# Count set bits in an integer

Write an efficient program to count number of 1s in binary representation of an integer.

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 11 is 1101 and has 3 set bits
```

1. Simple Method Loop through all bits in an integer, check if a bit is set and if it is then increment the set bit count. See below program.

## C++

 `// C++ program to Count set ` `// bits in an integer  ` `#include       ` `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; ` `} ` ` `  `/* Program to test function countSetBits */` `int` `main() ` `{ ` `    ``int` `i = 9; ` `    ``cout << countSetBits(i); ` `    ``return` `0; ` `} ` ` `  `// This code is contributed  ` `// by Akanksha Rai `

/div>

## C

 `// C program to Count set ` `// bits in an integer  ` `#include         ` ` `  `/* 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; ` `} ` ` `  `/* Program to test function countSetBits */` `int` `main() ` `{ ` `    ``int` `i = 9; ` `    ``printf``(``"%d"``, countSetBits(i)); ` `    ``return` `0; ` `} `

## Java

 `// Java program to Count set ` `// bits in an integer  ` `import` `java.io.*;  ` ` `  `class` `countSetBits ` `{ ` `    ``/* 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; ` `    ``} ` ` `  `    ``// driver program ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `i = ``9``; ` `        ``System.out.println(countSetBits(i)); ` `    ``} ` `} ` ` `  `// This code is contributed by Anshika Goyal. `

## Python3

 `# Python3 program to Count set ` `# bits in an integer  ` ` `  `# 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 */ ` `i ``=` `9` `print``(countSetBits(i)) ` ` `  `# This code is contributed by ` `# Smitha Dinesh Semwal `

## C#

 `// C# program to Count set ` `// bits in an integer  ` `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; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `i = 9; ` `        ``Console.Write(countSetBits(i)); ` `    ``} ` `} ` ` `  `// This code is contributed by Sam007 `

## PHP

 `>= 1; ` `    ``} ` `    ``return` `\$count``; ` `} ` ` `  `// Driver Code ` `\$i` `= 9; ` `echo` `countSetBits(``\$i``); ` ` `  `// This code is contributed by ajit ` `?> `

Output :

```2
```

Time Complexity: (-)(logn) (Theta of logn)

Recursive Approach :

## C++

 `// cpp implementation of recursive ` `// approach to find the number ` `// of set bits in binary representation ` `// of positive integer n ` `#include ` `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() ` `{ ` `    ``// get value from user ` `    ``int` `n = 9; ` ` `  `    ``// function calling ` `    ``cout << countSetBits(n); ` ` `  `    ``return` `0; ` `} ` ` `  `// This code is contributed by Raj. `

## Java

 `// Java implementation of recursive ` `// approach to find the number ` `// of set bits in binary representation ` `// of positive integer n ` `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)); ` `    ``} ` `} ` ` `  `// This code is contributes by sunnysingh `

## Python3

 `# Python3 implementation of recursive ` `# approach to find the number of set ` `# bits in binary representation of  ` `# positive integer 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))      ` `         `  `# This code is contributed by sunnysingh `

## C#

 `// C# implementation of recursive ` `// approach to find the number of  ` `// set bits in binary representation ` `// of positive integer 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)); ` `    ``} ` `} ` ` `  `// This code is contributed by aj_36 `

## PHP

 `> 1); ` `} ` ` `  `// Driver code ` ` `  `// get value from user ` `\$n` `= 9; ` ` `  `// function calling ` `echo` `countSetBits(``\$n``); ` ` `  `// This code is contributed by m_kit. ` `?> `

Output :

```2
```

2. Brian Kernighan’s Algorithm:
Subtraction of 1 from a number toggles all the bits (from right to left) till the rightmost set bit(including the rightmost set bit). So if we subtract a number by 1 and do bitwise & with itself (n & (n-1)), we unset the rightmost set bit. If we do n & (n-1) in a loop and count the no of times 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
```

Implementation of Brian Kernighan’s Algorithm:

## C++

 `// C++ program to Count set ` `// bits in an integer  ` `#include ` `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; ` `} `

## C

 `// C program to Count set ` `// bits in an integer  ` `#include ` ` `  `/* 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; ` `} `

## Java

 `// Java program to Count set  ` `// bits in an integer  ` `import` `java.io.*;  ` ` `  `class` `countSetBits ` `{ ` `    ``/* 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; ` `    ``} ` ` `  `    ``// driver program ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `           ``int` `i = ``9``; ` `        ``System.out.println(countSetBits(i)); ` `    ``} ` `} ` ` `  `// This code is contributed by Anshika Goyal. `

## Python3

 `# 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)) ` `  `  `# This code is contributed by ` `# Smitha Dinesh Semwal `

## C#

 `// C# program to Count set  ` `// bits in an integer ` `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; ` `    ``} ` ` `  `    ``// Driver Code ` `    ``static` `public` `void` `Main () ` `    ``{ ` `        ``int` `i = 9; ` `        ``Console.WriteLine(countSetBits(i)); ` `    ``} ` `} ` ` `  `// This code is contributed by ajit `

## PHP

 ` `

Output :

```2
```

Example for Brian Kernighan’s Algorithm:

```   n =  9 (1001)
count = 0

Since 9 > 0, subtract by 1 and do bitwise & with (9-1)
n = 9&8  (1001 & 1000)
n = 8
count  = 1

Since 8 > 0, subtract by 1 and do bitwise & with (8-1)
n = 8&7  (1000 & 0111)
n = 0
count = 2

Since n = 0, return count which is 2 now.
```

Time Complexity: O(logn)

Recursive Approach :

## C++

 `// CPP implementation for recursive  ` `// approach to find the number of set ` `// bits using Brian Kernighan’s Algorithm ` `#include ` `using` `namespace` `std; ` ` `  `// recursive function to count set bits ` `int` `countSetBits(``int` `n) ` `{ ` `    ``// base case ` `    ``if` `(n == 0) ` `        ``return` `0; ` `    ``else` `        ``return` `1 + countSetBits(n & (n - 1)); ` `} ` ` `  `// driver code  ` `int` `main() ` `{ ` `    ``// get value from user ` `    ``int` `n = 9; ` `     `  `    ``// function calling ` `    ``cout << countSetBits(n); ` `     `  `    ``return` `0; ` `} ` ` `  `// This code is contributed by Raj. `

## Java

 `// Java implementation for recursive ` `// approach to find the number of set ` `// bits using Brian Kernighan Algorithm ` `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` `            ``return` `1` `+ countSetBits(n & (n - ``1``)); ` `    ``} ` `     `  `    ``// Driver function ` `    ``public` `static` `void` `main(String[] args) { ` ` `  `        ``// get value from user ` `        ``int` `n = ``9``; ` `     `  `        ``// function calling ` `        ``System.out.println(countSetBits(n)); ` `    ``} ` `} ` ` `  `// This code is contributed by sunnysingh `

## Python3

 `# Python3 implementation for ` `# recursive approach to find ` `# the number of set bits using ` `# Brian Kernighan’s Algorithm ` ` `  `# recursive function to count ` `# set bits ` `def` `countSetBits(n): ` ` `  `    ``# base case ` `    ``if` `(n ``=``=` `0``): ` `        ``return` `0` `    ``else``: ` `        ``return` `1` `+` `countSetBits(n & (n ``-` `1``)) ` `             `  `             `  `# Get value from user ` `n ``=` `9` `     `  `# function calling ` `print``(countSetBits(n)) ` ` `  `# This code is contributed by sunnysingh `

## C#

 `// C# implementation for recursive ` `// approach to find the number of set ` `// bits using Brian Kernighan Algorithm ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `    ``// recursive function  ` `    ``// to count set bits ` `    ``public` `static` `int` `countSetBits(``int` `n)  ` `    ``{ ` `         `  `        ``// base case ` `        ``if` `(n == 0) ` `            ``return` `0; ` `        ``else` `            ``return` `1 +  ` `                   ``countSetBits(n &  ` `                               ``(n - 1)); ` `    ``} ` `     `  `    ``// Driver Code ` `    ``static` `public` `void` `Main () ` `    ``{ ` `         `  `        ``// get value from user ` `        ``int` `n = 9; ` `     `  `        ``// function calling ` `        ``Console.WriteLine(countSetBits(n)); ` `    ``} ` `} ` ` `  `// This code is contributed by aj_36 `

## PHP

 ` `

Output :

```2
```

3. Using Lookup table: We can count bits in O(1) time using lookup table. Please see http://graphics.stanford.edu/~seander/bithacks.html#CountBitsSetTable for details.

We can find one use of counting set bits at Count number of bits to be flipped to convert A to B

Note: In GCC, we can directly count set bits using __builtin_popcount(). So we can avoid a separate function for counting set bits.

## C++

 `// C++ program to demonstrate __builtin_popcount() ` `#include ` `using` `namespace` `std; ` ` `  `int` `main() ` `{ ` `   ``cout << __builtin_popcount (4) << endl; ` `   ``cout << __builtin_popcount (15); ` ` `  `   ``return` `0; ` `} `

## Java

 `// java program to demonstrate ` `// __builtin_popcount() ` ` `  `import` `java.io.*; ` ` `  `class` `GFG { ` `     `  `    ``//Driver code ` `    ``public` `static` `void` `main (String[] args) { ` `         `  `        ``System.out.println(Integer.bitCount(``4``)); ` `        ``System.out.println(Integer.bitCount(``15``)); ` `    ``} ` `} ` ` `  `// This code is contributed by Raj `

## Python3

 `# Python3 program to demonstrate __builtin_popcount() ` ` `  `print``(``bin``(``4``).count(``'1'``)); ` `print``(``bin``(``15``).count(``'1'``)); ` ` `  `# This code is Contributed by mits `

## C#

 `// C# program to demonstrate  ` `// __builtin_popcount()  ` `using` `System; ` `using` `System.Linq; ` ` `  `class` `GFG {  ` `     `  `    ``//Driver code  ` `    ``public` `static` `void` `Main () {  ` `         `  `        ``Console.WriteLine(Convert.ToString(4, 2). ` `                            ``Count(c => c == ``'1'``));  ` `        ``Console.WriteLine(Convert.ToString(15, 2). ` `                            ``Count(c => c == ``'1'``));  ` `    ``}  ` `}  ` ` `  `// This code is contributed by mits `

## PHP

 ` `

Output :

```1
4```

4. Mapping numbers with the bit. It simply maintains a Map(or array) of numbers to bits for a nibble. A Nibble contains 4bits. So we need an array 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 given long/int/word etc recuresively.

## C++

 `// C++ program to count set bits by pre-storing  ` `// count set bits in nibbles.  ` `#include ` `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);  ` `}  ` ` `  `// Driver code  ` `int` `main()  ` `{  ` `    ``int` `num = 31;  ` `    ``cout<

## C

 `// C program to count set bits by pre-storing ` `// count set bits in nibbles. ` `#include         ` ` `  `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); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `   ``int` `num = 31; ` `   ``printf``(````"%d "````, countSetBitsRec(num)); ` `} `

## Java

 `// Java program to count set bits by pre-storing  ` `// count set bits in nibbles.  ` ` `  `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``};  ` ` `  `/* 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  ` `public` `static` `void` `main(String[] args)  ` `{  ` `int` `num = ``31``;  ` `System.out.println(countSetBitsRec(num));  ` `}  ` `} ` `// this code is contributed by mits `

## Python3

 `# Python3 program to count set bits by pre-storing  ` `# count set bits in nibbles.  ` ` `  `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 ``=` `31``;  ` `print``(countSetBitsRec(num));  ` ` `  ` `  `# this code is contributed by mits `

## C#

 `// C# program to count set bits by pre-storing  ` `// count set bits in nibbles.  ` ` `  `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 = 31;  ` `System.Console.WriteLine(countSetBitsRec(num));  ` `}  ` `} ` `// this code is contributed by mits `

## PHP

 `> 4);  ` `}  ` ` `  `// Driver code  ` `\$num` `= 31;  ` `echo` `(countSetBitsRec(``\$num``));  ` ` `  `// This code is contributed by mits ` `?> `

Output :

```5
```

Time Complexity: O(1)
Storage Complexity: O(1) Whether given number is short, int, long or long long we require array of 16 size only which is constant.

Count set bits in an integer Using Lookup Table