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Set all odd bits of a number

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  • Difficulty Level : Hard
  • Last Updated : 12 Jul, 2022
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Given a number, the task is to set all odd bits of a number. Positions of bits are counted from LSB (least significant bit) to MSB (Most significant bit). Position of LSB is considered as 1.

Examples : 

Input : 20
Output : 21
Explanation : Binary representation of 20
is 10100. Setting all odd
bits make the number 10101 which is binary
representation of 21.

Input : 10
Output : 15
Recommended Practice

Method 1 (Using OR) 
1. First generate a number that contains odd position bits. 
2. Take OR with the original number. Note that 1 | 1 = 1 and 1 | 0 = 1.

Let’s understand this approach with below code.  

C++




// CPP code Set all odd bits
// of a number
#include <iostream>
using namespace std;
 
// set all odd bit
int oddbitsetnumber(int n)
{
    int count = 0;
 
    // res for store 010101.. number
    int res = 0;
 
    // generate number form of 010101.....till
    // temp size
    for (int temp = n; temp > 0; temp >>= 1) {
 
        // if bit is odd, then generate
        // number and or with res
        if (count % 2 == 0)
            res |= (1 << count);
 
        count++;
    }
 
    return (n | res);
}
 
// Driver code
int main()
{
    int n = 10;
    cout << oddbitsetnumber(n);
    return 0;
}

Java




// Java code to Set all odd
// bits of a number
 
class GFG
{
 
    // set all odd bit
    static int oddbitsetnumber(int n)
    {
        int count = 0;
 
        // res for store 010101.. number
        int res = 0;
 
        // generate number form of
        // 010101.....till temp size
        for (int temp = n; temp > 0; temp >>= 1)
        {
 
            // if bit is odd, then generate
            // number and or with res
            if (count % 2 == 0)
                res |= (1 << count);
 
            count++;
        }
 
        return (n | res);
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int n = 10;
        System.out.println(oddbitsetnumber(n));
    }
}
 
// This code is contributed
// by prerna saini

Python3




''' Python3 code Set all odd bits
   of a number'''
    
# set all odd bit
def oddbitsetnumber(n):
    count = 0
    # res for store 010101.. number
    res = 0
 
    # generate number form of 010101.....till
    # temp size
    temp = n
    while temp > 0:
 
        # if bit is odd, then generate
        # number and or with res
        if count % 2 == 0:
            res |= (1 << count)
 
        count += 1
        temp >>= 1
 
    return (n | res)
 
n = 10
print (oddbitsetnumber(n))
 
#This code is contributed by Shreyanshi Arun.

C#




// C# code to Set all odd
// bits of a number
using System;
 
class GFG
{
    static int oddbitsetnumber(int n)
    {
        int count = 0;
 
        // res for store 010101.. number
        int res = 0;
 
        // generate number form of
        // 010101.....till temp size
        for (int temp = n; temp > 0;
                           temp >>= 1)
        {
 
            // if bit is odd, then
            // generate number and
            // or with res
            if (count % 2 == 0)
                res |= (1 << count);
 
            count++;
        }
 
        return (n | res);
    }
     
    // Driver Code
    static public void Main ()
    {
        int n = 10;
        Console.WriteLine(oddbitsetnumber(n));
    }
}
 
// This code is contributed
// by prerna ajit

PHP




<?php
// php code Set all odd
// bits  of a number
 
// set all odd bit
function oddbitsetnumber($n)
{
    $count = 0;
 
    // res for store 010101..
    // number
    $res = 0;
 
    // generate number form of
    // 010101... till temp size
    for ($temp = $n; $temp > 0; $temp >>= 1)
    {
 
        // if bit is odd, then generate
        // number and or with res
        if ($count % 2 == 0)
            $res |= (1 << $count);
 
        $count++;
    }
 
    return ($n | $res);
}
 
    // Driver code
    $n = 10;
    echo oddbitsetnumber($n);
 
// This code is contributed by mits
?>

Javascript




<script>
 
// JavaScript Program to Set all odd
// bits of a number
 
    // set all odd bit
    function oddbitsetnumber(n)
    {
        let count = 0;
  
        // res for store 010101.. number
        let res = 0;
  
        // generate number form of
        // 010101.....till temp size
        for (let temp = n; temp > 0; temp >>= 1)
        {
  
            // if bit is odd, then generate
            // number and or with res
            if (count % 2 == 0)
                res |= (1 << count);
  
            count++;
        }
        return (n | res);
    }
   
// Driver Code
        let n = 10;
        document.write(oddbitsetnumber(n));
        
       // This code is contributed by chinmoy1997pal.
</script>

Output

15

Method 2 (A O(1) solution for 32 bit numbers) 

C++




// Efficient CPP program to set all
// odd bits number
#include <iostream>
using namespace std;
 
// return MSB set number
int getmsb(int n)
{
    // set all bits including MSB.
    n |= n >> 1;
    n |= n >> 2;
    n |= n >> 4;
    n |= n >> 8;
    n |= n >> 16;
 
    // return MSB
    return (n + 1) >> 1;
}
 
// Returns a number of same size (MSB at
// same position) as n and all odd bits
// set.
int getevenbits(int n)
{
    n = getmsb(n);
 
    // generate odd bits like 010101..
    n |= n >> 2;
    n |= n >> 4;
    n |= n >> 8;
    n |= n >> 16;
 
    // if bits is even then shift by 1
    if ((n&1) == 0)
        n = n >> 1;
     
    // return odd set bits number
    return n; 
}
 
// set all odd bits here
int setalloddbits(int n)
{   
    // take OR with odd set bits number
    return n | getevenbits(n);   
}
 
// Driver code
int main()
{
    int n = 10;
    cout << setalloddbits(n);
    return 0;
}

Java




// Efficient Java program to set
// all odd bits number
class GFG {
 
    // return MSB set number
    static int getmsb(int n)
    {
        // set all bits including MSB.
        n |= n >> 1;
        n |= n >> 2;
        n |= n >> 4;
        n |= n >> 8;
        n |= n >> 16;
 
        // return MSB
        return (n + 1) >> 1;
    }
 
    // Returns a number of same
    // size (MSB at same position)
    // as n and all odd bits set.
    static int getevenbits(int n)
    {
        n = getmsb(n);
 
        // generate odd bits
        // like 010101..
        n |= n >> 2;
        n |= n >> 4;
        n |= n >> 8;
        n |= n >> 16;
 
        // if bits is even
        // then shift by 1
        if ((n & 1) == 0)
            n = n >> 1;
 
        // return odd set bits number
        return n;
    }
 
    // set all odd bits here
    static int setalloddbits(int n)
    {
        // take OR with odd
        // set bits number
        return n | getevenbits(n);
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int n = 10;
        System.out.println(setalloddbits(n));
    }
}
 
// This code is contributed
// by prerna saini

Python3




# Efficient python3 program to 
# set all odd bits number
import math
 
# return MSB set number
def getmsb( n):
 
    # set all bits including MSB.
    n |= n >> 1
    n |= n >> 2
    n |= n >> 4
    n |= n >> 8
    n |= n >> 16
 
    # return MSB
    return (n + 1) >> 1
 
 
# Returns a number of same
# size (MSB at same position)
# as n and all odd bits set.
def getevenbits(n):
 
    n = getmsb(n)
 
    # generate odd bits
    # like 010101..
    n |= n >> 2
    n |= n >> 4
    n |= n >> 8
    n |= n >> 16
 
    # if bits is even
    # then shift by 1
    if ((n & 1) == 0):
        n = n >> 1
     
    # return odd set bits number
    return n
 
 
# set all odd bits here
def setalloddbits( n):
 
    # take OR with odd
    # set bits number
    return n | getevenbits(n)
 
 
# Driver Program
n = 10
print(setalloddbits(n))
     
 
# This code is contributed
# by Gitanjali.

C#




// Efficient C# program to
// set all odd bits number
using System;
 
class GFG
{
     
    // return MSB set number
    static int getmsb(int n)
    {
        // set all bits
        // including MSB.
        n |= n >> 1;
        n |= n >> 2;
        n |= n >> 4;
        n |= n >> 8;
        n |= n >> 16;
 
        // return MSB
        return (n + 1) >> 1;
    }
     
    // Returns a number of same
    // size (MSB at same position)
    // as n and all odd bits set.
    static int getevenbits(int n)
    {
        n = getmsb(n);
 
        // generate odd bits
        // like 010101..
        n |= n >> 2;
        n |= n >> 4;
        n |= n >> 8;
        n |= n >> 16;
 
        // if bits is even
        // then shift by 1
        if ((n & 1) == 0)
            n = n >> 1;
 
        // return odd
        // set bits number
        return n;
    }
 
    // set all odd bits here
    static int setalloddbits(int n)
    {
        // take OR with odd
        // set bits number
        return n | getevenbits(n);
    }
 
    // Driver Code
    static public void Main ()
    {
        int n = 10;
        Console.WriteLine(setalloddbits(n));
    }
}
 
// This code is contributed ajit

PHP




<?php
// Efficient php program to
// set all  odd bits number
 
// return MSB set number
function getmsb($n)
{
     
    // set all bits
    // including MSB.
    $n |= $n >> 1;
    $n |= $n >> 2;
    $n |= $n >> 4;
    $n |= $n >> 8;
    $n |= $n >> 16;
 
    // return MSB
    return ($n + 1) >> 1;
}
 
// Returns a number of
// same size (MSB at
// same position) as n
// and all odd bits set
function getevenbits($n)
{
    $n = getmsb($n);
 
    // generate odd bits
    // like 010101..
    $n |= $n >> 2;
    $n |= $n >> 4;
    $n |= $n >> 8;
    $n |= $n >> 16;
 
    // if bits is even
    // then shift by 1
    if (($n&1) == 0)
        $n = $n >> 1;
     
    // return odd set
    // bits number
    return $n;
}
 
// set all odd bits here
function setalloddbits($n)
{
     
    // take OR with odd
    // set bits number
    return $n | getevenbits($n);
}
 
    // Driver code
    $n = 10;
    echo setalloddbits($n);
 
// This code is contributed by mits
?>

Javascript




<script>
 
// Efficient Javascript program to
// set all odd bits number
 
// Return MSB set number
function getmsb(n)
{
     
    // Set all bits
    // including MSB.
    n |= n >> 1;
    n |= n >> 2;
    n |= n >> 4;
    n |= n >> 8;
    n |= n >> 16;
 
    // Return MSB
    return (n + 1) >> 1;
}
  
// Returns a number of same
// size (MSB at same position)
// as n and all odd bits set.
function getevenbits(n)
{
    n = getmsb(n);
 
    // Generate odd bits
    // like 010101..
    n |= n >> 2;
    n |= n >> 4;
    n |= n >> 8;
    n |= n >> 16;
 
    // If bits is even
    // then shift by 1
    if ((n & 1) == 0)
        n = n >> 1;
 
    // Return odd
    // set bits number
    return n;
}
 
// Set all odd bits here
function setalloddbits(n)
{
     
    // Take OR with odd
    // set bits number
    return n | getevenbits(n);
}
 
// Driver Code
let n = 10;
document.write(setalloddbits(n));
 
// This code is contributed by decode2207 
 
</script>

Output

15

Another approach:

O(1) approach which supports even long long (64-bit).

C++




#include <iostream>
using namespace std;
 
long long int setAllOddBits(long long int n) {
        // code here
        long long mask;
          //find required num such that it
          //is of form 000.....1010
          if(__builtin_clz(n)%2==0){
            mask=0x5555555555555555>>(__builtin_clzll(n));
        }else{
            mask=0xAAAAAAAAAAAAAAAA>>(__builtin_clzll(n));
        }
        // return toggled number
        return n|mask;
    }
 
// Driver code
int main()
{
    int n = 10;
    cout << setAllOddBits(n);
    return 0;
}

Output

15

Time complexity: O(1)

Space complexity: O(1)

Another Approach:

To set a bit, we can take OR of 1 and that bit (as 1 | 1 = 1, and 1 | 0 = 1). Therefore, to set all odd bits of an n bit number, we need to use a bit mask which is an n bit binary number with all odd bits set. This mask can be generated in 1 step using the formula of sum of a geometric progression, as an n bit number …0101 is equal to 20 + 22 + 24 + …. 2 (n – 1 – !(n % 1)) .

C++




#include <bits/stdc++.h>
using namespace std;
 
// function to set all the odd bits
long long int setAllOddBits(long long int n)
{
    // calculating number of bits using log
    int numOfBits = 1 + (int)log2(n);
    // calculating the max power of GP series
    int m = (numOfBits + (numOfBits % 2)) / 2;
    // calculating mask using GP sum
    // which is a(r ^ n - 1) / (r - 1)
    // where a = 1, r = 4, n = m
    int mask = (pow(4, m) - 1) / 3;
    // setting all odd bits using mask | n
    return mask | n;
}
 
// Driver code
int main()
{
    int n = 10;
    // function call
    cout << setAllOddBits(n);
    return 0;
}
 
// this code is contributed by phasing17

Javascript




//JavaScript program to implement the approach
 
 
// function to set all the odd bits
function setAllOddBits(n)
{
     
    // calculating number of bits using log
    let numOfBits = 1 + Math.floor(Math.log2(n));
     
    // calculating the max power of GP series
    let m = Math.floor((numOfBits + (numOfBits % 2)) / 2);
     
    // calculating mask using GP sum
    // which is a(r ^ n - 1) / (r - 1)
    // where a = 1, r = 4, n = m
    let mask = Math.floor((Math.pow(4, m) - 1) / 3);
     
    // setting all odd bits using mask | n
    return mask | n;
}
 
 
// Driver code
let n = 10;
 
// function call
console.log(setAllOddBits(n));
 
 
 
// this code is contributed by phasing17

Java




// Java code to implement the approach
 
class GFG {
    // function to set all the odd bits
    static int setAllOddBits(int n)
    {
        // calculating number of bits using log
        int numOfBits
            = 1 + (int)(Math.log(n) / Math.log(2));
 
        // calculating the max power of GP series
        int m = (numOfBits + (numOfBits % 2)) / 2;
 
        // calculating mask using GP sum
        // which is a(r ^ n - 1) / (r - 1)
        // where a = 1, r = 4, n = m
        int mask = (int)(Math.pow(4, m) - 1) / 3;
 
        // setting all odd bits using mask | n
        return mask | n;
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int n = 10;
 
        // function call
        System.out.println(setAllOddBits(n));
    }
}
 
// this code is contributed by phasing17

Output

15

Time complexity: O(1)

Space complexity: O(1)


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