# Absolute difference between set and unset bit count in N

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:
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:
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:

1. Count the total number of bits in the binary representation of the given number.
2. Use bitset function defined in the STL library, to count the number of set bits efficiently.
3. 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 ` `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 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#

 `// 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

 ``

Output:

`2`

Time Complexity: O(log N)

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

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