Next greater integer having one more number of set bits

Given a positive integer ‘n’ having ‘x’ number of set bits in its binary representation. The problem is to find the next greater integer(smallest integer greater than n), having (x+1) number of set bits in its binary representation.


Examples :

Input : 10
Output : 11
(10)10 = (1010)2
is having 2 set bits.

(11)10 = (1011)2
is having 3 set bits and is the next greater.

Input : 39
Output : 47

Approach: Following are the steps:

  1. Find the position of the rightmost unset bit(considering last bit at position 0, second last bit at position 1 and so on) in the binary representation of n.
  2. Let the position be represented by pos.
  3. Set the bit at position pos. Refer this post.
  4. If there are no unset bits in the binary representation, then perform bitwise left shift by 1 on the given number and then add 1 to it.

How to get the position of rightmost unset bit?



  1. Perform bitwise not on the given number(operation equivalent to 1’s complement).Let it be num = ~n.
  2. Get the position of rightmost set bit of num.

C++

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// C++ implementation to find the next greater integer
// with one more number of set bits
#include <bits/stdc++.h>
  
using namespace std;
  
// function to find the position of rightmost
// set bit. Returns -1 if there are no set bits
int getFirstSetBitPos(int n)
{
    return (log2(n&-n)+1) - 1;
}
  
// function to find the next greater integer
int nextGreaterWithOneMoreSetBit(int n)
{
    // position of rightmost unset bit of n
    // by passing ~n as argument
    int pos = getFirstSetBitPos(~n);
      
    // if n consists of unset bits, then
    // set the rightmost unset bit
    if (pos > -1)
        return (1 << pos) | n;
          
    //n does not consists of unset bits    
    return ((n << 1) + 1);    
}
  
// Driver program to test above
int main()
{
    int n = 10;
    cout << "Next greater integer = "
          << nextGreaterWithOneMoreSetBit(n);
    return 0;

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Java

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// Java implementation to find the next greater integer
// with one more number of set bits
class GFG {
      
    // function to find the position of rightmost
    // set bit. Returns -1 if there are no set bits
    static int getFirstSetBitPos(int n)
    {
        return ((int)(Math.log(n & -n) / Math.log(2)) + 1) - 1;
    }
  
    // function to find the next greater integer
    static int nextGreaterWithOneMoreSetBit(int n)
    {
          
        // position of rightmost unset bit of n
        // by passing ~n as argument
        int pos = getFirstSetBitPos(~n);
  
        // if n consists of unset bits, then
        // set the rightmost unset bit
        if (pos > -1)
            return (1 << pos) | n;
  
        // n does not consists of unset bits
        return ((n << 1) + 1);
    }
      
    // Driver code
    public static void main(String[] args)
    {
        int n = 10;
        System.out.print("Next greater integer = "
                + nextGreaterWithOneMoreSetBit(n));
    }
}
  
// This code is contributed by Anant Agarwal.

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Python3

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# Python3 implementation to find
# the next greater integer with
# one more number of set bits
import math
  
# Function to find the position
# of rightmost set bit. Returns -1
# if there are no set bits
def getFirstSetBitPos(n):
  
    return ((int)(math.log(n & -n) /
                  math.log(2)) + 1) - 1
  
# Function to find the next greater integer
def nextGreaterWithOneMoreSetBit(n):
  
    # position of rightmost unset bit of 
    # n by passing ~n as argument
    pos = getFirstSetBitPos(~n)
      
    # if n consists of unset bits, then
    # set the rightmost unset bit
    if (pos > -1):
        return (1 << pos) | n
          
    # n does not consists of unset bits 
    return ((n << 1) + 1
  
# Driver code
n = 10
print("Next greater integer = ",
       nextGreaterWithOneMoreSetBit(n))
         
# This code is contributed by Anant Agarwal.

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C#

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// C# implementation to find the next greater
// integer with one more number of set bits
using System;
  
class GFG {
      
    // function to find the position of rightmost
    // set bit. Returns -1 if there are no set bits
    static int getFirstSetBitPos(int n)
    {
        return ((int)(Math.Log(n & -n) / Math.Log(2))
                                            + 1) - 1;
    }
       
    // function to find the next greater integer
    static int nextGreaterWithOneMoreSetBit(int n)
    {
          
        // position of rightmost unset bit of n
        // by passing ~n as argument
        int pos = getFirstSetBitPos(~n);
           
        // if n consists of unset bits, then
        // set the rightmost unset bit
        if (pos > -1)
            return (1 << pos) | n;
               
        // n does not consists of unset bits    
        return ((n << 1) + 1);    
    }
      
    // Driver code
    public static void Main()
    {
        int n = 10;
          
        Console.Write("Next greater integer = "
              + nextGreaterWithOneMoreSetBit(n));
    }
}
  
// This code is contributed by Anant Agarwal.

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PHP

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<?php
// PHP implementation to find the
// next greater integer with
// one more number of set bits
  
// function to find the position
// of rightmost set bit. Returns 
// -1 if there are no set bits
  
function getFirstSetBitPos($n)
{
    return (log($n & -$n + 1)) - 1;
}
  
// function to find the
// next greater integer
  
function nextGreaterWithOneMoreSetBit($n)
{
    // position of rightmost unset bit of n
    // by passing ~n as argument
      
    $pos = getFirstSetBitPos(~$n);
      
    // if n consists of unset bits, then
    // set the rightmost unset bit
    if ($pos > -1)
        return (1 << $pos) | $n;
          
    //n does not consists of unset bits 
    return (($n << 1) + 1); 
}
  
// Driver Code
$n = 10;
echo "Next greater integer = ",
    nextGreaterWithOneMoreSetBit($n);
  
// This code is contributed by Ajit
?>

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Output :

Next greater integer = 11

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