Count set bits in an integer

Try it on GfG Practice

Given a positive number n count the set bit .
Examples : 

Input : n = 6
Output : 2
Binary representation of 6 is 110 and has 2 set bits

Input : n = 13
Output : 3
Binary representation of 13 is 1101 and has 3 set bits

[Naive Approach] - One by One Counting

This approach counts the set bits by checking each bit from right to left. It uses n & 1 to check if the least significant bit is 1, increments the count if so, then right-shifts the number to check the next bit. This repeats until n becomes 0, returning the total number of set bits.

#include <bits/stdc++.h> using namespace std; /* Function to get no of set bits in binary representation of positive integer n */ unsigned int countSetBits(unsigned int n) {  unsigned int count = 0;  while (n) {  count += n & 1;  n >>= 1;  }  return count; } int main() {  int i = 9;  cout << countSetBits(i);  return 0; } 

#include <stdio.h> /* Function to get no of set bits in binary  representation of positive integer n */ unsigned int countSetBits(unsigned int n) {  unsigned int count = 0;  while (n) {  count += n & 1;  n >>= 1;  }  return count; } int main() {  int i = 9;  printf("%d", countSetBits(i));  return 0; } 

import java.io.*;  class GFG{  /* Function to get no of set   bits in binary representation   of positive integer n */  static int countSetBits(int n)  {  int count = 0;  while (n > 0) {  count += n & 1;  n >>= 1;  }  return count;  }  public static void main(String args[])  {  int i = 9;  System.out.println(countSetBits(i));  } } 

 # Function to get no of set # bits in binary representation # of positive integer n def countSetBits(n): count = 0 while (n): count += n & 1 n >>= 1 return count # Program to test function countSetBits if __name__ == "__main__": i = 9 print(countSetBits(i)) 

using System; class GFG {  // Function to get no of set  // bits in binary representation  // of positive integer n  static int countSetBits(int n)  {  int count = 0;  while (n > 0) {  count += n & 1;  n >>= 1;  }  return count;  }  public static void Main()  {  int i = 9;  Console.Write(countSetBits(i));  } } 

   // Javascript program to Count set  // bits in an integer  /* Function to get no of set bits in binary  representation of positive integer n */  function countSetBits(n)  {  var count = 0;  while (n)  {  count += n & 1;  n >>= 1;  }  return count;  }  // Driver Code   var i = 9;  console.log(countSetBits(i));   

<?php // Function to get no of set  // bits in binary representation  // of positive integer n  function countSetBits($n) { $count = 0; while ($n) { $count += $n & 1; $n >>= 1; } return $count; } $i = 9; echo countSetBits($i); ?> 

2

Time Complexity: O(log n) 
Auxiliary Space: O(1)

Recursive Implementation The function checks if the least significant bit is 1 and adds to the count. It then right-shifts the number and repeats this process recursively until all bits are checked, returning the total count of set bits.

#include <bits/stdc++.h> using namespace std; // recursive function to count set bits int countSetBits(int n) {  // base case  if (n == 0)  return 0;  else  // if last bit set add 1 else add 0  return (n & 1) + countSetBits(n >> 1); } // driver code int main() {  int n = 9;  // function calling  cout << countSetBits(n);  return 0; } 

#include <stdio.h> // recursive function to count set bits int countSetBits(int n) {  // base case  if (n == 0)  return 0;  else  // if last bit set add 1 else add 0  return (n & 1) + countSetBits(n >> 1); } // driver code int main() {  int n = 9;  // function calling  printf("%d", countSetBits(n));  return 0; } 

import java.io.*; class GFG {  // recursive function to count set bits  public static int countSetBits(int n)  {  // base case  if (n == 0)  return 0;  else  // if last bit set add 1 else add 0  return (n & 1) + countSetBits(n >> 1);  }  // Driver code  public static void main(String[] args)  {  // get value from user  int n = 9;  // function calling  System.out.println(countSetBits(n));  } } 

def countSetBits( n): # base case if (n == 0): return 0 else: # if last bit set add 1 else # add 0 return (n & 1) + countSetBits(n >> 1) # Get value from user n = 9 # Function calling print( countSetBits(n)) 

using System; class GFG {  // recursive function  // to count set bits  public static int countSetBits(int n)  {  // base case  if (n == 0)  return 0;  else  // if last bit set  // add 1 else add 0  return (n & 1) + countSetBits(n >> 1);  }  // Driver code  static public void Main()  {  // get value  // from user  int n = 9;  // function calling  Console.WriteLine(countSetBits(n));  } } 

// recursive function to count set bits function countSetBits(n) {  // base case  if (n == 0)  return 0;  else  // if last bit set add 1 else add 0  return (n & 1) + countSetBits(n >> 1); } // driver code  let n = 9  console.log (countSetBits(n)); 

<?php // recursive function  // to count set bits function countSetBits($n) { // base case if ($n == 0) return 0; else // if last bit set  // add 1 else add 0 return ($n & 1) + countSetBits($n >> 1); } $n = 9; // function calling echo countSetBits($n); ?> 

2

Time Complexity: O(log n)
Auxiliary Space: O(log n)for recursive stack space

[Expected Approach 1] - Brian Kernighan's Algorithm

Brian Kernighan’s algorithm counts set bits efficiently by clearing them one by one. The key operation is n &= (n - 1), which removes the least significant set bit from n. Each time this is done, it means one set bit has been counted and removed. The process repeats until n becomes 0, and the total number of times the loop runs gives the count of set bits. This is faster than checking each bit individually because it only iterates as many times as there are set bits in the number.

Subtracting 1 from a decimal number flips all the bits after the rightmost set bit(which is 1) including the rightmost set bit. 
for example : 
10 in binary is 00001010 
9 in binary is 00001001 
8 in binary is 00001000 
7 in binary is 00000111 
So if we subtract a number by 1 and do it bitwise & with itself (n & (n-1)), we unset the rightmost set bit. If we do n & (n-1) in a loop and count the number of times the loop executes, we get the set bit count. 

The beauty of this solution is the number of times it loops is equal to the number of set bits in a given integer. 

1 Initialize count: = 0
2 If integer n is not zero
(a) Do bitwise & with (n-1) and assign the value back to n
n: = n&(n-1)
(b) Increment count by 1
(c) go to step 2
3 Else return count

#include <iostream> using namespace std; class gfg {  /* Function to get no of set bits in binary representation of passed binary no. */ public:  unsigned int countSetBits(int n)  {  unsigned int count = 0;  while (n) {  n &= (n - 1);  count++;  }  return count;  } }; /* Program to test function countSetBits */ int main() {  gfg g;  int i = 9;  cout << g.countSetBits(i);  return 0; } 

#include <stdio.h> /* Function to get no of set bits in binary  representation of passed binary no. */ unsigned int countSetBits(int n) {  unsigned int count = 0;  while (n) {  n &= (n - 1);  count++;  }  return count; } /* Program to test function countSetBits */ int main() {  int i = 9;  printf("%d", countSetBits(i));  getchar();  return 0; } 

import java.io.*; class GFG {  /* Function to get no of set   bits in binary representation   of passed binary no. */  static int countSetBits(int n)  {  int count = 0;  while (n > 0) {  n &= (n - 1);  count++;  }  return count;  }  public static void main(String args[])  {  int i = 9;  System.out.println(countSetBits(i));  } } // This code is contributed by Anshika Goyal. 

# Function to get no of set bits in binary # representation of passed binary no. */ def countSetBits(n): count = 0 while (n): n &= (n-1) count+= 1 return count # Program to test function countSetBits  i = 9 print(countSetBits(i)) 

using System; class GFG {  /* Function to get no of set   bits in binary representation   of passed binary no. */  static int countSetBits(int n)  {  int count = 0;  while (n > 0) {  n &= (n - 1);  count++;  }  return count;  }  static public void Main()  {  int i = 9;  Console.WriteLine(countSetBits(i));  } } // This code is contributed by ajit 

/* Function to get no of set  bits in binary representation  of passed binary no. */ function countSetBits(n) {  var count = 0;  while (n > 0)  {  n &= (n - 1);  count++;  }  return count; } // driver program var i = 9; console.log (countSetBits(i)); 

<?php /* Function to get no of  set bits in binary representation of passed  binary no. */ function countSetBits($n) { $count = 0; while ($n) { $n &= ($n - 1) ; $count++; } return $count; } $i = 9; echo countSetBits($i); ?> 

2

Time Complexity: O(log n)
Auxiliary Space: O(1)

[Expected Approach 2] - Using Lookup table

It first builds a table BitsSetTable256[] storing the count of set bits for all 8-bit numbers (0–255). In countSetBits, the 32-bit number is divided into four 8-bit chunks, and the table is used to quickly find the set bits in each byte. Summing these gives the total set bit count. This method is efficient because it replaces bitwise loops with quick table lookups, making it ideal when frequent set bit counting is needed.

#include <bits/stdc++.h> using namespace std; int BitsSetTable256[256]; // Function to initialise the lookup table  void initialize()  {   // To initially generate the   // table algorithmically   BitsSetTable256[0] = 0;   for (int i = 0; i < 256; i++)  {   BitsSetTable256[i] = (i & 1) +   BitsSetTable256[i / 2];   }  }  // Function to return the count  // of set bits in n  int countSetBits(int n)  {   return (BitsSetTable256[n & 0xff] +   BitsSetTable256[(n >> 8) & 0xff] +   BitsSetTable256[(n >> 16) & 0xff] +   BitsSetTable256[n >> 24]);  }  int main()  {   // Initialise the lookup table   initialize();   int n = 9;   cout << countSetBits(n); }  

import java.util.*; class GFG {  static int[] BitsSetTable256 = new int[256];  // Function to initialise the lookup table  public static void initialize()  {  // To initially generate the  // table algorithmically  BitsSetTable256[0] = 0;  for (int i = 0; i < 256; i++) {  BitsSetTable256[i] = (i & 1) + BitsSetTable256[i / 2];  }  }  // Function to return the count  // of set bits in n  public static int countSetBits(int n)  {  return (BitsSetTable256[n & 0xff]  + BitsSetTable256[(n >> 8) & 0xff]  + BitsSetTable256[(n >> 16) & 0xff]  + BitsSetTable256[n >> 24]);  }  // Driver code  public static void main(String[] args)  {  // Initialise the lookup table  initialize();  int n = 9;  System.out.print(countSetBits(n));  } } 

BitsSetTable256 = [0] * 256 # Function to initialise the lookup table  def initialize(): # To initially generate the  # table algorithmically  BitsSetTable256[0] = 0 for i in range(256): BitsSetTable256[i] = (i & 1) + BitsSetTable256[i // 2] # Function to return the count  # of set bits in n  def countSetBits(n): return (BitsSetTable256[n & 0xff] + BitsSetTable256[(n >> 8) & 0xff] + BitsSetTable256[(n >> 16) & 0xff] + BitsSetTable256[n >> 24]) if __name__ == "__main__": initialize() n = 9 print(countSetBits(n)) 

using System; using System.Collections.Generic; class GFG  {  static int[] BitsSetTable256 = new int[256];  // Function to initialise the lookup table  public static void initialize()  {  // To initially generate the  // table algorithmically  BitsSetTable256[0] = 0;  for (int i = 0; i < 256; i++)  {  BitsSetTable256[i] = (i & 1) + BitsSetTable256[i / 2];  }  }  // Function to return the count  // of set bits in n  public static int countSetBits(int n)  {  return (BitsSetTable256[n & 0xff]  + BitsSetTable256[(n >> 8) & 0xff]  + BitsSetTable256[(n >> 16) & 0xff]  + BitsSetTable256[n >> 24]);  }  public static void Main(String[] args)  {  // Initialise the lookup table  initialize();  int n = 9;  Console.Write(countSetBits(n));  } } 

var BitsSetTable256 = Array.from({length: 256}, (_, i) => 0); // Function to initialise the lookup table function initialize() {  // To initially generate the  // table algorithmically  BitsSetTable256[0] = 0;  for (var i = 0; i < 256; i++) {  BitsSetTable256[i] = (i & 1) +   BitsSetTable256[parseInt(i / 2)];  } } // Function to return the count // of set bits in n function countSetBits(n) {  return (BitsSetTable256[n & 0xff]  + BitsSetTable256[(n >> 8) & 0xff]  + BitsSetTable256[(n >> 16) & 0xff]  + BitsSetTable256[n >> 24]); } // Driver code initialize(); var n = 9; console.log (countSetBits(n)); 

2

Time Complexity: O(1)
Auxiliary Space: O(1)

[Expected Approach 3] - Mapping Nibbles

It simply maintains a map(or array) of numbers to bits for a nibble. A Nibble contains 4 bits. So we need an array of up to 15. 
int num_to_bits[16] = {0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4}; 
Now we just need to get nibbles of a given long/int/word etc recursively.

#include <bits/stdc++.h> using namespace std; int num_to_bits[16] = { 0, 1, 1, 2, 1, 2, 2, 3,  1, 2, 2, 3, 2, 3, 3, 4 }; /* Recursively get nibble of a given number  and map them in the array */ unsigned int countSetBitsRec(unsigned int num) {  int nibble = 0;  if (0 == num)  return num_to_bits[0];  // Find last nibble  nibble = num & 0xf;  // Use pre-stored values to find count  // in last nibble plus recursively add  // remaining nibbles.  return num_to_bits[nibble] + countSetBitsRec(num >> 4); } int main() {  int num = 9;  cout << countSetBitsRec(num);  return 0; } 

#include <stdio.h> int num_to_bits[16] = { 0, 1, 1, 2, 1, 2, 2, 3,  1, 2, 2, 3, 2, 3, 3, 4 }; /* Recursively get nibble of a given number   and map them in the array */ unsigned int countSetBitsRec(unsigned int num) {  int nibble = 0;  if (0 == num)  return num_to_bits[0];  // Find last nibble  nibble = num & 0xf;  // Use pre-stored values to find count  // in last nibble plus recursively add  // remaining nibbles.  return num_to_bits[nibble] + countSetBitsRec(num >> 4); } int main() {  int num = 9;  printf("%d\n", countSetBitsRec(num)); } 

import java.util.*; class GFG {  static int[] num_to_bits = new int[] { 0, 1, 1, 2, 1, 2, 2,  3, 1, 2, 2, 3, 2, 3, 3, 4 };  static int countSetBitsRec(int num)  {  int nibble = 0;  if (0 == num)  return num_to_bits[0];  // Find last nibble  nibble = num & 0xf;  // Use pre-stored values to find count  // in last nibble plus recursively add  // remaining nibbles.  return num_to_bits[nibble] + countSetBitsRec(num >> 4);  }  public static void main(String[] args)  {  int num = 9;  System.out.println(countSetBitsRec(num));  } } 

num_to_bits =[0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4]; # Recursively get nibble of a given number  # and map them in the array def countSetBitsRec(num): nibble = 0; if(0 == num): return num_to_bits[0]; # Find last nibble nibble = num & 0xf; # Use pre-stored values to find count # in last nibble plus recursively add # remaining nibbles. return num_to_bits[nibble] + countSetBitsRec(num >> 4); # Driver code  num = 9; print(countSetBitsRec(num)); # this code is contributed by mits 

class GFG {  static int[] num_to_bits = new int[16] { 0, 1, 1, 2, 1, 2, 2,  3, 1, 2, 2, 3, 2, 3, 3, 4 };  /* Recursively get nibble of a given number  and map them in the array */  static int countSetBitsRec(int num)  {  int nibble = 0;  if (0 == num)  return num_to_bits[0];  // Find last nibble  nibble = num & 0xf;  // Use pre-stored values to find count  // in last nibble plus recursively add  // remaining nibbles.  return num_to_bits[nibble] + countSetBitsRec(num >> 4);  }  // Driver code  static void Main()  {  int num = 9;  System.Console.WriteLine(countSetBitsRec(num));  } } // this code is contributed by mits 

var num_to_bits =[ 0, 1, 1, 2, 1, 2, 2,  3, 1, 2, 2, 3, 2, 3, 3, 4 ]; /* Recursively get nibble of a given number  and map them in the array */ function countSetBitsRec(num) {  var nibble = 0;  if (0 == num)  return num_to_bits[0];  // Find last nibble  nibble = num & 0xf;  // Use pre-stored values to find count  // in last nibble plus recursively add  // remaining nibbles.  return num_to_bits[nibble] + countSetBitsRec(num >> 4); } // Driver code var num = 9; console.log (countSetBitsRec(num)); 

<?php $num_to_bits = array(0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4); /* Recursively get nibble of a given  number and map them in the array */ function countSetBitsRec( $num) { global $num_to_bits; $nibble = 0; if (0 == $num) return $num_to_bits[0]; // Find last nibble  $nibble = $num & 0xf; // Use pre-stored values to find count  // in last nibble plus recursively add  // remaining nibbles.  return $num_to_bits[$nibble] + countSetBitsRec($num >> 4); } // Driver code  $num = 9; echo (countSetBitsRec($num)); // This code is contributed by mits ?> 

2

Time Complexity: O(log n), because we have log(16, n) levels of recursion.
Storage Complexity: O(1) Whether the given number is short, int, long, or long long we require an array of 16 sizes only, which is constant.

Using power of 2 (efficient method to find for large value also)

Iterate from k to 0 , where k is the largest power of 2 such that pow(2, k) <= num . And check if the Bitwise AND of num and pow(2, i) is greater than zero or not. If it is greater than zero , Then i-th bit is set ,then increase the count by 1.

#include <bits/stdc++.h> using namespace std; // Function to find largest power of 2 such that // pow(2,k) <= N  int findk(int n) { int k; int i=0; int val=pow(2,i);    while(val<=n)  {   k=i; i++;  val=pow(2,i);  }  return k; } // Function to count set bits in a number int countSetBits(int N) {  int count = 0;  int k=findk(N);  int val , x;    // Iterating from largest power to 2 such that   // pow(2,k) to 0  for (int i = k; i >= 0; i--)  {  val=pow(2,i);  x=val & N; //x will store Bitwise AND of N & val    if(x > 0)  { count++;  }  }  return count;//return count of set bits } int main() {  int N = 9;    // Function call  cout << countSetBits(N) << endl;  return 0; } 

import java.io.*; public class GFG {  // Function to find largest power of 2 such that  // pow(2,k) <= N  static int findk(int n)  {  int k = 0;  int i = 0;  int val = (int)Math.pow(2, i);  while (val <= n) {  k = i;  i++;  val = (int)Math.pow(2, i);  }  return k;  }  // Function to count set bits in a number  static int countSetBits(int N)  {  int count = 0;  int k = findk(N);  int val, x;  // Iterating from largest   // power to 2 such that  // pow(2,k) to 0  for (int i = k; i >= 0; i--) {  val = (int)Math.pow(2, i);  x = val  & N;  // x will store Bitwise AND of N & val  if (x > 0) {  count++;  }  }  return count;   // return count of set bits  }  public static void main(String[] args)  {  int N = 9;  System.out.println(countSetBits(N));  } } 

import math # Function to find largest  # power of 2 such that # pow(2,k) <= N def findk(n): i = 0 val = math.pow(2, i) while val <= n: k = i i += 1 val = math.pow(2, i) return k # Function to count set bits in a number def countSetBits(N): count = 0 k = findk(N) for i in range(k, -1, -1): val = int(math.pow(2, i)) x = val & N # x will store Bitwise AND of N & val if x > 0: count += 1 return count if __name__ == '__main__': N = 9 print(countSetBits(N)) 

using System; class Program {  // Function to find largest power of 2 such that  // pow(2,k) <= N  static int FindK(int n)  {  int k = 0;  int i = 0;  int val = (int)Math.Pow(2, i);  while (val <= n)  {  k = i;  i++;  val = (int)Math.Pow(2, i);  }  return k;  }  // Function to count set bits in a numnber  static int CountSetBits(int N)  {  int count = 0;  int k = FindK(N);  int val, x;  // Iterating from largest power to 2 such that  // pow(2,k) to 0  for (int i = k; i >= 0; i--)  {  val = (int)Math.Pow(2, i);  x = val & N;   //x will store Bitwise AND of N & val  if (x > 0)  {  count++;  }  }  return count;  //return count of set bits  }  static void Main()  {  int N = 9;  // Function call  Console.WriteLine(CountSetBits(N));  } } 

// function to find largest power of 2 such that // pow(2,k) <= N function findk(n){  let k;  let i = 0;  let val = Math.pow(2,i);  while(val <= n){  k=i;  i++;  val = Math.pow(2,i);  }  return k; } // function to count set bits in a number function countSetBits(N){  let count = 0;  let k = findk(N);  let val;  let x;    // iterating from largest power to 2 such that  // pow(2,k) to 0  for(let i = k; i>=0; i--){  val = Math.pow(2,i);  x = val & N;     // x will store bitwise and of N and val  if(x > 0) count++;  }    // return count of set bits  return count;  } // driver program let N = 9; console.log(countSetBits(N)); 

2 

Time Complexity: O(logn) 
Auxiliary Space: O(1)

Using Library or Quick Syntax

In C++ GCC, we can directly count set bits using __builtin_popcount(). So we can avoid a separate function for counting set bits. Similarly, we have direct syntax in other programming languages.

// C++ program to demonstrate __builtin_popcount() #include <iostream> using namespace std; int main() {    cout << __builtin_popcount(9);  return 0; } 

// java program to demonstrate // __builtin_popcount() import java.io.*; class GFG {  // Driver code  public static void main(String[] args)  {  System.out.println(Integer.bitCount(9));  } } 

print(bin(9).count('1')); 

using System; class Program {  static void Main(string[] args)  {  Console.WriteLine(Convert.ToString(9, 2).Replace("0", "").Length);  } } 

// Javascript program to demonstrate // __builtin_popcount() console.log ((9).toString(2).split('').  filter(x => x == '1').length + "<br>"); 

<?php // PHP program to demonstrate popcount equivalent echo substr_count(decbin(9), '1'); ?> 

4