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Code Bit Logic

Find the sum of bit differences among all pairs

Swapping the values of variables is a common operation in programming. Typically, programmers use a temporary (fourth) variable to perform the swap. However, there are methods to perform variable swapping without using an additional variable. In this article, we will discuss a method to swap three variables using the XOR operation.

Problem Statement

The problem is to swap the values of three variables x, y, and z without using any extra variable. In other words, after the swap, x should contain the initial value of y, y should contain the initial value of z, and z should contain the initial value of x.

Explanation with Suitable Example

Let's take an example to understand the problem better: Suppose we have three variables:

int x = 10;
int y = 20;
int z = 30;

We want to swap their values such that:

x = 20;
y = 30;
z = 10;

Standard Pseudocode

The swap function can be implemented using XOR as follows:

function swapThreeVariables(x, y, z):
    x = x ^ y ^ z
    y = x ^ y ^ z
    z = x ^ y ^ z
    x = x ^ y ^ z
    return x, y, z

Algorithm Explanation

  1. We take the XOR of all three variables and store it in x. At this point, x will contain the combined value of x, y, and z.
  2. Then, we use the XOR operation to find the original values and store them in y and z. Since x now holds the combined value, XORing it with the current value of y gives us the original value of z, and XORing it with the current value of z gives us the original value of y.
  3. Finally, we again XOR the combined value (now stored in x) with the new values in y and z to obtain the original value of x.

Code Solution

Here given code implementation process.

// C program 
// Find the sum of bit differences among all pairs
#include <stdio.h>

// Display array elements
void display(int num[], int n)
{
	printf("\n Given number : ");
	for (int i = 0; i < n; ++i)
	{
		printf(" %d", num[i]);
	}
}
// Find sum of bit differences of all existing pair in given array
void pair_bit_diff(int num[], int n)
{
	display(num, n);
	// Work with 4 byte integer
	// 1 byte 8 bit so 4 byte 32 bit
	int bits = 32;
	// Use to collect result
	int result = 0;
	// Set bit counter
	int count = 0;
	// Execute loop through by 4 bytes
	for (int i = 0; i < bits; ++i)
	{
		// Execute loop through by size of num
		for (int j = 0; j < n; ++j)
		{
			if ((1 << i) & num[j])
			{
				// When ith bit is active
				count++;
			}
		}
		// Add different bits result
		// Here count indicates active bits
		// n is total number of bits
		result += (count *(n - count)) *2;
		// Reset bit counter
		count = 0;
	}
	// Display calculated result
	printf("\n Bit Different : %d\n", result);
}
int main(int argc, char
	const *argv[])
{
	int num[] = {
		3 , 8 , 1 , 2
	};
	// Get the number of elements
	int n = sizeof(num) / sizeof(num[0]);
	// Test
	pair_bit_diff(num, n);
	return 0;
}

Output

 Given number :  3 8 1 2
 Bit Different : 22
/*
  Java program
  Find the sum of bit differences among all pairs
*/
public class Difference
{
	// Display array elements
	public void display(int[] num, int n)
	{
		System.out.print("\n Given number  : ");
		for (int i = 0; i < n; ++i)
		{
			System.out.print("  " + num[i]);
		}
	}
	// Find sum of bit differences of all existing pair in given array
	public void pairBitDifference(int[] num, int n)
	{
		display(num, n);
		// Work with 4 byte integer
		// 1 byte 8 bit so 4 byte 32 bit
		int bits = 32;
		// Use to collect result
		int result = 0;
		// Set bit counter
		int count = 0;
		// Execute loop through by 4 bytes
		for (int i = 0; i < bits; ++i)
		{
			// Execute loop through by size of num
			for (int j = 0; j < n; ++j)
			{
				if (((1 << i) & num[j]) != 0)
				{
					// When ith bit is active
					count++;
				}
			}
			// Add different bits result
			// Here count indicates active bits
			// n is total number of bits
			result += (count * (n - count)) * 2;
			// Reset bit counter
			count = 0;
		}
		// Display calculated result
		System.out.print("\n Bit Different : " + result + "\n");
	}
	public static void main(String[] args)
	{
		Difference task = new Difference();
		int[] num = {
			3 , 8 , 1 , 2
		};
		// Get the number of elements
		int n = num.length;
		// Test
		task.pairBitDifference(num, n);
	}
}

Output

 Given number  :   3  8  1  2
 Bit Different : 22
// Include header file
#include <iostream>

using namespace std;
/*
  C++ program
  Find the sum of bit differences among all pairs
*/
class Difference
{
	public:
		// Display array elements
		void display(int num[], int n)
		{
			cout << "\n Given number  : ";
			for (int i = 0; i < n; ++i)
			{
				cout << "  " << num[i];
			}
		}
	// Find sum of bit differences of all existing pair in given array
	void pairBitDifference(int num[], int n)
	{
		this->display(num, n);
		// Work with 4 byte integer
		// 1 byte 8 bit so 4 byte 32 bit
		int bits = 32;
		// Use to collect result
		int result = 0;
		// Set bit counter
		int count = 0;
		// Execute loop through by 4 bytes
		for (int i = 0; i < bits; ++i)
		{
			// Execute loop through by size of num
			for (int j = 0; j < n; ++j)
			{
				if (((1 << i) &num[j]) != 0)
				{
					// When ith bit is active
					count++;
				}
			}
			// Add different bits result
			// Here count indicates active bits
			// n is total number of bits
			result += (count *(n - count)) *2;
			// Reset bit counter
			count = 0;
		}
		// Display calculated result
		cout << "\n Bit Different : " << result << "\n";
	}
};
int main()
{
	Difference task = Difference();
	int num[] = {
		3 , 8 , 1 , 2
	};
	// Get the number of elements
	int n = sizeof(num) / sizeof(num[0]);
	// Test
	task.pairBitDifference(num, n);
	return 0;
}

Output

 Given number  :   3  8  1  2
 Bit Different : 22
// Include namespace system
using System;
/*
  C# program
  Find the sum of bit differences among all pairs
*/
public class Difference
{
	// Display array elements
	public void display(int[] num, int n)
	{
		Console.Write("\n Given number  : ");
		for (int i = 0; i < n; ++i)
		{
			Console.Write("  " + num[i]);
		}
	}
	// Find sum of bit differences of all existing pair in given array
	public void pairBitDifference(int[] num, int n)
	{
		display(num, n);
		// Work with 4 byte integer
		// 1 byte 8 bit so 4 byte 32 bit
		int bits = 32;
		// Use to collect result
		int result = 0;
		// Set bit counter
		int count = 0;
		// Execute loop through by 4 bytes
		for (int i = 0; i < bits; ++i)
		{
			// Execute loop through by size of num
			for (int j = 0; j < n; ++j)
			{
				if (((1 << i) & num[j]) != 0)
				{
					// When ith bit is active
					count++;
				}
			}
			// Add different bits result
			// Here count indicates active bits
			// n is total number of bits
			result += (count * (n - count)) * 2;
			// Reset bit counter
			count = 0;
		}
		// Display calculated result
		Console.Write("\n Bit Different : " + result + "\n");
	}
	public static void Main(String[] args)
	{
		Difference task = new Difference();
		int[] num = {
			3 , 8 , 1 , 2
		};
		// Get the number of elements
		int n = num.Length;
		// Test
		task.pairBitDifference(num, n);
	}
}

Output

 Given number  :   3  8  1  2
 Bit Different : 22
<?php
/*
  Php program
  Find the sum of bit differences among all pairs
*/
class Difference
{
	// Display array elements
	public	function display( & $num, $n)
	{
		echo "\n Given number  : ";
		for ($i = 0; $i < $n; ++$i)
		{
			echo "  ". $num[$i];
		}
	}
	// Find sum of bit differences of all existing pair in given array
	public	function pairBitDifference( & $num, $n)
	{
		$this->display($num, $n);
		// Work with 4 byte integer
		// 1 byte 8 bit so 4 byte 32 bit
		$bits = 32;
		// Use to collect result
		$result = 0;
		// Set bit counter
		$count = 0;
		// Execute loop through by 4 bytes
		for ($i = 0; $i < $bits; ++$i)
		{
			// Execute loop through by size of num
			for ($j = 0; $j < $n; ++$j)
			{
				if (((1 << $i) & $num[$j]) != 0)
				{
					// When ith bit is active
					$count++;
				}
			}
			// Add different bits result
			// Here count indicates active bits
			// n is total number of bits
			$result += ($count * ($n - $count)) * 2;
			// Reset bit counter
			$count = 0;
		}
		// Display calculated result
		echo "\n Bit Different : ". $result ."\n";
	}
}

function main()
{
	$task = new Difference();
	$num = array(3, 8, 1, 2);
	// Get the number of elements
	$n = count($num);
	// Test
	$task->pairBitDifference($num, $n);
}
main();

Output

 Given number  :   3  8  1  2
 Bit Different : 22
/*
  Node Js program
  Find the sum of bit differences among all pairs
*/
class Difference
{
	// Display array elements
	display(num, n)
	{
		process.stdout.write("\n Given number  : ");
		for (var i = 0; i < n; ++i)
		{
			process.stdout.write("  " + num[i]);
		}
	}
	// Find sum of bit differences of all existing pair in given array
	pairBitDifference(num, n)
	{
		this.display(num, n);
		// Work with 4 byte integer
		// 1 byte 8 bit so 4 byte 32 bit
		var bits = 32;
		// Use to collect result
		var result = 0;
		// Set bit counter
		var count = 0;
		// Execute loop through by 4 bytes
		for (var i = 0; i < bits; ++i)
		{
			// Execute loop through by size of num
			for (var j = 0; j < n; ++j)
			{
				if (((1 << i) & num[j]) != 0)
				{
					// When ith bit is active
					count++;
				}
			}
			// Add different bits result
			// Here count indicates active bits
			// n is total number of bits
			result += (count * (n - count)) * 2;
			// Reset bit counter
			count = 0;
		}
		// Display calculated result
		process.stdout.write("\n Bit Different : " + result + "\n");
	}
}

function main()
{
	var task = new Difference();
	var num = [3, 8, 1, 2];
	// Get the number of elements
	var n = num.length;
	// Test
	task.pairBitDifference(num, n);
}
main();

Output

 Given number  :   3  8  1  2
 Bit Different : 22
#   Python 3 program
#   Find the sum of bit differences among all pairs

class Difference :
	#  Display list elements
	def display(self, num, n) :
		print("\n Given number  : ", end = "")
		i = 0
		while (i < n) :
			print("  ", num[i], end = "")
			i += 1
		
	
	#  Find sum of bit differences of all existing pair in given list
	def pairBitDifference(self, num, n) :
		self.display(num, n)
		#  Work with 4 byte integer
		#  1 byte 8 bit so 4 byte 32 bit
		bits = 32
		#  Use to collect result
		result = 0
		#  Set bit counter
		count = 0
		#  Execute loop through by 4 bytes
		i = 0
		while (i < bits) :
			#  Execute loop through by size of num
			j = 0
			while (j < n) :
				if (((1 << i) & num[j]) != 0) :
					#  When ith bit is active
					count += 1
				
				j += 1
			
			#  Add different bits result
			#  Here count indicates active bits
			#  n is total number of bits
			result += (count * (n - count)) * 2
			#  Reset bit counter
			count = 0
			i += 1
		
		#  Display calculated result
		print("\n Bit Different : ", result )
	

def main() :
	task = Difference()
	num = [3, 8, 1, 2]
	#  Get the number of elements
	n = len(num)
	#  Test
	task.pairBitDifference(num, n)

if __name__ == "__main__": main()

Output

 Given number  :    3   8   1   2
 Bit Different :  22
#   Ruby program
#   Find the sum of bit differences among all pairs

class Difference 
	#  Display array elements
	def display(num, n) 
		print("\n Given number  : ")
		i = 0
		while (i < n) 
			print("  ", num[i])
			i += 1
		end

	end

	#  Find sum of bit differences of all existing pair in given array
	def pairBitDifference(num, n) 
		self.display(num, n)
		#  Work with 4 byte integer
		#  1 byte 8 bit so 4 byte 32 bit
		bits = 32
		#  Use to collect result
		result = 0
		#  Set bit counter
		count = 0
		#  Execute loop through by 4 bytes
		i = 0
		while (i < bits) 
			#  Execute loop through by size of num
			j = 0
			while (j < n) 
				if (((1 << i) & num[j]) != 0) 
					#  When ith bit is active
					count += 1
				end

				j += 1
			end

			#  Add different bits result
			#  Here count indicates active bits
			#  n is total number of bits
			result += (count * (n - count)) * 2
			#  Reset bit counter
			count = 0
			i += 1
		end

		#  Display calculated result
		print("\n Bit Different : ", result ,"\n")
	end

end

def main() 
	task = Difference.new()
	num = [3, 8, 1, 2]
	#  Get the number of elements
	n = num.length
	#  Test
	task.pairBitDifference(num, n)
end

main()

Output

 Given number  :   3  8  1  2
 Bit Different : 22
/*
  Scala program
  Find the sum of bit differences among all pairs
*/
class Difference
{
	// Display array elements
	def display(num: Array[Int], n: Int): Unit = {
		print("\n Given number  : ");
		var i: Int = 0;
		while (i < n)
		{
			print("  " + num(i));
			i += 1;
		}
	}
	// Find sum of bit differences of all existing pair in given array
	def pairBitDifference(num: Array[Int], n: Int): Unit = {
		this.display(num, n);
		// Work with 4 byte integer
		// 1 byte 8 bit so 4 byte 32 bit
		var bits: Int = 32;
		// Use to collect result
		var result: Int = 0;
		// Set bit counter
		var count: Int = 0;
		// Execute loop through by 4 bytes
		var i: Int = 0;
		while (i < bits)
		{
			// Execute loop through by size of num
			var j: Int = 0;
			while (j < n)
			{
				if (((1 << i) & num(j)) != 0)
				{
					// When ith bit is active
					count += 1;
				}
				j += 1;
			}
			// Add different bits result
			// Here count indicates active bits
			// n is total number of bits
			result += (count * (n - count)) * 2;
			// Reset bit counter
			count = 0;
			i += 1;
		}
		// Display calculated result
		print("\n Bit Different : " + result + "\n");
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var task: Difference = new Difference();
		var num: Array[Int] = Array(3, 8, 1, 2);
		// Get the number of elements
		var n: Int = num.length;
		// Test
		task.pairBitDifference(num, n);
	}
}

Output

 Given number  :   3  8  1  2
 Bit Different : 22
/*
  Swift 4 program
  Find the sum of bit differences among all pairs
*/
class Difference
{
	// Display array elements
	func display(_ num: [Int], _ n: Int)
	{
		print("\n Given number  : ", terminator: "");
		var i: Int = 0;
		while (i < n)
		{
			print("  ", num[i], terminator: "");
			i += 1;
		}
	}
	// Find sum of bit differences of all existing pair in given array
	func pairBitDifference(_ num: [Int], _ n: Int)
	{
		self.display(num, n);
		// Work with 4 byte integer
		// 1 byte 8 bit so 4 byte 32 bit
		let bits: Int = 32;
		// Use to collect result
		var result: Int = 0;
		// Set bit counter
		var count: Int = 0;
		// Execute loop through by 4 bytes
		var i: Int = 0;
		while (i < bits)
		{
			// Execute loop through by size of num
			var j: Int = 0;
			while (j < n)
			{
				if (((1 << i) & num[j])  != 0)
				{
					// When ith bit is active
					count += 1;
				}
				j += 1;
			}
			// Add different bits result
			// Here count indicates active bits
			// n is total number of bits
			result += (count * (n - count)) * 2;
			// Reset bit counter
			count = 0;
			i += 1;
		}
		// Display calculated result
		print("\n Bit Different : ", result );
	}
}
func main()
{
	let task: Difference = Difference();
	let num: [Int] = [3, 8, 1, 2];
	// Get the number of elements
	let n: Int = num.count;
	// Test
	task.pairBitDifference(num, n);
}
main();

Output

 Given number  :    3   8   1   2
 Bit Different :  22
/*
  Kotlin program
  Find the sum of bit differences among all pairs
*/
class Difference
{
	// Display array elements
	fun display(num: Array < Int > , n: Int): Unit
	{
		print("\n Given number  : ");
		var i: Int = 0;
		while (i < n)
		{
			print("  " + num[i]);
			i += 1;
		}
	}
	// Find sum of bit differences of all existing pair in given array
	fun pairBitDifference(num: Array < Int > , n: Int): Unit
	{
		this.display(num, n);
		// Work with 4 byte integer
		// 1 byte 8 bit so 4 byte 32 bit
		var bits: Int = 32;
		// Use to collect result
		var result: Int = 0;
		// Set bit counter
		var count: Int = 0;
		// Execute loop through by 4 bytes
		var i: Int = 0;
		while (i < bits)
		{
			// Execute loop through by size of num
			var j: Int = 0;
			while (j < n)
			{
				if (((1 shl i) and num[j]) != 0)
				{
					// When ith bit is active
					count += 1;
				}
				j += 1;
			}
			// Add different bits result
			// Here count indicates active bits
			// n is total number of bits
			result += (count * (n - count)) * 2;
			// Reset bit counter
			count = 0;
			i += 1;
		}
		// Display calculated result
		print("\n Bit Different : " + result + "\n");
	}
}
fun main(args: Array < String > ): Unit
{
	var task: Difference = Difference();
	var num: Array < Int > = arrayOf(3, 8, 1, 2);
	// Get the number of elements
	var n: Int = num.count();
	// Test
	task.pairBitDifference(num, n);
}

Output

 Given number  :   3  8  1  2
 Bit Different : 22

Time Complexity

The time complexity of the swap function is O(1) because the XOR operation takes constant time, irrespective of the values of the variables involved.

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