# M-th smallest number having k number of set bits.

Last Updated : 17 Mar, 2023

Given two non-negative integers m and k. The problem is to find the m-th smallest number having k number of set bits.
Constraints: 1 <= m, k.
Examples:

```Input : m = 4, k = 2
Output : 9
(9)10 = (1001)2, it is the 4th smallest
number having 2 set bits.

Input : m = 6, k = 4
Output : 39```

Approach: Following are the steps:

1. Find the smallest number having k number of set bits. Let it be num, where num = (1 << k) – 1.
2. Loop for m-1 times and each time replace num with the next higher number than ‘num’ having same number of bits as in ‘num’. Refer this post to find the required next higher number.
3. Finally return num.

## C++

 `// C++ implementation to find the mth smallest` `// number having k number of set bits` `#include ` `using` `namespace` `std;`   `typedef` `unsigned ``int` `uint_t;`   `// function to find the next higher number` `// with same number of set bits as in 'x'` `uint_t nxtHighWithNumOfSetBits(uint_t x)` `{` `    ``uint_t rightOne;` `    ``uint_t nextHigherOneBit;` `    ``uint_t rightOnesPattern;`   `    ``uint_t next = 0;`   `    ``/* the approach is same as discussed in` `       ``https://www.geeksforgeeks.org/next-higher-number-with-same-number-of-set-bits/` `    ``*/` `    ``if` `(x) {` `        ``rightOne = x & -(``signed``)x;`   `        ``nextHigherOneBit = x + rightOne;`   `        ``rightOnesPattern = x ^ nextHigherOneBit;`   `        ``rightOnesPattern = (rightOnesPattern) / rightOne;`   `        ``rightOnesPattern >>= 2;`   `        ``next = nextHigherOneBit | rightOnesPattern;` `    ``}`   `    ``return` `next;` `}`   `// function to find the mth smallest number` `// having k number of set bits` `int` `mthSmallestWithKSetBits(uint_t m, uint_t k)` `{` `    ``// smallest number having 'k'` `    ``// number of set bits` `    ``uint_t num = (1 << k) - 1;`   `    ``// finding the mth smallest number` `    ``// having k set bits` `    ``for` `(``int` `i = 1; i < m; i++)` `        ``num = nxtHighWithNumOfSetBits(num);`   `    ``// required number` `    ``return` `num;` `}`   `// Driver program to test above` `int` `main()` `{` `    ``uint_t m = 6, k = 4;` `    ``cout << mthSmallestWithKSetBits(m, k);` `    ``return` `0;` `}`

## Javascript

Output:

`39`

Time Complexity: O(m)

Space Complexity: O(1)