# 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++

 `// C++ implementation to find the next greater integer``// with one more number of set bits``#include ` `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;``} `

## Java

 `// 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.`

## Python3

 `# 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.`

## C#

 `// 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.`

## PHP

 ` -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``?>`

## Javascript

 ``

Output :

`Next greater integer = 11`

Time Complexity: O(log(log N))
Auxiliary Space: O(1)

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