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# Nelson Number Program

The Nelson number problem is an interesting mathematical concept. A Nelson number is a number that is divisible by 111. It is named after the mathematician Edward Nelson, who worked in the field of logic and mathematical physics. In this problem, we are given a number, and our task is to determine whether it is a Nelson number or not.

## Problem Statement

Given an integer input, we need to check whether it is a Nelson number or not. If the number is divisible by 111, then it is a Nelson number; otherwise, it is not.

## Explanation with Suitable Example

Let's take an example to understand the Nelson number problem better. Consider the number 666. To check if it is a Nelson number, we divide it by 111:

666 ÷ 111 = 6

Since the remainder is 0, 666 is a Nelson number.

## Standard Pseudocode

``````function isNelsonNumber(number):
if number % 111 == 0:
return True
else:
return False

``````

## Algorithm with Explanation

1. Start the program.
2. Define the function `isNelsonNumber(number)` that takes an integer `number` as input.
3. Check if the `number` is divisible by 111 using the modulo operator (`%`).
4. If the result of `number % 111` is equal to 0, return `True`, indicating that the number is a Nelson number.
5. If the result is not 0, return `False`, indicating that the number is not a Nelson number.
6. End the function.
7. In the `main()` function, call the `isNelsonNumber()` function for different test cases to check if they are Nelson numbers or not.
8. Print the result for each test case.
9. End the program.

## Code Solution

Here given code implementation process.

``````// C program
// Nelson Number Program
#include <stdio.h>

// Determine that given number is Nelson Number or not
void isNelsonNo(int number)
{
if ((number % 111) == 0)
{
// When number is nelson
printf(" %d is nelson number \n", number);
}
else
{
printf(" %d is not nelson number \n", number);
}
}
int main()
{
// Test Case
isNelsonNo(444);
isNelsonNo(113);
isNelsonNo(333);
return 0;
}``````

#### input

`````` 444 is nelson number
113 is not nelson number
333 is nelson number``````
``````/*
Java Program for
Nelson Number
*/
class NelsonNo
{
// Determine that given number is Nelson Number or not
public void isNelsonNo(int number)
{
if ((number % 111) == 0)
{
// When number is nelson
System.out.println(" [" + number + "] is nelson number");
}
else
{
System.out.println(" [" + number + "] is not nelson number");
}
}
public static void main(String[] args)
{
// Test Case
}
}``````

#### input

`````` [444] is nelson number
[113] is not nelson number
[333] is nelson number``````
``````// Include header file
#include <iostream>
using namespace std;

/*
C++ Program for
Nelson Number
*/

class NelsonNo
{
public:
// Determine that given number is Nelson Number or not
void isNelsonNo(int number)
{
if ((number % 111) == 0)
{
// When number is nelson
cout << " [" << number << "] is nelson number" << endl;
}
else
{
cout << " [" << number << "] is not nelson number" << endl;
}
}
};
int main()
{
// Test Case
return 0;
}``````

#### input

`````` [444] is nelson number
[113] is not nelson number
[333] is nelson number``````
``````// Include namespace system
using System;
/*
Csharp Program for
Nelson Number
*/
public class NelsonNo
{
// Determine that given number is Nelson Number or not
public void isNelsonNo(int number)
{
if ((number % 111) == 0)
{
// When number is nelson
Console.WriteLine(" [" + number + "] is nelson number");
}
else
{
Console.WriteLine(" [" + number + "] is not nelson number");
}
}
public static void Main(String[] args)
{
// Test Case
}
}``````

#### input

`````` [444] is nelson number
[113] is not nelson number
[333] is nelson number``````
``````<?php
/*
Php Program for
Nelson Number
*/
class NelsonNo
{
// Determine that given number is Nelson Number or not
public	function isNelsonNo(\$number)
{
if ((\$number % 111) == 0)
{
// When number is nelson
echo " [".\$number.
"] is nelson number".
"\n";
}
else
{
echo " [".\$number.
"] is not nelson number".
"\n";
}
}
}

function main()
{
// Test Case
}
main();``````

#### input

`````` [444] is nelson number
[113] is not nelson number
[333] is nelson number``````
``````/*
Node JS Program for
Nelson Number
*/
class NelsonNo
{
// Determine that given number is Nelson Number or not
isNelsonNo(number)
{
if ((number % 111) == 0)
{
// When number is nelson
console.log(" [" + number + "] is nelson number");
}
else
{
console.log(" [" + number + "] is not nelson number");
}
}
}

function main()
{
// Test Case
}
main();``````

#### input

`````` [444] is nelson number
[113] is not nelson number
[333] is nelson number``````
``````#  Python 3 Program for
#  Nelson Number
class NelsonNo :
#  Determine that given number is Nelson Number or not
def isNelsonNo(self, number) :
if ((number % 111) == 0) :
#  When number is nelson
print(" [", number ,"] is nelson number")
else :
print(" [", number ,"] is not nelson number")

def main() :
#  Test Case

if __name__ == "__main__": main()``````

#### input

`````` [ 444 ] is nelson number
[ 113 ] is not nelson number
[ 333 ] is nelson number``````
``````#  Ruby Program for
#  Nelson Number
class NelsonNo
#  Determine that given number is Nelson Number or not
def isNelsonNo(number)
if ((number % 111) == 0)
#  When number is nelson
print(" [", number ,"] is nelson number", "\n")
else
print(" [", number ,"] is not nelson number", "\n")
end

end

end

def main()
#  Test Case
end

main()``````

#### input

`````` [444] is nelson number
[113] is not nelson number
[333] is nelson number
``````
``````/*
Scala Program for
Nelson Number
*/
class NelsonNo()
{
// Determine that given number is Nelson Number or not
def isNelsonNo(number: Int): Unit = {
if ((number % 111) == 0)
{
// When number is nelson
println(" [" + number + "] is nelson number");
}
else
{
println(" [" + number + "] is not nelson number");
}
}
}
object Main
{
def main(args: Array[String]): Unit = {
var task: NelsonNo = new NelsonNo();
// Test Case
}
}``````

#### input

`````` [444] is nelson number
[113] is not nelson number
[333] is nelson number``````
``````/*
Swift 4 Program for
Nelson Number
*/
class NelsonNo
{
// Determine that given number is Nelson Number or not
func isNelsonNo(_ number: Int)
{
if ((number % 111) == 0)
{
// When number is nelson
print(" [", number ,"] is nelson number");
}
else
{
print(" [", number ,"] is not nelson number");
}
}
}
func main()
{
// Test Case
}
main();``````

#### input

`````` [ 444 ] is nelson number
[ 113 ] is not nelson number
[ 333 ] is nelson number``````
``````/*
Kotlin Program for
Nelson Number
*/
class NelsonNo
{
// Determine that given number is Nelson Number or not
fun isNelsonNo(number: Int): Unit
{
if ((number % 111) == 0)
{
// When number is nelson
println(" [" + number + "] is nelson number");
}
else
{
println(" [" + number + "] is not nelson number");
}
}
}
fun main(args: Array < String > ): Unit
{
// Test Case
}``````

#### input

`````` [444] is nelson number
[113] is not nelson number
[333] is nelson number``````

## Resultant Output Explanation

Here's the explanation of each test case:

1. Test Case 1 (444): 444 is divisible by 111, so it is a Nelson number.
2. Test Case 2 (113): 113 is not divisible by 111, so it is not a Nelson number.
3. Test Case 3 (333): 333 is divisible by 111, so it is a Nelson number.

## Time Complexity of the Code

The time complexity of the provided code is O(1) because the function `isNelsonNumber()` performs a constant number of operations, regardless of the magnitude of the input number. The operations involved are simple arithmetic operations and a single modulo operation. Thus, the time complexity remains constant for any input size.

## Comment

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