

// Driver function.
int main()
{
    int mat[N][N] = { { 1, 3, 5, 3 },
                      { 0, 4, 6, 2 },
                      { 0, 0, 2, 5 },
                      { 0, 0, 0, 6 } };
    if (isUpperTriangularMatrix(mat))
        cout << "Yes";
    else
        cout << "No";
    return 0;
}

Java

// Java Program to check upper
// triangular matrix.
import java.util.*;
import java.lang.*;

public class GfG
{
    private static final int N = 4;

    // Function to check matrix is in
    // upper triangular form or not.
    public static Boolean isUpperTriangularMatrix(int mat[][])
    {
        for (int i = 1; i < N ; i++)
            for (int j = 0; j < i; j++)
                if (mat[i][j] != 0)
                    return false;
        return true;
    }

    // driver function
    public static void main(String argc[]){
        int[][] mat= { { 1, 3, 5, 3 },
                       { 0, 4, 6, 2 },
                       { 0, 0, 2, 5 },
                       { 0, 0, 0, 6 } };

        if (isUpperTriangularMatrix(mat))
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}

/* This code is contributed by Sagar Shukla */

Python3

# Python3 Program to check upper
# triangular matrix.

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

# Driver function.
M = [[1,3,5,3],
    [0,4,6,2],
    [0,0,2,5],
    [0,0,0,6]]

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

# This code is contributed by Anurag Rawat

C#

// C# Program to check upper
// triangular matrix.
using System;

public class GfG
{
    private static int N = 4;

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

    // Driver function
    public static void Main(){
        int [,]mat= { { 1, 3, 5, 3 },
                    { 0, 4, 6, 2 },
                    { 0, 0, 2, 5 },
                    { 0, 0, 0, 6 } };

        if (isUpperTriangularMatrix(mat))
            Console.WriteLine("Yes");
        else
            Console.WriteLine("No");
    }
}

/* This code is contributed by vt_m */

PHP

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

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

    // Driver Code
    $mat = array(array(1, 3, 5, 3),
                 array(0, 4, 6, 2) ,
                 array(0, 0, 2, 5),
                 array(0, 0, 0, 6));

    if (isUpperTriangularMatrix($mat))
        echo "Yes";
    else
        echo"No";

// This code is contributed by anuj_67.
?>

Javascript

<script>
// Java script  Program to check upper
// triangular matrix.
let  N = 4;

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

    // driver function

        let mat= [[1, 3, 5, 3 ],
                    [ 0, 4, 6, 2 ],
                    [ 0, 0, 2, 5 ],
                    [ 0, 0, 0, 6 ]];

        if (isUpperTriangularMatrix(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.