给定一个数字n,请使用按位运算运算符检查它是否可被17整除。
例子:
Input : n = 34
Output : 34 is divisible by 17
Input : n = 43
Output : 43 is not divisible by 17
一个简单的方法是由%运算符检查它是否保留0的余数。
要使用按位运算符进行除法,我们必须以2的幂重写表达式。
n/17 = (16*n)/(17*16)
= (17 - 1)*n/(17*16)
= (n/16) - (n/(17*16))
我们可以使用一般的除法规则将n / 16重写为floor(n / 16)+(n%16)/ 16。
n/17 = floor(n/16) + (n%16)/16 -
(floor(n/16) + (n%16)/16)/17
= floor(n/16) - (floor(n/16) -
17*(n%16)/16 + (n%16)/16)/17
= floor(n/16) - (floor(n/16)-n%16)/17
该方程式的左侧是n / 17。仅当右侧是整数时,它才是整数。 floor(n / 16)根据定义是整数。因此,如果(floor(n / 16)-n%16)/ 17也是整数,则整个左侧将是一个整数。
这意味着如果(floor(n / 16)-n%16)可被17整除,则n可被17整除。
(floor(n / 16)-n%16)可以按位表示为(int)(n >> 4)–(int)(n&15) ,其中n >> 4表示n / 16,n%15表示n% 15
下面是上述方法的实现:
CPP
// CPP program to check if a number is
// divisible by 17 or not using bitwise
// operator.
#include
using namespace std;
// function to check recursively if the
// number is divisible by 17 or not
bool isDivisibleby17(int n)
{
// if n=0 or n=17 then yes
if (n == 0 || n == 17)
return true;
// if n is less then 17, not
// divisible by 17
if (n < 17)
return false;
// reducing the number by floor(n/16)
// - n%16
return isDivisibleby17((int)(n >> 4) - (int)(n & 15));
}
// driver code to check the above function
int main()
{
int n = 35;
if (isDivisibleby17(n))
cout << n << " is divisible by 17";
else
cout << n << " is not divisible by 17";
return 0;
}
Java
// Java program to check if a number is
// divisible by 17 or not using bitwise
// operator.
class GFG{
// function to check recursively if the
// number is divisible by 17 or not
static boolean isDivisibleby17(int n)
{
// if n=0 or n=17 then yes
if (n == 0 || n == 17)
return true;
// if n is less then 17, not
// divisible by 17
if (n < 17)
return false;
// reducing the number by
// floor(n/16) - n%16
return isDivisibleby17((int)(n >> 4)
- (int)(n & 15));
}
// driver function
public static void main(String[] args)
{
int n = 35;
if (isDivisibleby17(n) == true)
System.out.printf
("%d is divisible by 17",n);
else
System.out.printf
("%d is not divisible by 17",n);
}
}
// This code is contributed by
// Smitha Dinesh Semwal
Python3
# Python 3 program to
# check if a number is
# divisible by 17 or
# not using bitwise
# operator.
# function to check recursively if the
# number is divisible by 17 or not
def isDivisibleby17(n):
# if n=0 or n=17 then yes
if (n == 0 or n == 17):
return True
# if n is less then 17, not
# divisible by 17
if (n < 17):
return False
# reducing the number by floor(n/16)
# - n%16
return isDivisibleby17((int)(n >> 4) - (int)(n & 15))
# driver code to check the above function
n = 35
if (isDivisibleby17(n)):
print(n,"is divisible by 17")
else:
print(n,"is not divisible by 17")
# This code is contributed by
# Smitha Dinesh Semwal
C#
// C# program to check if a number is
// divisible by 17 or not using bitwise
// operator.
using System;
class GFG
{
// function to check recursively if the
// number is divisible by 17 or not
static bool isDivisibleby17(int n)
{
// if n=0 or n=17 then yes
if (n == 0 || n == 17)
return true;
// if n is less then 17, not
// divisible by 17
if (n < 17)
return false;
// reducing the number by
// floor(n/16) - n%16
return isDivisibleby17((int)(n >> 4)
- (int)(n & 15));
}
// Driver function
public static void Main()
{
int n = 35;
if (isDivisibleby17(n) == true)
Console.WriteLine
(n +"is divisible by 17");
else
Console.WriteLine
( n+ " is not divisible by 17");
}
}
// This code is contributed by
// vt_m
PHP
> 4) -
(int)($n & 15));
}
// Driver Code
$n = 35;
if (isDivisibleby17($n))
echo $n." is divisible by 17";
else
echo $n." is not divisible by 17";
// This code is contributed by mits
?>
Javascript
输出:
35 is not divisible by 17