Check if a number is a Krishnamurthy Number or not

Last Updated : 07 Jan, 2024

A Krishnamurthy number is a number whose sum of the factorial of digits is equal to the number itself.
For example, 145 is the sum of the factorial of each digit.
1! + 4! + 5! = 1 + 24 + 120 = 145

Examples:

Input : 145
Output : YES
Explanation: 1! + 4! + 5! = 
1 + 24 + 120 = 145, which is equal to input,
hence YES.
Input : 235
Output : NO
Explanation: 2! + 3! + 5! = 
2 + 6 + 120 = 128, which is not equal to input, 
hence NO.

The idea is simple, we compute the sum of factorials of all digits and then compare the sum with n.

C++

// C++ program to check if a number
// is a krishnamurthy number
#include <bits/stdc++.h>
using namespace std;

// Function to calculate the factorial of any number
int factorial(int n)
{
    int fact = 1;
    while (n != 0) {
        fact = fact * n;
        n--;
    }
    return fact;
}

// function to Check if number is krishnamurthy
bool isKrishnamurthy(int n)
{
    int sum = 0;

    int temp = n;
    while (temp != 0) {
        // calculate factorial of last digit
        // of temp and add it to sum
        sum += factorial(temp % 10);

        // replace value of temp by temp/10
        temp = temp / 10;
    }

    // Check if number is krishnamurthy
    return (sum == n);
}

// Driver code
int main()
{
    int n = 145;
    if (isKrishnamurthy(n))
        cout << "YES";
    else
        cout << "NO";
    return 0;
}

Java

// Java program to check if a number
// is a krishnamurthy number.
import java.util.*;
import java.io.*;

class Krishnamurthy {
    // function to calculate the factorial
    // of any number
    static int factorial(int n)
    {
        int fact = 1;
        while (n != 0) {
            fact = fact * n;
            n--;
        }
        return fact;
    }

    // function to Check if number is krishnamurthy
    static boolean isKrishnamurthy(int n)
    {
        int sum = 0;

        int temp = n;
        while (temp != 0) {
            // calculate factorial of last digit
            // of temp and add it to sum
            sum += factorial(temp % 10);

            // replace value of temp by temp/10
            temp = temp / 10;
        }

        // Check if number is krishnamurthy
        return (sum == n);
    }

    // Driver code
    public static void main(String[] args)
    {
        int n = 145;
        if (isKrishnamurthy(n))
            System.out.println("YES");
        else
            System.out.println("NO");
    }
}

Python3

# Python program to check if a number
# is a krishnamurthy number

# function to calculate the factorial
# of any number
def factorial(n) :
    fact = 1
    while (n != 0) :
        fact = fact * n
        n = n - 1
    return fact

# function to Check if number is
# krishnamurthy/special
def isKrishnamurthy(n) :
    sum = 0
    temp = n
    while (temp != 0) :

        # calculate factorial of last digit
        # of temp and add it to sum
        rem = temp%10
        sum = sum + factorial(rem)

        # replace value of temp by temp / 10
        temp = temp // 10
        
    # Check if number is krishnamurthy
    return (sum == n)

# Driver code
n = 145
if (isKrishnamurthy(n)) :
    print("YES")
else :
    print("NO")


# This code is contributed by Prashant Aggarwal

// C# program to check if a number
// is a krishnamurthy number.
using System;

class GFG {
    
    // function to calculate the
    // factorial of any number
    static int factorial(int n)
    {
        int fact = 1;
        
        while (n != 0) {
            fact = fact * n;
            n--;
        }
        
        return fact;
    }

    // function to Check if number is
    // krishnamurthy
    static bool isKrishnamurthy(int n)
    {
        int sum = 0;

        int temp = n;
        while (temp != 0) {
            
            // calculate factorial of
            // last digit of temp and
            // add it to sum
            sum += factorial(temp % 10);

            // replace value of temp
            // by temp/10
            temp = temp / 10;
        }

        // Check if number is
        // krishnamurthy
        return (sum == n);
    }

    // Driver code
    public static void Main()
    {
        int n = 145;
        if (isKrishnamurthy(n))
            Console.Write("YES");
        else
            Console.Write("NO");
    }
}

// This code is contributed by nitin mittal.

JavaScript

<script>
    
// Javascript program to check if a number
// is a krishnamurthy number

// Function to find Factorial 
// of any number
function factorial(n)
{
    let fact = 1;
    
    while (n != 0)
    {
        fact = fact * n;
        n--;
    }
    
    return fact;
}

// Function to check if number
// is krishnamurthy
function isKrishnamurthyNumber(n)
{
    let sum = 0;
    
    // Storing the value in
    // other variable
    let temp = n;
    
    while (temp != 0)
    {
        
        // Calculate factorial of last digit
        // of temp and add it to sum
        sum = sum + factorial(temp % 10);
        
        // Integer Division
        // replace value of temp by temp/10
        temp = parseInt(temp / 10);
    }
    
    // Check if number is krishnamurthy
    return sum == n;
}

// Driver code
let n = 145;

if (isKrishnamurthyNumber(n))
    document.write("YES");
else
    document.write("NO");

// This code is contributed by _saurabh_jaiswal

</script>

PHP

<?php
// PHP program to check if a number
// is a krishnamurthy number

// Function to find Factorial 
// of any number
function factorial($n)
{
    $fact = 1;
    while($n != 0)
    {
        $fact = $fact * $n;
        $n--;
    }
    
    return $fact;
}

// function to Check if number
// is krishnamurthy
function isKrishnamurthyNumber($n)
{
    $sum = 0;
    
    // Storing the value in
    // other variable
    $temp = $n;
    
    while($temp != 0)
    {
        // calculate factorial of last digit
        // of temp and add it to sum
        $sum = $sum + factorial($temp % 10);
        
        // Integer Division
        // replace value of temp by temp/10
        $temp = intdiv($temp, 10);
    }
    
    // Check if number is krishnamurthy
    return $sum == $n;
}

// Driver code
$n = 145;

if (isKrishnamurthyNumber($n))
    echo "YES";
else
    echo "NO";


// This code is contributed by akash7981
?>

Output

YES

Time Complexity: O(n log₁₀n) where n is a given number
Auxiliary Space: O(1)
Interestingly, there are exactly four Krishnamurthy numbers i.e. 1, 2, 145, and 40585 known to us.

Approach 2: Precomputing factorials and checking each digit of the number against the precomputed factorials.

The declaration int factorial[10]; creates an array factorial of 10 integers to store the precomputed factorials.
The precomputeFactorials() function calculates and stores the factorials of numbers 0 to 9 in the factorial array. It uses a for loop to iterate through each number and calculates its factorial by multiplying it with the factorial of the previous number.
The isKrishnamurthy(int n) function takes an integer n as input and checks if it is a Krishnamurthy number or not. It first declares a variable sum to store the sum of factorials of digits in n and a variable temp to store a copy of n.
It then enters a while loop that continues until temp becomes zero. In each iteration of the loop, it calculates the rightmost digit of temp using the modulo operator (temp % 10) and adds the factorial of that digit to sum. It then updates the value of temp by removing the rightmost digit using integer division (temp /= 10).
After the while loop completes, the function returns true if sum is equal to n, indicating that n is a Krishnamurthy number, or false otherwise.
In the main() function, we call precomputeFactorials() to precompute the factorials of numbers 0 to 9 and store them in the factorial array.
We then set n to 145, which is a Krishnamurthy number, and call isKrishnamurthy(n) to check if n is a Krishnamurthy number or not.
Finally, we use cout to print "YES" if isKrishnamurthy(n) returns true, indicating that n is a Krishnamurthy number, or "NO" otherwise. We also use endl to insert a newline character after the output.

C++

#include <iostream>
using namespace std;

int factorial[10];

void precomputeFactorials() {
    factorial[0] = 1;
    for (int i = 1; i < 10; i++) {
        factorial[i] = i * factorial[i-1];
    }
}

bool isKrishnamurthy(int n) {
    int sum = 0;
    int temp = n;
    while (temp > 0) {
        int digit = temp % 10;
        sum += factorial[digit];
        temp /= 10;
    }
    return (sum == n);
}

int main() {
    precomputeFactorials();
    int n = 145;
    if (isKrishnamurthy(n)) {
        cout <<"YES" << endl;
    } else {
        cout <<"NO" << endl;
    }
    return 0;
}

Java

// This is the Java code which checks if a given
// number is a Krishnamurthy number or not. 
//A Krishnamurthy number is a number whose sum of factorials
// of its digits is equal to the number itself

import java.util.Arrays;

public class KrishnamurthyNumber {

    // Declare an array to store factorials of digits 0-9
    static int[] factorial = new int[10];

    // Function to precompute the factorials and store them
    // in the array
    public static void precomputeFactorials()
    {
        factorial[0] = 1;
        for (int i = 1; i < 10; i++) {
            factorial[i] = i * factorial[i - 1];
        }
    }

    // Function to check if a given number is a
    // Krishnamurthy number or not
    public static boolean isKrishnamurthy(int n)
    {
        int sum = 0;
        int temp = n;
        // Compute the sum of factorials of digits of the
        // number
        while (temp > 0) {
            int digit = temp % 10;
            sum += factorial[digit];
            temp /= 10;
        }
        // Check if the sum of factorials is equal to the
        // input number
        return (sum == n);
    }

    public static void main(String[] args)
    {
        // Compute the factorials using
        // precomputeFactorials() function
        precomputeFactorials();
        int n = 145;
        // Check if 145 is a Krishnamurthy number using
        // isKrishnamurthy() function
        if (isKrishnamurthy(n)) {
            System.out.println("YES");
        }
        else {
            System.out.println("NO");
        }
    }
}

Python3

# Precompute factorials of digits 0-9
factorial = [1] * 10
def precompute_factorials():
    for i in range(1, 10):
        factorial[i] = i * factorial[i-1]

precompute_factorials()

# Check if a number is a Krishnamurthy number
def is_krishnamurthy(n):
    # Compute sum of factorials of digits
    sum = 0
    temp = n
    while temp > 0:
        digit = temp % 10
        sum += factorial[digit]
        temp //= 10

    # Check if sum equals the original number
    return (sum == n)

# Test if a given number is a Krishnamurthy number
n = 145
if is_krishnamurthy(n):
    print("YES")
else:
    print("NO")

using System;

namespace KrishnamurthyNumber
{
    class Program
    {
        static int[] factorial = new int[10];

        static void precomputeFactorials()
        {
            factorial[0] = 1;
            for (int i = 1; i < 10; i++)
            {
                factorial[i] = i * factorial[i - 1];
            }
        }

        static bool isKrishnamurthy(int n)
        {
            int sum = 0;
            int temp = n;
            while (temp > 0)
            {
                int digit = temp % 10;
                sum += factorial[digit];
                temp /= 10;
            }
            return (sum == n);
        }

        static void Main(string[] args)
        {
            precomputeFactorials();
            int n = 145;
            if (isKrishnamurthy(n))
            {
                Console.WriteLine("YES");
            }
            else
            {
                Console.WriteLine("NO");
            }
        }
    }
}

JavaScript

let factorial = [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880];

function precomputeFactorials() {
for (let i = 1; i < 10; i++) {
factorial[i] = i * factorial[i-1];
}
}

function isKrishnamurthy(n) {
let sum = 0;
let temp = n;
while (temp > 0) {
let digit = temp % 10;
sum += factorial[digit];
temp = Math.floor(temp / 10);
}
return (sum === n);
}

precomputeFactorials();
let n = 145;
if (isKrishnamurthy(n)) {
console.log("YES");
} else {
console.log("NO");
}

Output

YES

Time Complexity: O(logN)
Auxiliary Space: O(1)

Last non-zero digit of a factorial

DANISH KALEEM

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Check if a number is a Krishnamurthy Number or not

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