商和余数除以2 ^ k(2的幂)

您将得到一个正整数n作为除数，并得到另一个数字m(2 ^ k的形式)，您必须在不进行实际除法的情况下找到商和余数。
例子：

Input : n = 43, m = 8
Output : Quotient = 5, Remainder = 3

Input : n = 58, m = 16
Output : Quotient = 3, Remainder = 10

在此，我们使用数字的按位表示来理解任何数字除以2 ^ k的除数的作用。所有为2的幂的数字在其表示中仅包含1个设置位，我们将使用此属性。
为了找到余数，我们将对除数(n)和除数减1(m-1)进行逻辑与，这将仅将除数的置位权赋予除数的设定位，在这种情况下，除数的设定位就是我们的实际余数。
此外，除数的左部分(从除数中的设置位的位置开始)将被视为商。因此，从除数(n)开始，将所有位从除数的置位位置上移去，将得到商，而将右数对数log2(m)右移将完成寻找商的工作。

• 余数= n＆(m-1)
• 商=(n >> log2(m))

注意：Log2(m)将给出m的二进制表示形式中存在的位数。

C++

// CPP to find remainder and quotient
#include
using namespace std;
 
// function to print remainder and quotient
void divide(int n,int m)
{
    // print Remainder by
    // n AND (m-1)
    cout <<"Remainder = " << ((n) &(m-1));
     
    // print quotient by
    // right shifting n by (log2(m)) times
    cout <<"\nQuotient = " <<(n >> (int)(log2(m)));
  
}
 
// driver program
int main()
{
    int n = 43, m = 8;
    divide(n, m);
    return 0;
}

Java

// Java to find remainder and quotient
import java.io.*;
 
public class GFG {
     
    // function to print remainder and
    // quotient
    static void divide(int n, int m)
    {
         
        // print Remainder by
        // n AND (m-1)
        System.out.println("Remainder = "
                        + ((n) &(m-1)));
         
        // print quotient by right shifting
        // n by (log2(m)) times
        System.out.println("Quotient = "
            + (n >> (int)(Math.log(m) / Math.log(2))));
    }
     
    // driver program
    static public void main (String[] args)
    {
        int n = 43, m = 8;
         
        divide(n, m);
    }
}
 
// This code is contributed by vt_m.

Python 3

# Python 3 to find remainder and
# quotient
import math
# function to print remainder and
# quotient
def divide(n, m):
 
    # print Remainder by
    # n AND (m-1)
    print("Remainder = ",
                  ((n) &(m-1)))
     
    # print quotient by
    # right shifting n by
    # (log2(m)) times
    print("Quotient = " ,(n >>
          (int)(math.log2(m))))
 
# driver program
n = 43
m = 8
divide(n, m)
 
# This code is contributed by
# Smitha

C#

// C# to find remainder and quotient
using System;
 
public class GFG
{
    // function to print remainder and quotient
    static void divide(int n,int m)
    {
        // print Remainder by
        // n AND (m-1)
        Console.WriteLine("Remainder = " +((n) & (m - 1)));
         
        // print quotient by
        // right shifting n by (log2(m)) times
        Console.WriteLine("Quotient = "
                           + (n >> (int)(Math.Log(m))));
     
    }
     
    // Driver program
    static public void Main ()
    {
        int n = 43, m = 8;
        divide(n, m);
         
    }
}
 
// This code is contributed by vt_m.

PHP

> (int)(log($m, 2)));
 
}
 
    // Driver Code
    $n = 43;
    $m = 8;
    divide($n, $m);
 
//This code is contributed by mits
?>

Javascript

// javascript program to find last index
// of character x in given string.
 
    // function to print remainder and
    // quotient
    function divide(n, m)
    {
           
        // print Remainder by
        // n AND (m-1)
        document.write("Remainder = "
                        + ((n) &(m-1)) + "<br/>");
           
        // print quotient by right shifting
        // n by (log2(m)) times
        document.write("Quotient = "
            + (n >> (Math.log(m) / Math.log(2))));
    }
       
// Driver code
    let n = 43, m = 8;
        divide(n, m);
     
    // This code is contributed by sanjoy_62.

输出：

Remainder = 3
Quotient = 5