Dado un número, la tarea es verificar si un número es divisible por 16 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 = 1128 Output : No Input : n = 11216 Output : Yes Input : n = 1124273542764284287 Output : No
Dado que el número de entrada puede ser muy grande, no podemos usar n % 16 para verificar si un número es divisible por 16 o no, especialmente en lenguajes como C/C++. La idea se basa en el siguiente hecho.
A number is divisible by 16 if number formed by last four digits of it is divisible by 16.
Ilustración:
For example, let us consider 769616 Number formed by last four digits = 9616 Since 9522 is divisible by 16, answer is YES.
¿Como funciona esto?
Let us consider 76952, we can write it as 76942 = 7*10000 + 6*1000 + 9*100 + 5*10 + 2 The proof is based on below observation: Remainder of 10i divided by 16 is 0 if i greater than or equal to four. Note that 10000, 100000,... etc lead to remainder 0 when divided by 16. So remainder of "7*10000 + 6*1000 + 9*100 + 5*10 + 2" divided by 16 is equivalent to remainder of following : 0 + 6*1000 + 9*100 + 5*10 + 2 = 6952 Therefore we can say that the whole number is divisible by 16 if 6952 is divisible by 16.
C++
// C++ program to find if a number
// is divisible by 16 or not
#include<bits/stdc++.h>
using namespace std;
// Function to find that
// number divisible by 16 or not
bool check(string str)
{
int n = str.length();
// Empty string
if (n == 0 && n == 1)
return false;
// If there is double digit
if (n == 2)
return (((str[n-2]-'0')*10 +
(str[n-1]-'0'))%16 == 0);
// If there is triple digit
if(n == 3)
return ( ((str[n-3]-'0')*100 +
(str[n-2]-'0')*10 +
(str[n-1]-'0'))%16 == 0);
// If number formed by last four
// digits is divisible by 16.
int last = str[n-1] - '0';
int second_last = str[n-2] - '0';
int third_last = str[n-3] - '0';
int fourth_last = str[n-4] - '0';
return ((fourth_last*1000 + third_last*100 +
second_last*10 + last) % 16 == 0);
}
// Driver code
int main()
{
string str = "769528";
check(str)? cout << "Yes" : cout << "No ";
return 0;
}
Java
// Java program to find if a number
// is divisible by 16 or not
import java.io.*;
class GFG {
// Function to find that
// number divisible by 16 or not
static boolean check(String str)
{
int n = str.length();
// Empty string
if (n == 0 && n == 1)
return false;
// If there is double digit
if (n == 2)
return (((str.charAt(n-2)-'0')*10 +
(str.charAt(n-1)-'0'))%16 == 0);
// If there is triple digit
if(n == 3)
return ( ((str.charAt(n-3)-'0')*100 +
(str.charAt(n-2)-'0')*10 +
(str.charAt(n-1)-'0'))%16 == 0);
// If number formed by last
// four digits is divisible by 16.
int last = str.charAt(n-1) - '0';
int second_last = str.charAt(n-2) - '0';
int third_last = str.charAt(n-3) - '0';
int fourth_last = str.charAt(n-4) - '0';
return ((fourth_last*1000 + third_last*100
+ second_last*10 + last) % 16 == 0);
}
// Driver code
public static void main(String args[])
{
String str = "769528";
if(check(str))
System.out.println("Yes");
else
System.out.println("No ");
}
}
// This code is contributed by Nikita Tiwari.
Python3
# Python 3 program to find
# if a number is divisible
# by 16 or not
# Function to find that
# number divisible by
# 16 or not
def check(st) :
n = len(st)
# Empty string
if (n == 0 and n == 1) :
return False
# If there is double digit
if (n == 2) :
return ((int)(st[n-2])*10 +
((int)(st[n-1])%16 == 0))
# If there is triple digit
if(n == 3) :
return ( ((int)(st[n-3])*100 +
(int)(st[n-2])*10 +
(int)(st[n-1]))%16 == 0)
# If number formed by last
# four digits is divisible
# by 16.
last = (int)(st[n-1])
second_last = (int)(st[n-2])
third_last = (int)(st[n-3])
fourth_last = (int)(st[n-4])
return ((fourth_last*1000 + third_last*100
+ second_last*10 + last) % 16 == 0)
# Driver code
st = "769528"
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 16 or not
using System;
class GFG {
// Function to find that number
// divisible by 16 or not
static bool check(String str)
{
int n = str.Length;
// Empty string
if (n == 0 && n == 1)
return false;
// If there is double digit
if (n == 2)
return (((str[n - 2] - '0') * 10 +
(str[n - 1] - '0')) % 16 == 0);
// If there is triple digit
if(n == 3)
return (((str[n - 3] - '0') * 100 +
(str[n - 2] - '0') * 10 +
(str[n - 1] - '0')) % 16 == 0);
// If number formed by last
// four digits is divisible by 16.
int last = str[n - 1] - '0';
int second_last = str[n - 2] - '0';
int third_last = str[n - 3] - '0';
int fourth_last = str[n - 4] - '0';
return ((fourth_last * 1000 + third_last * 100
+ second_last * 10 + last) % 16 == 0);
}
// Driver code
public static void Main()
{
String str = "769528";
if(check(str))
Console.Write("Yes");
else
Console.Write("No ");
}
}
// This code is contributed by Nitin Mittal.
PHP
<?php
// PHP program to find if a number
// is divisible by 16 or not
// Function to find that
// number divisible by 16 or not
function check($str)
{
$n = strlen($str);
// Empty string
if ($n == 0 && $n == 1)
return false;
// If there is double digit
if ($n == 2)
return ((($str[$n - 2] - '0') * 10 +
($str[$n - 1] - '0')) % 16 == 0);
// If there is triple digit
if($n == 3)
return ((($str[$n -3] - '0') *
100 + ($str[$n - 2] -
'0') * 10 + ($str[$n -
1] - '0')) % 16 == 0);
// If number formed by last four
// digits is divisible by 16.
$last = $str[$n - 1] - '0';
$second_last = $str[$n - 2] - '0';
$third_last = $str[$n - 3] - '0';
$fourth_last = $str[$n - 4] - '0';
return (($fourth_last * 1000 +
$third_last * 100 +
$second_last * 10 +
$last) % 16 == 0);
}
// Driver code
$str = "769528";
$x = check($str) ? "Yes" : "No ";
echo($x);
// This code is contributed by Ajit.
?>
Javascript
<script>
// Javascript program to find if a number
// is divisible by 16 or not
// Function to find that number
// divisible by 16 or not
function check(str)
{
let n = str.length;
// Empty string
if (n == 0 && n == 1)
return false;
// If there is double digit
if (n == 2)
return (((str[n - 2] - '0') * 10 +
(str[n - 1] - '0')) % 16 == 0);
// If there is triple digit
if(n == 3)
return (((str[n - 3] - '0') * 100 +
(str[n - 2] - '0') * 10 +
(str[n - 1] - '0')) % 16 == 0);
// If number formed by last
// four digits is divisible by 16.
let last = str[n - 1] - '0';
let second_last = str[n - 2] - '0';
let third_last = str[n - 3] - '0';
let fourth_last = str[n - 4] - '0';
return ((fourth_last * 1000 + third_last * 100 +
second_last * 10 + last) % 16 == 0);
}
// Driver code
let str = "769528";
if (check(str))
document.write("Yes");
else
document.write("No ");
// This code is contributed by decode2207
</script>
Producción:
No
Tiempo Complejidad: O(1)
Espacio Auxiliar: O(1)
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Publicación traducida automáticamente
Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA