Comprobar si un número grande es divisible por 5 o no

Dado un número, la tarea es verificar si el número es divisible por 5. El número de entrada puede ser grande y puede que no sea posible almacenarlo incluso si usamos long long int.

Ejemplos: 

Input  : n = 56945255
Output : Yes

Input  : n = 1234567589333150
Output : Yes

Input  : n = 3635883959606670431112222
Output : No

Dado que el número de entrada puede ser muy grande, no podemos usar n % 5 para verificar si un número es divisible por 5 o no, especialmente en lenguajes como C/C++. La idea se basa en el siguiente hecho. 

   A number is divisible by 5 if its  
   digits last digit will be 0 or 5 .

Ilustración:  

For example, let us consider 769555 
Number formed by last digit is = 5
Since 5 is divisible by 5 , answer is YES.

¿Como funciona esto? 

Let us consider 5335, we can write it as
5335 = 5*1000 + 3*100 + 3*10 + 5

The proof is based on below observation:
Remainder of 10i divided by 5 is 0 if i greater 
than or equal to one. Note than 10, 100, 1000,
... etc lead to remainder 0 when divided by 5.

So remainder of " 5*1000 + 3*100 + 
3*10 + 5" divided by 5 is equivalent to remainder 
of following : 
0 + 0 + 0 + 5 = 5

Since 5 is divisible by 5, answer is yes.

A continuación se muestra la implementación de la idea anterior.

// C++ program to find if a number is
// divisible by 5 or not
#include<bits/stdc++.h>
using namespace std;
 
// Function to find that number divisible
// by 5 or not. The function assumes that
// string length is at least one.
bool isDivisibleBy5(string str)
{
    int n = str.length();
 
    return ( ((str[n-1]-'0') == 0) ||
             ((str[n-1]-'0') == 5));
}
 
// Driver code
int main()
{
    string str = "76955";
    isDivisibleBy5(str)?  cout << "Yes" :
                          cout << "No ";
    return 0;
}

// Java program to find if a number is
// divisible by 5 or not
class IsDivisible
{
    // Function to find that number divisible
    // by 5 or not. The function assumes that
    // string length is at least one.
    static boolean isDivisibleBy5(String str)
    {
        int n = str.length();
      
        return ( ((str.charAt(n-1)-'0') == 0) ||
                 ((str.charAt(n-1)-'0') == 5));
    }
     
    // main function
    public static void main (String[] args)
    {
        String str = "76955";
        if(isDivisibleBy5(str))
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}

# Python program to find if a number is
# divisible by 5 or not
 
# Function to find that number divisible
# by 5 or not. The function assumes that
# string length is at least one.
def isDivisibleBy5(st) :
    n = len(st)
    return ( (st[n-1] == '0') or
           (st[n-1] == '5'))
  
# Driver code
st = "76955"
if isDivisibleBy5(st) :
    print ("Yes")
else :
    print ("No")
     
# This code is contributed by Nikita Tiwari.

// C# program to find if a number is
// C# program to find if a number
// is divisible by 5 or not.
using System;
 
class IsDivisible
{
    // Function to find that number divisible
    // by 5 or not. The function assumes that
    // string length is at least one.
    static bool isDivisibleBy5(String str)
    {
        int n = str.Length;
     
        return (((str[n - 1] - '0') == 0) ||
                ((str[n - 1] - '0') == 5));
    }
     
    // Driver Code
    public static void Main ()
    {
        String str = "76955";
        if(isDivisibleBy5(str))
        Console.Write("Yes");
        else
        Console.Write("No");
    }
}
 
// This code is contributed by Nitin Mittal.

<?php
// PHP program to find if a number
// is divisible by 5 or not
 
// Function to find that number divisible
// by 5 or not. The function assumes that
// string length is at least one.
function isDivisibleBy5($str)
{
    $n = strlen($str);
 
    return ( (($str[$n-1]-'0') == 0) ||
            (($str[$n-1]-'0') == 5));
}
 
// Driver code
$str = "76955";
$x = isDivisibleBy5($str) ? "Yes" : "No";
echo($x);
 
// This code is contributed by Ajit.
?>

<script>
 
// Javascript program to find if a number
// is divisible by 5 or not
   
// Function to find that number divisible
// by 5 or not. The function assumes that
// string length is at least one.
function  isDivisibleBy5(str)
{
    n = str.length;
   
    return (((str[n - 1] - '0') == 0) ||
            ((str[n - 1] - '0') == 5));
}
   
// Driver Code
var str = "76955";
var x = isDivisibleBy5(str) ? "Yes" : "No";
 
document.write(x);
 
// This code is contributed by bunnyram19
 
</script>

Producción: 

Yes

Complejidad de tiempo: O (1), ya que no estamos usando ningún bucle para atravesar.

Espacio auxiliar: O(1), ya que no estamos utilizando ningún espacio adicional.
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