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 bitsetconst int sz = 64;// Function to return the total bits// in the binary representation// of a numberint totalbits(int N){ return (int)(1 + log2(N));}// Function to calculate the// absolute differenceint 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 Codeint 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 bitsetstatic final int sz = 64;// Function to return the total bits// in the binary representation// of a numberstatic int totalbits(int N){ return (1 + (int)(Math.log(N) / Math.log(2)));}// Function to calculate the// absolute differencestatic 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 codepublic 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 bitsetsz = 64# Function to return the total bits# in the binary representation# of a numberdef totalbits(N) : return (1 + (int)(math.log(N) / math.log(2)))# Function to calculate the# absolute differencedef 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 ansdef countSetBits(n) : count = 0 while (n > 0) : n = n & (n - 1) count += 1 return count# Given NumberN = 14# Function Callprint(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
<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:
2
Time Complexity: O(log N)
Auxiliary Space: O(1) as constant space for variables and bitset arr is used
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