Swap bits in a given number

Difficulty Level : Hard
Last Updated : 23 Dec, 2020

Given a number x and two positions (from the right side) in the binary representation of x, write a function that swaps n bits at given two positions and returns the result. It is also given that the two sets of bits do not overlap.

Method 1
Let p1 and p2 be the two given positions.
Example 1

Input:
x = 47 (00101111)
p1 = 1 (Start from the second bit from the right side)
p2 = 5 (Start from the 6th bit from the right side)
n = 3 (No of bits to be swapped)
Output:
227 (11100011)
The 3 bits starting from the second bit (from the right side) are 
swapped with 3 bits starting from 6th position (from the right side)

Example 2

Input:
x = 28 (11100)
p1 = 0 (Start from first bit from right side)
p2 = 3 (Start from 4th bit from right side)
n = 2 (No of bits to be swapped)
Output:
7 (00111)
The 2 bits starting from 0th position (from right side) are
swapped with 2 bits starting from 4th position (from right side)

Solution
We need to swap two sets of bits. XOR can be used in a similar way as it is used to swap 2 numbers. Following is the algorithm.

1) Move all bits of the first set to the rightmost side
   set1 =  (x >> p1) & ((1U << n) - 1)
Here the expression (1U << n) - 1 gives a number that 
contains last n bits set and other bits as 0. We do & 
with this expression so that bits other than the last 
n bits become 0.
2) Move all bits of second set to rightmost side
   set2 =  (x >> p2) & ((1U << n) - 1)
3) XOR the two sets of bits
   xor = (set1 ^ set2) 
4) Put the xor bits back to their original positions. 
   xor = (xor << p1) | (xor << p2)
5) Finally, XOR the xor with original number so 
   that the two sets are swapped.
   result = x ^ xor

Implementation:

C++

// C++ Program to swap bits
// in a given number
#include <bits/stdc++.h>
using namespace std;
 
int swapBits(unsigned int x, unsigned int p1,
             unsigned int p2, unsigned int n)
{
    /* Move all bits of first set to rightmost side */
    unsigned int set1 = (x >> p1) & ((1U << n) - 1);
 
    /* Move all bits of second set to rightmost side */
    unsigned int set2 = (x >> p2) & ((1U << n) - 1);
 
    /* Xor the two sets */
    unsigned int Xor = (set1 ^ set2);
 
    /* Put the Xor bits back to their original positions */
    Xor = (Xor << p1) | (Xor << p2);
 
    /* Xor the 'Xor' with the original number so that the 
    two sets are swapped */
    unsigned int result = x ^ Xor;
 
    return result;
}
 
/* Driver code*/
int main()
{
    int res = swapBits(28, 0, 3, 2);
    cout << "Result = " << res;
    return 0;
}
 
// This code is contributed by rathbhupendra

C

// C Program to swap bits
// in a given number
#include <stdio.h>
 
int swapBits(unsigned int x, unsigned int p1, unsigned int p2, unsigned int n)
{
    /* Move all bits of first set to rightmost side */
    unsigned int set1 = (x >> p1) & ((1U << n) - 1);
 
    /* Move all bits of second set to rightmost side */
    unsigned int set2 = (x >> p2) & ((1U << n) - 1);
 
    /* XOR the two sets */
    unsigned int xor = (set1 ^ set2);
 
    /* Put the xor bits back to their original positions */
    xor = (xor << p1) | (xor << p2);
 
    /* XOR the 'xor' with the original number so that the 
       two sets are swapped */
    unsigned int result = x ^ xor;
 
    return result;
}
 
/* Driver program to test above function*/
int main()
{
    int res = swapBits(28, 0, 3, 2);
    printf("\nResult = %d ", res);
    return 0;
}

Java

// Java Program to swap bits
// in a given number
 
class GFG {
 
    static int swapBits(int x, int p1, int p2, int n)
    {
        // Move all bits of first set
        // to rightmost side
        int set1 = (x >> p1) & ((1 << n) - 1);
 
        // Move all bits of second set
        // to rightmost side
        int set2 = (x >> p2) & ((1 << n) - 1);
 
        // XOR the two sets
        int xor = (set1 ^ set2);
 
        // Put the xor bits back to
        // their original positions
        xor = (xor << p1) | (xor << p2);
 
        // XOR the 'xor' with the original number
        // so that the  two sets are swapped
        int result = x ^ xor;
 
        return result;
    }
 
    // Driver program
    public static void main(String[] args)
    {
        int res = swapBits(28, 0, 3, 2);
        System.out.println("Result = " + res);
    }
}
 
// This code is contributed by prerna saini.

Python3

# Python program to
# swap bits in a given number
 
def swapBits(x, p1, p2, n):
 
    # Move all bits of first
    # set to rightmost side 
    set1 =  (x >> p1) & ((1<< n) - 1)
  
    # Moce all bits of second
    # set to rightmost side 
    set2 =  (x >> p2) & ((1 << n) - 1)
  
    # XOR the two sets 
    xor = (set1 ^ set2)
  
    # Put the xor bits back
    # to their original positions 
    xor = (xor << p1) | (xor << p2)
  
      # XOR the 'xor' with the
      # original number so that the 
      # two sets are swapped
    result = x ^ xor
  
    return result
     
# Driver code
 
res = swapBits(28, 0, 3, 2)
print("Result =", res)
 
# This code is contributed
# by Anant Agarwal.

C#

// C# Program to swap bits
// in a given number
using System;
 
class GFG {
 
    static int swapBits(int x, int p1, int p2, int n)
    {
        // Move all bits of first
        // set to rightmost side
        int set1 = (x >> p1) & ((1 << n) - 1);
 
        // Move all bits of second set
        // set to rightmost side
        int set2 = (x >> p2) & ((1 << n) - 1);
 
        // XOR the two sets
        int xor = (set1 ^ set2);
 
        // Put the xor bits back to
        // their original positions
        xor = (xor << p1) | (xor << p2);
 
        // XOR the 'xor' with the original number
        // so that the two sets are swapped
        int result = x ^ xor;
 
        return result;
    }
 
    // Driver program
    public static void Main()
    {
        int res = swapBits(28, 0, 3, 2);
        Console.WriteLine("Result = " + res);
    }
}
 
// This code is contributed by vt_m.

PHP

<?php
// PHP Program to swap bits 
// in a given number
 
// function returns
// the swapped bits
function swapBits($x, $p1, $p2, $n)
{
     
    // Move all bits of first 
    // set to rightmost side 
    $set1 = ($x >> $p1) & 
            ((1 << $n) - 1);
 
    // Move all bits of second
    // set to rightmost side 
    $set2 = ($x >> $p2) & 
            ((1 << $n) - 1);
 
    // XOR the two sets 
    $xor = ($set1 ^ $set2);
 
    // Put the xor bits back to 
    // their original positions 
    $xor = ($xor << $p1) | 
           ($xor << $p2);
 
    // XOR the 'xor' with the 
    // original number so that
    // the two sets are swapped 
    $result = $x ^ $xor;
 
    return $result;
}
 
    // Driver Code
    $res = swapBits(28, 0, 3, 2);
    echo "\nResult = ", $res;
     
// This code is contributed by anuj_67.
?>

Output:

 Result = 7

Following is a shorter implementation of the same logic

C

int swapBits(unsigned int x, unsigned int p1, unsigned int p2, unsigned int n)
{
    /* xor contains xor of two sets */
    unsigned int xor = ((x >> p1) ^ (x >> p2)) & ((1U << n) - 1);
 
    /* To swap two sets, we need to again XOR the xor with original sets */
    return x ^ ( (xor << p1) | (xor << p2));
}

Method 2 –
This solution focuses on calculating the values of bits to be swapped using AND gate. Then we can set/unset those bits based on whether the bits are to be swapped. For the number of bits to be swapped (n) –

Calculate shift1 = The value after setting bit at p1 position to 1
Calculate shift2 = The value after setting bit at p2 position to 1
value1 = Number to check if num at position p1 is set or not.
value2 = Number to check if num at position p2 is set or not.
If value1 and value2 are different is when we have to swap the bits.

Example:

[28 0 3 2] num=28 (11100) p1=0 p2=3 n=2
   Given = 11100
   Required output = 00111 i.e. (00)1(11) msb 2 bits replaced with lsb 2 bits

n=2
  p1=0,  p2=3
  shift1= 1,  shift2= 1000
  value1= 0,  value2= 1000
 After swap
  num= 10101

n=3
  p1=1,  p2=4
  shift1= 10,  shift2= 10000
  value1= 0,  value2= 10000
 After swap
  num= 00111

Implementation

C++

#include <iostream>
using namespace std;
 
int swapBits(unsigned int num, unsigned int p1,
             unsigned int p2, unsigned int n)
{
    int shift1, shift2, value1, value2;
    while (n--) {
        // Setting bit at p1 position to 1
        shift1 = 1 << p1;
        // Setting bit at p2 position to 1
        shift2 = 1 << p2;
 
        // value1 and value2 will have 0 if num
        // at the respective positions - p1 and p2 is 0.
        value1 = ((num & shift1));
        value2 = ((num & shift2));
 
        // check if value1 and value2 are different
        // i.e. at one position bit is set and other it is not
        if ((!value1 && value2) || (!value2 && value1)) {
            // if bit at p1 positon is set
            if (value1) {
                // unset bit at p1 position
                num = num & (~shift1);
                // set bit at p2 position
                num = num | shift2;
            }
            // if bit at p2 position is set
            else {
                // set bit at p2 position
                num = num & (~shift2);
                // unset bit at p2 position
                num = num | shift1;
            }
        }
        p1++;
        p2++;
    }
    // return final result
    return num;
}
 
/* Driver code*/
int main()
{
    int res = swapBits(28, 0, 3, 2);
    cout << "Result = " << res;
    return 0;
}

Java

class GFG
{
    static int swapBits(int num, int p1, int p2, int n) 
    { 
        int shift1, shift2, value1, value2; 
        while (n-- > 0) 
        { 
           
            // Setting bit at p1 position to 1 
            shift1 = 1 << p1; 
           
            // Setting bit at p2 position to 1 
            shift2 = 1 << p2; 
       
            // value1 and value2 will have 0 if num 
            // at the respective positions - p1 and p2 is 0. 
            value1 = ((num & shift1)); 
            value2 = ((num & shift2)); 
       
            // check if value1 and value2 are different 
            // i.e. at one position bit is set and other it is not 
            if ((value1 == 0 && value2 != 0) || 
                (value2 == 0 && value1 != 0))
            {
               
                // if bit at p1 positon is set 
                if (value1 != 0) 
                { 
                   
                    // unset bit at p1 position 
                    num = num & (~shift1);
                   
                    // set bit at p2 position 
                    num = num | shift2; 
                }
               
                // if bit at p2 position is set 
                else
                {
                   
                    // set bit at p2 position 
                    num = num & (~shift2);
                   
                    // unset bit at p2 position 
                    num = num | shift1; 
                } 
            } 
            p1++; 
            p2++; 
        }
       
        // return final result 
        return num; 
    } 
   
  // Driver code
  public static void main(String[] args) 
  {
    int res = swapBits(28, 0, 3, 2); 
    System.out.println("Result = " + res);
  }
}
 
// This code is contributed by divyeshrabadiya07

Python3

def swapBits(num, p1, p2, n):
    shift1 = 0
    shift2 = 0
    value1 = 0
    value2 = 0
 
    while(n > 0):
       
        # Setting bit at p1 position to 1 
        shift1 = 1 << p1
 
        # Setting bit at p2 position to 1 
        shift2 = 1 << p2
 
        # value1 and value2 will have 0 if num 
        # at the respective positions - p1 and p2 is 0. 
        value1 = ((num & shift1))
        value2 = ((num & shift2))
 
        # check if value1 and value2 are different 
        # i.e. at one position bit is set and other it is not 
        if((value1 == 0 and value2 != 0) or (value2 == 0 and value1 != 0)):
             
            # if bit at p1 positon is set 
            if(value1 != 0):
 
                # unset bit at p1 position 
                num = num & (~shift1)
 
                # set bit at p2 position 
                num = num | shift2
 
            # if bit at p2 position is set 
            else:
 
                # set bit at p2 position 
                num = num & (~shift2)
 
                # unset bit at p2 position
                num = num | shift1
        p1 += 1
        p2 += 1
        n -= 1
 
    # return final result 
    return num
 
# Driver code
res = swapBits(28, 0, 3, 2)
print("Result =", res)
 
# This code is contributed by avanitrachhadiya2155

C#

using System;
class GFG 
{
     
  static int swapBits(int num, int p1, 
                      int p2, int n) 
  { 
    int shift1, shift2, value1, value2; 
    while (n-- > 0) 
    {
 
      // Setting bit at p1 position to 1 
      shift1 = 1 << p1;
 
      // Setting bit at p2 position to 1 
      shift2 = 1 << p2; 
 
      // value1 and value2 will have 0 if num 
      // at the respective positions - p1 and p2 is 0. 
      value1 = ((num & shift1)); 
      value2 = ((num & shift2)); 
 
      // check if value1 and value2 are different 
      // i.e. at one position bit is set and other it is not 
      if ((value1 == 0 && value2 != 0) || (value2 == 0 && value1 != 0)) 
      { 
 
        // if bit at p1 positon is set 
        if (value1 != 0) 
        { 
 
          // unset bit at p1 position 
          num = num & (~shift1); 
 
          // set bit at p2 position 
          num = num | shift2; 
        } 
 
        // if bit at p2 position is set 
        else
        { 
 
          // set bit at p2 position 
          num = num & (~shift2); 
 
          // unset bit at p2 position 
          num = num | shift1; 
        } 
      } 
      p1++; 
      p2++; 
    } 
 
    // return final result 
    return num; 
  } 
 
  // Driver code
  static void Main() 
  {
    int res = swapBits(28, 0, 3, 2); 
    Console.WriteLine("Result = " + res);
  }
}
 
// This code is contributed by divyesh072019

Output:

 Result = 7

References:
Swapping individual bits with XOR
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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