Krishnamurthy number program

Krishnamurthy numbers, also known as Strong Numbers, are special types of numbers in mathematics. A number is said to be a Krishnamurthy number if the sum of the factorial of its individual digits is equal to the number itself. For example, let's take the number 145:

1! + 4! + 5! = 1 + 24 + 120 = 145

In this case, 145 is a Krishnamurthy number because the sum of the factorials of its digits is equal to the number itself.

The problem statement can be summarized as follows: Given a positive integer, we need to determine if it is a Krishnamurthy number or not.

Explanation with Suitable Example

Let's understand the problem statement with the example of the number 145.

1. Extract the individual digits of the number: 1, 4, and 5.
2. Calculate the factorial of each digit: 1! = 1, 4! = 24, and 5! = 120.
3. Sum the factorials: 1 + 24 + 120 = 145.
4. Check if the sum obtained is equal to the original number (145 in this case).
5. Since the sum (145) is equal to the original number (145), we can conclude that 145 is a Krishnamurthy number.

Standard Pseudocode

Function isKrishnamurthyNo(number):
    If number < 1:
        Return
    Initialize i = 1, remainder = 0, sum = 0
    Initialize an array factorial[10] to store factorials of digits
    factorial[0] = 1
    For i = 1 to 9:
        factorial[i] = factorial[i-1] * i
    Set i = number
    While i != 0:
        remainder = i % 10
        sum += factorial[remainder]
        i /= 10
    If sum == number:
        Print "number is a Krishnamurthy number"
    Else:
        Print "number is not a Krishnamurthy number"

Algorithm with Proper Explanation

1. The function isKrishnamurthyNo takes an integer number as input and checks if it is a Krishnamurthy number or not.

2. The function begins by checking if the input number is less than 1. If so, it immediately returns, as negative or zero values cannot be Krishnamurthy numbers.

3. It then initializes some variables: i (for iteration), remainder (to store the last digit of i), and sum (to store the sum of factorials of digits).

4. The function also initializes an array factorial[10] to store the factorials of digits from 0 to 9. factorial[0] is set to 1 since 0! is 1.

5. Using a loop, the function calculates and stores the factorials of digits from 1 to 9 in the factorial array.

6. The variable i is set to the value of the input number, and now the function proceeds to calculate the sum of the factorials of its digits.

7. The while loop runs until i becomes 0. In each iteration, it extracts the last digit of i using the modulo operation and finds its factorial from the factorial array. The factorial is added to the sum, and the last digit is removed from i by dividing it by 10.

8. After the while loop, the function checks if the sum is equal to the original number. If they are equal, it means the number is a Krishnamurthy number and is printed as such. Otherwise, the number is not a Krishnamurthy number, and this is also printed.

Code Solution

Here given code implementation process.

• C
• Java
• C++
• C#
• Php
• Node Js
• Python
• Ruby
• Scala
• Swift 4
• Kotlin

// C program
// krishnamurthy number 
#include <stdio.h>

// Check whether given number is krishnamurthy number or not
void isKrishnamurthyNo(int number)
{
	if (number < 1)
	{
		return;
	}
	// Define some auxiliary variable
	int i = 1;
	int remainder = 0;
	int sum = 0;
	// Auxiliary space to store factorial
	int factorial[10];
	// First factorial
	factorial[0] = 1;
	// Calculate the factorial of range (1..9)
	for (i = 1; i <= 9; ++i)
	{
		factorial[i] = factorial[i - 1] *i;
	}
	i = number;
	// Calculate digit factorial sum of given number
	while (i != 0)
	{
		// Get the last digit
		remainder = i % 10;
		// Factorial sum
		sum += factorial[remainder];
		// Remove last digit
		i /= 10;
	}
	if (sum == number)
	{
		printf(" %d is krishnamurthy number \n", number);
	}
	else
	{
		printf(" %d is not krishnamurthy number \n", number);
	}
}
int main()
{
	// Test Case
	isKrishnamurthyNo(40585);
	isKrishnamurthyNo(65);
	isKrishnamurthyNo(145);
	return 0;
}

 40585 is krishnamurthy number
 65 is not krishnamurthy number
 145 is krishnamurthy number

/*
  Java Program for
  Krishnamurthy number 
*/
class FlaviusNumber
{
	// Auxiliary space to store factorial
	int[] factorial;
	public FlaviusNumber()
	{
		factorial = new int[10];
		this.findFactorial();
	}
	public void findFactorial()
	{
		int i = 0;
		// First factorial
		factorial[0] = 1;
		// Calculate the factorial of range (1..9)
		for (i = 1; i <= 9; ++i)
		{
			factorial[i] = factorial[i - 1] * i;
		}
	}
	// Check whether given number is krishnamurthy number or not
	public void isKrishnamurthyNo(int number)
	{
		if (number < 1)
		{
			return;
		}
		// Define some auxiliary variable
		int i = number;
		int remainder = 0;
		int sum = 0;
		// Calculate digit factorial sum of given number
		while (i != 0)
		{
			// Get the last digit
			remainder = i % 10;
			// Factorial sum
			sum += factorial[remainder];
			// Remove last digit
			i /= 10;
		}
		if (sum == number)
		{
          	// When result is krishnamurthy number
			System.out.println(" [" + number + "] is krishnamurthy number");
		}
		else
		{
			System.out.println(" [" + number + "] is not krishnamurthy number");
		}
	}
	public static void main(String[] args)
	{
		FlaviusNumber task = new FlaviusNumber();
		// Test case
		task.isKrishnamurthyNo(40585);
		task.isKrishnamurthyNo(65);
		task.isKrishnamurthyNo(145);
	}
}

 [40585] is krishnamurthy number
 [65] is not krishnamurthy number
 [145] is krishnamurthy number

// Include header file
#include <iostream>

using namespace std;
/*
  C++ Program for
  Krishnamurthy number 
*/
class FlaviusNumber
{
	public:
	// Auxiliary space to store factorial
	int *factorial;
	FlaviusNumber()
	{
		this->factorial = new int[10];
		this->findFactorial();
	}
	void findFactorial()
	{
		int i = 0;
		// First factorial
		this->factorial[0] = 1;
		// Calculate the factorial of range (1..9)
		for (i = 1; i <= 9; ++i)
		{
			this->factorial[i] = this->factorial[i - 1] * i;
		}
	}
	// Check whether given number is krishnamurthy number or not
	void isKrishnamurthyNo(int number)
	{
		if (number < 1)
		{
			return;
		}
		// Define some auxiliary variable
		int i = number;
		int remainder = 0;
		int sum = 0;
		// Calculate digit factorial sum of given number
		while (i != 0)
		{
			// Get the last digit
			remainder = i % 10;
			// Factorial sum
			sum += this->factorial[remainder];
			// Remove last digit
			i /= 10;
		}
		if (sum == number)
		{
			// When result is krishnamurthy number
			cout << " [" << number << "] is krishnamurthy number" << endl;
		}
		else
		{
			cout << " [" << number << "] is not krishnamurthy number" << endl;
		}
	}
};
int main()
{
	FlaviusNumber *task = new FlaviusNumber();
	// Test case
	task->isKrishnamurthyNo(40585);
	task->isKrishnamurthyNo(65);
	task->isKrishnamurthyNo(145);
	return 0;
}

 [40585] is krishnamurthy number
 [65] is not krishnamurthy number
 [145] is krishnamurthy number

// Include namespace system
using System;
/*
  Csharp Program for
  Krishnamurthy number 
*/
public class FlaviusNumber
{
	// Auxiliary space to store factorial
	int[] factorial;
	public FlaviusNumber()
	{
		this.factorial = new int[10];
		this.findFactorial();
	}
	public void findFactorial()
	{
		int i = 0;
		// First factorial
		this.factorial[0] = 1;
		// Calculate the factorial of range (1..9)
		for (i = 1; i <= 9; ++i)
		{
			this.factorial[i] = this.factorial[i - 1] * i;
		}
	}
	// Check whether given number is krishnamurthy number or not
	public void isKrishnamurthyNo(int number)
	{
		if (number < 1)
		{
			return;
		}
		// Define some auxiliary variable
		int i = number;
		int remainder = 0;
		int sum = 0;
		// Calculate digit factorial sum of given number
		while (i != 0)
		{
			// Get the last digit
			remainder = i % 10;
			// Factorial sum
			sum += this.factorial[remainder];
			// Remove last digit
			i /= 10;
		}
		if (sum == number)
		{
			// When result is krishnamurthy number
			Console.WriteLine(" [" + number + "] is krishnamurthy number");
		}
		else
		{
			Console.WriteLine(" [" + number + "] is not krishnamurthy number");
		}
	}
	public static void Main(String[] args)
	{
		FlaviusNumber task = new FlaviusNumber();
		// Test case
		task.isKrishnamurthyNo(40585);
		task.isKrishnamurthyNo(65);
		task.isKrishnamurthyNo(145);
	}
}

 [40585] is krishnamurthy number
 [65] is not krishnamurthy number
 [145] is krishnamurthy number

<?php
/*
  Php Program for
  Krishnamurthy number 
*/
class FlaviusNumber
{
	// Auxiliary space to store factorial
	public $factorial;
	public function __construct()
	{
		$this->factorial = array_fill(0, 10, 0);
		$this->findFactorial();
	}
	public function findFactorial()
	{
		$i = 0;
		// First factorial
		$this->factorial[0] = 1;
		// Calculate the factorial of range (1..9)
		for ($i = 1; $i <= 9; ++$i)
		{
			$this->factorial[$i] = $this->factorial[$i - 1] * $i;
		}
	}
	// Check whether given number is krishnamurthy number or not
	public	function isKrishnamurthyNo($number)
	{
		if ($number < 1)
		{
			return;
		}
		// Define some auxiliary variable
		$i = $number;
		$remainder = 0;
		$sum = 0;
		// Calculate digit factorial sum of given number
		while ($i != 0)
		{
			// Get the last digit
			$remainder = $i % 10;
			// Factorial sum
			$sum += $this->factorial[$remainder];
			// Remove last digit
			$i = (int)($i / 10);
		}
		if ($sum == $number)
		{
			// When result is krishnamurthy number
			echo " [".$number."] is krishnamurthy number"."\n";
		}
		else
		{
			echo " [".$number."] is not krishnamurthy number"."\n";
		}
	}
}

function main()
{
	$task = new FlaviusNumber();
	// Test case
	$task->isKrishnamurthyNo(40585);
	$task->isKrishnamurthyNo(65);
	$task->isKrishnamurthyNo(145);
}
main();

 [40585] is krishnamurthy number
 [65] is not krishnamurthy number
 [145] is krishnamurthy number

/*
  Node JS Program for
  Krishnamurthy number 
*/
class FlaviusNumber
{
	constructor()
	{
		this.factorial = Array(10).fill(0);
		this.findFactorial();
	}
	findFactorial()
	{
		var i = 0;
		// First factorial
		this.factorial[0] = 1;
		// Calculate the factorial of range (1..9)
		for (i = 1; i <= 9; ++i)
		{
			this.factorial[i] = this.factorial[i - 1] * i;
		}
	}
	// Check whether given number is krishnamurthy number or not
	isKrishnamurthyNo(number)
	{
		if (number < 1)
		{
			return;
		}
		// Define some auxiliary variable
		var i = number;
		var remainder = 0;
		var sum = 0;
		// Calculate digit factorial sum of given number
		while (i != 0)
		{
			// Get the last digit
			remainder = i % 10;
			// Factorial sum
			sum += this.factorial[remainder];
			// Remove last digit
			i = parseInt(i / 10);
		}
		if (sum == number)
		{
			// When result is krishnamurthy number
			console.log(" [" + number + "] is krishnamurthy number");
		}
		else
		{
			console.log(" [" + number + "] is not krishnamurthy number");
		}
	}
}

function main()
{
	var task = new FlaviusNumber();
	// Test case
	task.isKrishnamurthyNo(40585);
	task.isKrishnamurthyNo(65);
	task.isKrishnamurthyNo(145);
}
main();

 [40585] is krishnamurthy number
 [65] is not krishnamurthy number
 [145] is krishnamurthy number

#  Python 3 Program for
#  Krishnamurthy number 
class FlaviusNumber :

	def __init__(self) :
		self.factorial = [0] * (10)
		self.findFactorial()
	
	def findFactorial(self) :
		i = 1
		#  First factorial
		self.factorial[0] = 1
		#  Calculate the factorial of range (1..9)
		while (i <= 9) :
			self.factorial[i] = self.factorial[i - 1] * i
			i += 1
		
	
	#  Check whether given number is krishnamurthy number or not
	def isKrishnamurthyNo(self, number) :
		if (number < 1) :
			return
		
		i = number
		remainder = 0
		sum = 0
		#  Calculate digit factorial sum of given number
		while (i != 0) :
			#  Get the last digit
			remainder = i % 10
			#  Factorial sum
			sum += self.factorial[remainder]
			#  Remove last digit
			i = int(i / 10)
		
		if (sum == number) :
			#  When result is krishnamurthy number
			print(" [", number ,"] is krishnamurthy number")
		else :
			print(" [", number ,"] is not krishnamurthy number")
		
	

def main() :
	task = FlaviusNumber()
	#  Test case
	task.isKrishnamurthyNo(40585)
	task.isKrishnamurthyNo(65)
	task.isKrishnamurthyNo(145)

if __name__ == "__main__": main()

 [ 40585 ] is krishnamurthy number
 [ 65 ] is not krishnamurthy number
 [ 145 ] is krishnamurthy number

#  Ruby Program for
#  Krishnamurthy number 
class FlaviusNumber 
	# Define the accessor and reader of class FlaviusNumber
	attr_reader :factorial
	attr_accessor :factorial
	#  Auxiliary space to store factorial
	def initialize() 
		self.factorial = Array.new(10) {0}
		self.findFactorial()
	end

	def findFactorial() 
		i = 0
		#  First factorial
		self.factorial[0] = 1
		#  Calculate the factorial of range (1..9)
		i = 1
		while (i <= 9) 
			self.factorial[i] = self.factorial[i - 1] * i
			i += 1
		end

	end

	#  Check whether given number is krishnamurthy number or not
	def isKrishnamurthyNo(number) 
		if (number < 1) 
			return
		end

		#  Define some auxiliary variable
		i = number
		remainder = 0
		sum = 0
		#  Calculate digit factorial sum of given number
		while (i != 0) 
			#  Get the last digit
			remainder = i % 10
			#  Factorial sum
			sum += self.factorial[remainder]
			#  Remove last digit
			i = i / 10
		end

		if (sum == number) 
			#  When result is krishnamurthy number
			print(" [", number ,"] is krishnamurthy number", "\n")
		else 
			print(" [", number ,"] is not krishnamurthy number", "\n")
		end

	end

end

def main() 
	task = FlaviusNumber.new()
	#  Test case
	task.isKrishnamurthyNo(40585)
	task.isKrishnamurthyNo(65)
	task.isKrishnamurthyNo(145)
end

main()

 [40585] is krishnamurthy number
 [65] is not krishnamurthy number
 [145] is krishnamurthy number

/*
  Scala Program for
  Krishnamurthy number 
*/
class FlaviusNumber(var factorial: Array[Int])
{
	def this()
	{
		this(Array.fill[Int](10)(0));
      	this.findFactorial();
	}
	def findFactorial(): Unit = {
		var i: Int = 0;
		// First factorial
		factorial(0) = 1;
		// Calculate the factorial of range (1..9)
		i = 1;
		while (i <= 9)
		{
			factorial(i) = factorial(i - 1) * i;
			i += 1;
		}
	}
	// Check whether given number is krishnamurthy number or not
	def isKrishnamurthyNo(number: Int): Unit = {
		if (number < 1)
		{
			return;
		}
		// Define some auxiliary variable
		var i: Int = number;
		var remainder: Int = 0;
		var sum: Int = 0;
		// Calculate digit factorial sum of given number
		while (i != 0)
		{
			// Get the last digit
			remainder = i % 10;
			// Factorial sum
			sum += factorial(remainder);
			// Remove last digit
			i = (i / 10).toInt;
		}
		if (sum == number)
		{
			// When result is krishnamurthy number
			println(" [" + number + "] is krishnamurthy number");
		}
		else
		{
			println(" [" + number + "] is not krishnamurthy number");
		}
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var task: FlaviusNumber = new FlaviusNumber();
		// Test case
		task.isKrishnamurthyNo(40585);
		task.isKrishnamurthyNo(65);
		task.isKrishnamurthyNo(145);
	}
}

 [40585] is krishnamurthy number
 [65] is not krishnamurthy number
 [145] is krishnamurthy number

/*
  Swift 4 Program for
  Krishnamurthy number 
*/
class FlaviusNumber
{
	// Auxiliary space to store factorial
	var factorial: [Int];
	init()
	{
		self.factorial = Array(repeating: 0, count: 10);
		self.findFactorial();
	}
	func findFactorial()
	{
		var i: Int = 0;
		// First factorial
		self.factorial[0] = 1;
		// Calculate the factorial of range (1..9)
		i = 1;
		while (i <= 9)
		{
			self.factorial[i] = self.factorial[i - 1] * i;
			i += 1;
		}
	}
	// Check whether given number is krishnamurthy number or not
	func isKrishnamurthyNo(_ number: Int)
	{
		if (number < 1)
		{
			return;
		}
		// Define some auxiliary variable
		var i: Int = number;
		var remainder: Int = 0;
		var sum: Int = 0;
		// Calculate digit factorial sum of given number
		while (i  != 0)
		{
			// Get the last digit
			remainder = i % 10;
			// Factorial sum
			sum += self.factorial[remainder];
			// Remove last digit
			i = i / 10;
		}
		if (sum == number)
		{
			// When result is krishnamurthy number
			print(" [", number ,"] is krishnamurthy number");
		}
		else
		{
			print(" [", number ,"] is not krishnamurthy number");
		}
	}
}
func main()
{
	let task: FlaviusNumber = FlaviusNumber();
	// Test case
	task.isKrishnamurthyNo(40585);
	task.isKrishnamurthyNo(65);
	task.isKrishnamurthyNo(145);
}
main();

 [ 40585 ] is krishnamurthy number
 [ 65 ] is not krishnamurthy number
 [ 145 ] is krishnamurthy number

/*
  Kotlin Program for
  Krishnamurthy number 
*/
class FlaviusNumber
{
	// Auxiliary space to store factorial
	var factorial: Array < Int > ;
	
	constructor()
	{
		this.factorial = Array(10)
		{
			0
		};
		this.findFactorial();
	}
	fun findFactorial(): Unit
	{
		var i: Int = 1;
		// First factorial
		this.factorial[0] = 1;
		while (i <= 9)
		{
			this.factorial[i] = this.factorial[i - 1] * i;
			i += 1;
		}
	}
	// Check whether given number is krishnamurthy number or not
	fun isKrishnamurthyNo(number: Int): Unit
	{
		if (number < 1)
		{
			return;
		}
		// Define some auxiliary variable
		var i: Int = number;
		var remainder: Int ;
		var sum: Int = 0;
		while (i != 0)
		{
			// Get the last digit
			remainder = i % 10;
			// Factorial sum
			sum += this.factorial[remainder];
			// Remove last digit
			i = i / 10;
		}
		if (sum == number)
		{
			// When result is krishnamurthy number
			println(" [" + number + "] is krishnamurthy number");
		}
		else
		{
			println(" [" + number + "] is not krishnamurthy number");
		}
	}
}
fun main(args: Array < String > ): Unit
{
	val task: FlaviusNumber = FlaviusNumber();
	// Test case
	task.isKrishnamurthyNo(40585);
	task.isKrishnamurthyNo(65);
	task.isKrishnamurthyNo(145);
}

 [40585] is krishnamurthy number
 [65] is not krishnamurthy number
 [145] is krishnamurthy number

Resultant Output Explanation

The given code contains a main function that tests the isKrishnamurthyNo function with three test cases: 40585, 65, and 145.

1. For the input 40585, the function calculates the sum of the factorials of its digits as follows: 4! + 0! + 5! + 8! + 5! = 24 + 1 + 120 + 40320 + 120 = 40585 Since the sum (40585) is equal to the original number (40585), it is a Krishnamurthy number. The output states that "40585 is a Krishnamurthy number."

2. For the input 65, the function calculates the sum of the factorials of its digits as follows: 6! + 5! = 720 + 120 = 840 Since the sum (840) is not equal to the original number (65), it is not a Krishnamurthy number. The output states that "65 is not a Krishnamurthy number."

3. For the input 145, the function calculates the sum of the factorials of its digits as follows: 1! + 4! + 5! = 1 + 24 + 120 = 145 Since the sum (145) is equal to the original number (145), it is a Krishnamurthy number. The output states that "145 is a Krishnamurthy number."

Time Complexity of the Code

1. Calculating the factorials from 1 to 9 takes O(9) time, which simplifies to O(1) since it's a constant operation.

2. The while loop iterates through the digits of the input number, and the number of digits in an integer n is given by log10(n). Therefore, the loop runs O(log10(number)) times.

3. Within the loop, each iteration involves modulo, division, and array look-up operations, which all take constant time.

Thus, the overall time complexity of the code is O(log10(number)), where 'number' is the input integer. This complexity indicates that the program's performance is efficient, as it scales logarithmically with the size of the input.