Dado un número, la tarea es verificar si el número es divisible por 11 o no. El número de entrada puede ser grande y puede que no sea posible almacenarlo incluso si usamos long long int.
Ejemplos:
Input : n = 76945 Output : Yes Input : n = 1234567589333892 Output : Yes Input : n = 363588395960667043875487 Output : No
Dado que el número de entrada puede ser muy grande, no podemos usar n % 11 para verificar si un número es divisible por 11 o no, especialmente en lenguajes como C/C++. La idea se basa en el siguiente hecho.
Un número es divisible por 11 si la diferencia de los dos siguientes es divisible por 11.
- Suma de dígitos en lugares impares.
- Suma de dígitos en lugares pares.
Ilustración:
For example, let us consider 76945 Sum of digits at odd places : 7 + 9 + 5 Sum of digits at even places : 6 + 4 Difference of two sums = 21 - 10 = 11 Since difference is divisible by 11, the number 7945 is divisible by 11.
¿Como funciona esto?
Let us consider 7694, we can write it as 7694 = 7*1000 + 6*100 + 9*10 + 4 The proof is based on below observation: Remainder of 10i divided by 11 is 1 if i is even Remainder of 10i divided by 11 is -1 if i is odd So the powers of 10 only result in values either 1 or -1. Remainder of "7*1000 + 6*100 + 9*10 + 4" divided by 11 can be written as : 7*(-1) + 6*1 + 9*(-1) + 4*1 The above expression is basically difference between sum of even digits and odd digits.
A continuación se muestra la implementación del hecho anterior:
C++
// C++ program to find if a number is divisible by
// 11 or not
#include<bits/stdc++.h>
using namespace std;
// Function to find that number divisible by 11 or not
int check(string str)
{
int n = str.length();
// Compute sum of even and odd digit
// sums
int oddDigSum = 0, evenDigSum = 0;
for (int i=0; i<n; i++)
{
// When i is even, position of digit is odd
if (i%2 == 0)
oddDigSum += (str[i]-'0');
else
evenDigSum += (str[i]-'0');
}
// Check its difference is divisible by 11 or not
return ((oddDigSum - evenDigSum) % 11 == 0);
}
// Driver code
int main()
{
string str = "76945";
check(str)? cout << "Yes" : cout << "No ";
return 0;
}
Java
// Java program to find if a number is
// divisible by 11 or not
class IsDivisible
{
// Function to find that number divisible by 11 or not
static boolean check(String str)
{
int n = str.length();
// Compute sum of even and odd digit
// sums
int oddDigSum = 0, evenDigSum = 0;
for (int i=0; i<n; i++)
{
// When i is even, position of digit is odd
if (i%2 == 0)
oddDigSum += (str.charAt(i)-'0');
else
evenDigSum += (str.charAt(i)-'0');
}
// Check its difference is divisible by 11 or not
return ((oddDigSum - evenDigSum) % 11 == 0);
}
// main function
public static void main (String[] args)
{
String str = "76945";
if(check(str))
System.out.println("Yes");
else
System.out.println("No");
}
}
Python3
# Python 3 code program to find if a number
# is divisible by 11 or not
# Function to find that number divisible by
# 11 or not
def check(st) :
n = len(st)
# Compute sum of even and odd digit
# sums
oddDigSum = 0
evenDigSum = 0
for i in range(0,n) :
# When i is even, position of digit is odd
if (i % 2 == 0) :
oddDigSum = oddDigSum + ((int)(st[i]))
else:
evenDigSum = evenDigSum + ((int)(st[i]))
# Check its difference is divisible by 11 or not
return ((oddDigSum - evenDigSum) % 11 == 0)
# Driver code
st = "76945"
if(check(st)) :
print( "Yes")
else :
print("No ")
# This code is contributed by Nikita tiwari.
C#
// C# program to find if a number is
// divisible by 11 or not
using System;
class GFG
{
// Function to find that number
// divisible by 11 or not
static bool check(string str)
{
int n = str.Length;
// Compute sum of even and odd digit
// sums
int oddDigSum = 0, evenDigSum = 0;
for (int i = 0; i < n; i++)
{
// When i is even, position of
// digit is odd
if (i % 2 == 0)
oddDigSum += (str[i] - '0');
else
evenDigSum += (str[i] - '0');
}
// Check its difference is
// divisible by 11 or not
return ((oddDigSum - evenDigSum)
% 11 == 0);
}
// main function
public static void Main ()
{
String str = "76945";
if(check(str))
Console.WriteLine("Yes");
else
Console.WriteLine("No");
}
}
// This code is contributed by vt_m.
PHP
<?php
// PHP program to find if a
// number is divisible by
// 11 or not
// Function to find that number
// divisible by 11 or not
function check($str)
{
$n = strlen($str);
// Compute sum of even
// and odd digit sums
$oddDigSum = 0; $evenDigSum = 0;
for ($i = 0; $i < $n; $i++)
{
// When i is even, position
// of digit is odd
if ($i % 2 == 0)
$oddDigSum += ($str[$i] - '0');
else
$evenDigSum += ($str[$i] - '0');
}
// Check its difference
// is divisible by 11 or not
return (($oddDigSum - $evenDigSum)
% 11 == 0);
}
// Driver code
$str = "76945";
$x = check($str)? "Yes" : "No ";
echo($x);
// This code is contributed by Ajit.
?>
Javascript
<script>
// JavaScript program for the above approach
// Function to find that number
// divisible by 11 or not
function check(str)
{
let n = str.length;
// Compute sum of even and odd digit
// sums
let oddDigSum = 0, evenDigSum = 0;
for (let i = 0; i < n; i++)
{
// When i is even, position of
// digit is odd
if (i % 2 == 0)
oddDigSum += (str[i] - '0');
else
evenDigSum += (str[i] - '0');
}
// Check its difference is
// divisible by 11 or not
return ((oddDigSum - evenDigSum)
% 11 == 0);
}
// Driver Code
let str = "76945";
if(check(str))
document.write("Yes");
else
document.write("No");
// This code is contributed by chinmoy1997pal.
</script>
Producción
Yes
Complejidad de tiempo : O(logN), donde N es el número dado.
Espacio auxiliar : O(1), ya que no estamos utilizando ningún espacio adicional.
Método: Comprobación de que el número dado es divisible por 11 o no mediante el operador de división de módulo «%».
Python3
# Python code
# To check whether the given number is divisible by 11 or not
#input
n=1234567589333892
# the above input can also be given as n=input() -> taking input from user
# finding given number is divisible by 11 or not
if int(n)%11==0:
print("Yes")
else:
print("No")
# this code is contributed by gangarajula laxmi
Producción
Yes
Método: Comprobar que el número dado es divisible por 11 o no usar la división de módulo.
C++
// C++ program to check if given number is divisible by 11
// or not using modulo division
#include <iostream>
using namespace std;
int main()
{
// input number
int num = 76945;
// checking if the given number is divisible by 11 or
// not using modulo division operator if the output of
// num%11 is equal to 0 then given number is divisible
// by 11 otherwise not divisible by 11
if (num % 11 == 0) {
cout << " divisible";
}
else {
cout << " not divisible";
}
return 0;
}
// this code is contributed by gangarajula laxmi
Java
// java program to check if given number is divisible by 11
// or not using modulo division
import java.io.*;
class GFG {
public static void main(String[] args)
{
// input number
int num = 76945;
// checking if the given number is divisible by 11
// or not
// using modulo division operator if the output of
// num%11 is equal to 0 then given number is
// divisible by 11 otherwise not divisible by 11
if (num % 11 == 0) {
System.out.println(" divisible");
}
else {
System.out.println(" not divisible");
}
}
}
// this code is contributed by gangarajula laxmi
Producción
divisible
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Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA