Count unset bits of a number

Given a number n, count unset bits after MSB (Most Significant Bit).
Examples :

Input : 17
Output : 3
Binary of 17 is 10001
so unset bit is 3

Input : 7
Output : 0

A Simple Solution is to traverse through all bits and count unset bits. 

C++

// C++ program to count unset bits in an integer
#include <iostream>
using namespace std;

int countunsetbits(int n)
{
    int count = 0;

    // x holds one set digit at a time
    // starting from LSB to MSB of n.
    for (int x = 1; x <= n; x = x<<1)
        if ((x & n) == 0)
            count++;

    return count;
}

// Driver code
int main()
{
    int n = 17;
    cout << countunsetbits(n);
    return 0;
}

Java

// JAVA Code to Count unset bits in a number
class GFG {

    public static int countunsetbits(int n)
    {
        int count = 0;

        // x holds one set digit at a time
        // starting from LSB to MSB of n.
        for (int x = 1; x <= n; x = x<<1)
            if ((x & n) == 0)
                count++;

        return count;
    }

    /* Driver program to test above function */
    public static void main(String[] args)
    {
        int n = 17;
        System.out.println(countunsetbits(n));
    }
}
// This code is contributed by Arnav Kr. Mandal.

Python3

# Python 3 program to count unset
# bits in an integer

def countunsetbits(n):
    count = 0

    # x holds one set digit at a time
    # starting from LSB to MSB of n.
    x = 1
    while(x < n + 1):
        if ((x & n) == 0):
            count += 1
        x = x << 1

    return count

# Driver code
if __name__ == '__main__':
    n = 17
    print(countunsetbits(n))

# This code is contributed by
# Shashank_Sharma

C#

// C# Code to Count unset
// bits in a number
using System;

class GFG {

    // Function to count unset bits
    public static int countunsetbits(int n)
    {
        int count = 0;

        // x holds one set digit at a time
        // starting from LSB to MSB of n.
        for (int x = 1; x <= n; x = x << 1)
            if ((x & n) == 0)
                count++;

        return count;
    }

    // Driver Code
    public static void Main()
    {
        int n = 17;
        Console.Write(countunsetbits(n));
    }
}

// This code is contributed by Nitin Mittal.

PHP

<?php
// PHp program to count
// unset bits in an integer
function countunsetbits($n)
{
    $count = 0;

    // x holds one set digit
    // at a time starting
    // from LSB to MSB of n.
    for ($x = 1; $x <= $n;
         $x = $x << 1)
        if (($x & $n) == 0)
            $count++;

    return $count;
}

// Driver code
$n = 17;
echo countunsetbits($n);

// This code is contributed
// by nitin mittal.
?>

Javascript

<script>

// Javascript program to count unset bits in an integer

function countunsetbits(n)
{
    var count = 0;

    // x holds one set digit at a time
    // starting from LSB to MSB of n.
    for (var x = 1; x <= n; x = x<<1)
        if ((x & n) == 0)
            count++;

    return count;
}

// Driver code
var n = 17;
document.write(countunsetbits(n));

</script>

Output :

3

Above solution complexity is log(n).

Space Complexity : O(1)
Efficient Solutions : 
The idea is to toggle bits in O(1) time. Then apply any of the methods discussed in count set bits article.
In GCC, we can directly count set bits using __builtin_popcount(). First toggle the bits and then apply above function __builtin_popcount().

C++

// An optimized C++ program to count unset bits
// in an integer.
#include <iostream>
using namespace std;

int countUnsetBits(int n)
{
    int x = n;

    // Make all bits set MSB
    // (including MSB)

    // This makes sure two bits
    // (From MSB and including MSB)
    // are set
    n |= n >> 1;

    // This makes sure 4 bits
    // (From MSB and including MSB)
    // are set
    n |= n >> 2;

    n |= n >> 4;
    n |= n >> 8;
    n |= n >> 16;

    // Count set bits in toggled number
    return  __builtin_popcount(x ^ n);
}

// Driver code
int main()
{
    int n = 17;
    cout << countUnsetBits(n);
    return 0;
}

Java

// An optimized Java program to count unset bits
// in an integer.
class GFG
{

static int countUnsetBits(int n)
{
    int x = n;

    // Make all bits set MSB
    // (including MSB)

    // This makes sure two bits
    // (From MSB and including MSB)
    // are set
    n |= n >> 1;

    // This makes sure 4 bits
    // (From MSB and including MSB)
    // are set
    n |= n >> 2;

    n |= n >> 4;
    n |= n >> 8;
    n |= n >> 16;

    // Count set bits in toggled number
    return Integer.bitCount(x^ n);
}

// Driver code
public static void main(String[] args)
{
    int n = 17;
    System.out.println(countUnsetBits(n));
}
}

/* This code contributed by PrinciRaj1992 */

Python3

# An optimized Python program to count
# unset bits in an integer.
import math

def countUnsetBits(n):
    x = n

    # Make all bits set MSB(including MSB)

    # This makes sure two bits(From MSB
    # and including MSB) are set
    n |= n >> 1

    # This makes sure 4 bits(From MSB and
    # including MSB) are set
    n |= n >> 2

    n |= n >> 4
    n |= n >> 8
    n |= n >> 16

    t = math.log(x ^ n, 2)

    # Count set bits in toggled number
    return math.floor(t)

# Driver code
n = 17
print(countUnsetBits(n))

# This code is contributed 29AjayKumar

C#

// An optimized C# program to count unset bits
// in an integer.
using System;

class GFG
{

static int countUnsetBits(int n)
{
    int x = n;

    // Make all bits set MSB
    // (including MSB)

    // This makes sure two bits
    // (From MSB and including MSB)
    // are set
    n |= n >> 1;

    // This makes sure 4 bits
    // (From MSB and including MSB)
    // are set
    n |= n >> 2;

    n |= n >> 4;
    n |= n >> 8;
    n |= n >> 16;

    // Count set bits in toggled number
    return BitCount(x^ n);
}

static int BitCount(long x)
{

    // To store the count
    // of set bits
    int setBits = 0;
    while (x != 0) {
        x = x & (x - 1);
        setBits++;
    }

    return setBits;
}

// Driver code
public static void Main(String[] args)
{
    int n = 17;
    Console.WriteLine(countUnsetBits(n));
}
}

// This code contributed by Rajput-Ji

PHP

<?php
// An optimized PHP program
// to count unset bits in
// an integer.

function countUnsetBits($n)
{
    $x = $n;

    // Make all bits set
    // MSB(including MSB)

    // This makes sure two
    // bits(From MSB and
    // including MSB) are set
    $n |= $n >> 1;

    // This makes sure 4
    // bits(From MSB and
    // including MSB) are set
    $n |= $n >> 2;

    $n |= $n >> 4;
    $n |= $n >> 8;
    $n |= $n >> 16;

    $t = log($x ^ $n,2);

    // Count set bits
    // in toggled number
    return floor($t);
}

// Driver code
$n = 17;
echo countUnsetBits($n);

// This code is contributed
// by ajit
?>

Javascript

<script>

// JavaScript program to count unset bits
// in an integer.

function countUnsetBits(n)
{
    let x = n;

    // Make all bits set MSB
    // (including MSB)

    // This makes sure two bits
    // (From MSB and including MSB)
    // are set
    n |= n >> 1;

    // This makes sure 4 bits
    // (From MSB and including MSB)
    // are set
    n |= n >> 2;

    n |= n >> 4;
    n |= n >> 8;
    n |= n >> 16;

    // Count set bits in toggled number
    return BitCount(x^ n);
}

function BitCount(x)
{

    // To store the count
    // of set bits
    let setBits = 0;
    while (x != 0) {
        x = x & (x - 1);
        setBits++;
    }

    return setBits;
}

// Driver Code

    let n = 17;
    document.write(countUnsetBits(n));

// This code is contributed by susmitakundugoaldanga.
</script>

Output :

3

Time Complexity: O(1)

Auxiliary Space:  O(1)
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