Count Set-bits of number using Recursion

Given a positive integer n, the task is to find the number of set bits in its binary representation using recursion.

Examples: 

Input : 21 
Output : 3 
Explanation: 21 represented as 10101 in binary representation.

Input : 16 
Output : 1 
Explanation: 16 represented as 10000 in binary representation.

Using Recursion and Right Shift Operator - O(log n) time and O(log n) space

The idea is to recursively check the least significant bit in the number. If the bit is 1, increment the result. Right shift the number by 1, and recursively find the number of set bits in the computed number.

Step by step approach:  

1. Recursively check the least significant bit of a number. Base case will return 0 if number is 0.
2. If the least significant bit is 1, add 1 to result.
3. Right shift the number by 1, to remove the least significant bit and recursively find the number of set bits in the computed number.  

// C++ program to find number
// of set bist in a number
#include <bits/stdc++.h>
using namespace std;

// Recursive function to find
// number of set bist in a number
int setBits(int n) {

	// Base condition
	if (n == 0)
		return 0;

	// If Least significant bit is set
	if((n & 1) == 1)
		return 1 + setBits(n >> 1);

	// If Least significant bit is not set
	else
		return setBits(n >> 1);
}

int main() {
	int n = 21;
	cout << setBits(n) << endl;

	return 0;
}

// Java program to find number
// of set bits in a number

class GfG {
    
    // Recursive function to find
    // number of set bits in a number
    static int setBits(int n) {
        
        // Base condition
        if (n == 0)
            return 0;

        // If Least significant bit is set
        if((n & 1) == 1)
            return 1 + setBits(n >> 1);

        // If Least significant bit is not set
        else
            return setBits(n >> 1);
    }

    public static void main(String[] args) {
        int n = 21;
        System.out.println(setBits(n));
    }
}

# Python program to find number
# of set bits in a number

# Recursive function to find
# number of set bits in a number
def setBits(n):
    
    # Base condition
    if n == 0:
        return 0

    # If Least significant bit is set
    if (n & 1) == 1:
        return 1 + setBits(n >> 1)

    # If Least significant bit is not set
    else:
        return setBits(n >> 1)

if __name__ == "__main__":
    n = 21
    print(setBits(n))

// C# program to find number
// of set bits in a number

using System;

class GfG {
    
    // Recursive function to find
    // number of set bits in a number
    static int setBits(int n) {
        // Base condition
        if (n == 0)
            return 0;

        // If Least significant bit is set
        if((n & 1) == 1)
            return 1 + setBits(n >> 1);

        // If Least significant bit is not set
        else
            return setBits(n >> 1);
    }

    static void Main() {
        int n = 21;
        Console.WriteLine(setBits(n));
    }
}

// JavaScript program to find number
// of set bits in a number

// Recursive function to find
// number of set bits in a number
function setBits(n) {
    
    // Base condition
    if (n === 0)
        return 0;

    // If Least significant bit is set
    if((n & 1) === 1)
        return 1 + setBits(n >> 1);

    // If Least significant bit is not set
    else
        return setBits(n >> 1);
}

let n = 21;
console.log(setBits(n));

3

Related Article:

• Count set bits in an integer