Absolute difference between set and unset bit count in N

Last Updated : 23 Apr, 2023

Prerequisite: Bitset function in STL library
Given a number N, the task is to find the absolute difference of the number of set and unset bits of this given number.

Examples:

Input: N = 14
Output: 2
Explanation:
Binary representation of 14 is "1110".
Here the number of set bits is 3 and the number of unset bits is 1.
Therefore, the absolute difference is 2.

Input: N = 56
Output: 0
Explanation:
Binary representation of 56 is "110100".
Here the number of set bits is 3 and the number of unset bits is 3.
Therefore, the absolute difference 0.

Approach:

Count the total number of bits in the binary representation of the given number.
Use bitset function defined in the STL library, to count the number of set bits efficiently.
Then, we will subtract the set bits from the total number of bits to get the number of unset bits.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Max size of bitset
const int sz = 64;

// Function to return the total bits
// in the binary representation
// of a number
int totalbits(int N)
{
    return (int)(1 + log2(N));
}

// Function to calculate the
// absolute difference
int absoluteDifference(int N)
{
    bitset<sz> arr(N);

    int total_bits = totalbits(N);

    // Calculate the number of
    // set bits
    int set_bits = arr.count();

    // Calculate the number of
    // unset bits
    int unset_bits = total_bits
                     - set_bits;

    int ans = abs(set_bits
                  - unset_bits);

    // Return the absolute difference
    return ans;
}

// Driver Code
int main()
{
    // Given Number
    int N = 14;

    // Function Call
    cout << absoluteDifference(N);
    return 0;
}

Java

// Java program for the above approach 
import java.util.*;

class GFG{

// Max size of bitset
static final int sz = 64;

// Function to return the total bits
// in the binary representation
// of a number
static int totalbits(int N)
{
    return (1 + (int)(Math.log(N) / 
                      Math.log(2)));
}

// Function to calculate the
// absolute difference
static int absoluteDifference(int N)
{
    int arr = N;

    int total_bits = totalbits(N);

    // Calculate the number of
    // set bits
    int set_bits = countSetBits(arr);

    // Calculate the number of
    // unset bits
    int unset_bits = total_bits - set_bits;

    int ans = Math.abs(set_bits - unset_bits);

    // Return the absolute difference
    return ans;
}

static int countSetBits(int n)
{
    int count = 0;
    while (n > 0)
    {
        n &= (n - 1);
        count++;
    }
    return count;
}

// Driver code
public static void main(String[] args)
{
    
    // Given Number
    int N = 14;

    // Function Call
    System.out.println(absoluteDifference(N));
}
}

// This code is contributed by offbeat

Python3

# Python3 program for the above approach 
import math

# Max size of bitset
sz = 64

# Function to return the total bits
# in the binary representation
# of a number
def totalbits(N) :

    return (1 + (int)(math.log(N) / math.log(2)))

# Function to calculate the
# absolute difference
def absoluteDifference(N) :

    arr = N

    total_bits = totalbits(N)

    # Calculate the number of
    # set bits
    set_bits = countSetBits(arr)

    # Calculate the number of
    # unset bits
    unset_bits = total_bits - set_bits

    ans = abs(set_bits - unset_bits)

    # Return the absolute difference
    return ans

def countSetBits(n) :

    count = 0
    while (n > 0) :
    
        n = n & (n - 1)
        count += 1
    
    return count

# Given Number
N = 14

# Function Call
print(absoluteDifference(N))

# This code is contributed by divyesh072019

// C# program for the above approach 
using System;
class GFG{
     
    // Function to return the total bits
    // in the binary representation
    // of a number
    static int totalbits(int N)
    {
        return (1 + (int)(Math.Log(N) / 
                          Math.Log(2)));
    }
     
    // Function to calculate the
    // absolute difference
    static int absoluteDifference(int N)
    {
        int arr = N;
     
        int total_bits = totalbits(N);
     
        // Calculate the number of
        // set bits
        int set_bits = countSetBits(arr);
     
        // Calculate the number of
        // unset bits
        int unset_bits = total_bits - set_bits;
     
        int ans = Math.Abs(set_bits - unset_bits);
     
        // Return the absolute difference
        return ans;
    }
     
    static int countSetBits(int n)
    {
        int count = 0;
        while (n > 0)
        {
            n &= (n - 1);
            count++;
        }
        return count;
    }

  // Driver code
  static void Main() {
      
        // Given Number
        int N = 14;
     
        // Function Call
        Console.WriteLine(absoluteDifference(N));
  }
}

// This code is contributed by divyeshrabadiya07

JavaScript

<script>

    // Javascript program for the above approach
    
    // Function to return the total bits
    // in the binary representation
    // of a number
    function totalbits(N)
    {
        return (1 + parseInt(Math.log(N) / Math.log(2), 10));
    }
      
    // Function to calculate the
    // absolute difference
    function absoluteDifference(N)
    {
        let arr = N;
      
        let total_bits = totalbits(N);
      
        // Calculate the number of
        // set bits
        let set_bits = countSetBits(arr);
      
        // Calculate the number of
        // unset bits
        let unset_bits = total_bits - set_bits;
      
        let ans = Math.abs(set_bits - unset_bits);
      
        // Return the absolute difference
        return ans;
    }
      
    function countSetBits(n)
    {
        let count = 0;
        while (n > 0)
        {
            n &= (n - 1);
            count++;
        }
        return count;
    }
    
    // Given Number
    let N = 14;

    // Function Call
    document.write(absoluteDifference(N));
    
</script>

Output:

Time Complexity: O(log N)

Auxiliary Space: O(1) as constant space for variables and bitset arr is used

Absolute difference between set and unset bit count in N

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