Dado un número entero N , la tarea es verificar si N divide la suma de los factoriales de sus dígitos.
Ejemplos:
Entrada: N = 19
Salida: Sí
1! + 9! = 1 + 362880 = 362881, que es divisible por 19.Entrada: N = 20
Salida: No
0! + 2! = 1 + 4 = 5, que no es divisible por 20.
Enfoque: primero, almacene los factoriales de todos los dígitos del 0 al 9 en una array. Y, para el número N dado, comprueba si divide la suma de los factoriales de sus dígitos.
A continuación se muestra la implementación del enfoque anterior:
C++
// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
// Function that returns true if n divides
// the sum of the factorials of its digits
bool isPossible(int n)
{
// To store factorials of digits
int fac[10];
fac[0] = fac[1] = 1;
for (int i = 2; i < 10; i++)
fac[i] = fac[i - 1] * i;
// To store sum of the factorials
// of the digits
int sum = 0;
// Store copy of the given number
int x = n;
// Store sum of the factorials
// of the digits
while (x) {
sum += fac[x % 10];
x /= 10;
}
// If it is divisible
if (sum % n == 0)
return true;
return false;
}
// Driver code
int main()
{
int n = 19;
if (isPossible(n))
cout << "Yes";
else
cout << "No";
return 0;
}
Java
// Java implementation of the approach
class GFG
{
// Function that returns true if n divides
// the sum of the factorials of its digits
static boolean isPossible(int n)
{
// To store factorials of digits
int fac[] = new int[10];
fac[0] = fac[1] = 1;
for (int i = 2; i < 10; i++)
fac[i] = fac[i - 1] * i;
// To store sum of the factorials
// of the digits
int sum = 0;
// Store copy of the given number
int x = n;
// Store sum of the factorials
// of the digits
while (x != 0)
{
sum += fac[x % 10];
x /= 10;
}
// If it is divisible
if (sum % n == 0)
return true;
return false;
}
// Driver code
public static void main (String[] args)
{
int n = 19;
if (isPossible(n))
System.out.println("Yes");
else
System.out.println("No");
}
}
// This code is contributed by Ryuga
Python3
# Python 3 implementation of the approach
# Function that returns true if n divides
# the sum of the factorials of its digits
def isPossible(n):
# To store factorials of digits
fac = [0 for i in range(10)]
fac[0] = 1
fac[1] = 1
for i in range(2, 10, 1):
fac[i] = fac[i - 1] * i
# To store sum of the factorials
# of the digits
sum = 0
# Store copy of the given number
x = n
# Store sum of the factorials
# of the digits
while (x):
sum += fac[x % 10]
x = int(x / 10)
# If it is divisible
if (sum % n == 0):
return True
return False
# Driver code
if __name__ == '__main__':
n = 19
if (isPossible(n)):
print("Yes")
else:
print("No")
# This code is contributed by
# Surendra_Gangwar
C#
// C# implementation of the approach
using System;
class GFG
{
// Function that returns true if n divides
// the sum of the factorials of its digits
static bool isPossible(int n)
{
// To store factorials of digits
int[] fac = new int[10];
fac[0] = fac[1] = 1;
for (int i = 2; i < 10; i++)
fac[i] = fac[i - 1] * i;
// To store sum of the factorials
// of the digits
int sum = 0;
// Store copy of the given number
int x = n;
// Store sum of the factorials
// of the digits
while (x != 0)
{
sum += fac[x % 10];
x /= 10;
}
// If it is divisible
if (sum % n == 0)
return true;
return false;
}
// Driver code
public static void Main ()
{
int n = 19;
if (isPossible(n))
Console.WriteLine("Yes");
else
Console.WriteLine("No");
}
}
// This code is contributed by Code_Mech.
PHP
<?php
// PHP implementation of the approach
// Function that returns true if n divides
// the sum of the factorials of its digits
function isPossible($n)
{
// To store factorials of digits
$fac = array();
$fac[0] = $fac[1] = 1;
for ($i = 2; $i < 10; $i++)
$fac[$i] = $fac[$i - 1] * $i;
// To store sum of the factorials
// of the digits
$sum = 0;
// Store copy of the given number
$x = $n;
// Store sum of the factorials
// of the digits
while ($x)
{
$sum += $fac[$x % 10];
$x /= 10;
}
// If it is divisible
if ($sum % $n == 0)
return true;
return false;
}
// Driver code
$n = 19;
if (isPossible($n))
echo "Yes";
else
echo "No";
// This code is contributed by Akanksha Rai
?>
Javascript
<script>
// JavaScript implementation of the approach
// Function that returns true if n divides
// the sum of the factorials of its digits
function isPossible(n)
{
// To store factorials of digits
var fac = new Array(10);
fac[0] = fac[1] = 1;
for(var i = 2; i < 10; i++)
fac[i] = fac[i - 1] * i;
// To store sum of the factorials
// of the digits
var sum = 0;
// Store copy of the given number
var x = n;
// Store sum of the factorials
// of the digits
while (x != 0)
{
sum += fac[x % 10];
x = parseInt(x / 10);
}
// If it is divisible
if (sum % n == 0)
return true;
return false;
}
// Driver Code
var n = 19;
if (isPossible(n))
document.write("Yes");
else
document.write("No");
// This code is contributed by Khushboogoyal499
</script>
Producción:
Yes
Complejidad de tiempo: O (logn)
Espacio Auxiliar: O(1)
Publicación traducida automáticamente
Artículo escrito por pawan_asipu y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA