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)= (1010)_{10}_{2}is having 2 set bits.(11)= (1011)_{10}_{2}is having 3 set bits and is the next greater. Input : 39 Output : 47

**Approach:** Following are the steps:

- 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**. - Let the position be represented by
**pos**. - Set the bit at position
**pos**. Refer this post. - 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?**

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

// 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; }

Output:

Next greater integer = 11

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