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# Find the smallest number with n set and m unset bits

• Difficulty Level : Medium
• Last Updated : 31 May, 2022

Given two non-negative numbers n and m. The problem is to find the smallest number having n number of set bits and m number of unset bits in its binary representation.
Constraints: 1 <= n, 0 <= m, (m+n) <= 31
Note : 0 bits before leading 1 (or leftmost 1) in binary representation are counted

Examples:

```Input : n = 2, m = 2
Output : 9
(9)10 = (1001)2
We can see that in the binary representation of 9
there are 2 set and 2 unsets bits and it is the
smallest number.

Input : n = 4, m = 1
Output : 23```

Approach: Following are the steps:

1. Calculate num = (1 << (n + m)) – 1. This will produce a number num having (n + m) number of bits and all are set.
2. Now, toggle bits in the range from n to (n+m-1) in num, i.e, to toggle bits from the rightmost nth bit to the rightmost (n+m-1)th bit and then return the toggled number. Refer this post.

## C++

 `// C++ implementation to find the smallest number` `// with n set and m unset bits` `#include `   `using` `namespace` `std;`   `// function to toggle bits in the given range` `unsigned ``int` `toggleBitsFromLToR(unsigned ``int` `n,` `                                ``unsigned ``int` `l,` `                                ``unsigned ``int` `r)` `{` `    ``// for invalid range` `    ``if` `(r < l)` `        ``return` `n;`   `    ``// calculating a number 'num' having 'r'` `    ``// number of bits and bits in the range l` `    ``// to r are the only set bits` `    ``int` `num = ((1 << r) - 1) ^ ((1 << (l - 1)) - 1);`   `    ``// toggle bits in the range l to r in 'n'` `    ``// and return the number` `    ``return` `(n ^ num);` `}`   `// function to find the smallest number` `// with n set and m unset bits` `unsigned ``int` `smallNumWithNSetAndMUnsetBits(unsigned ``int` `n,` `                                           ``unsigned ``int` `m)` `{` `    ``// calculating a number 'num' having '(n+m)' bits` `    ``// and all are set` `    ``unsigned ``int` `num = (1 << (n + m)) - 1;`   `    ``// required smallest number` `    ``return` `toggleBitsFromLToR(num, n, n + m - 1);` `}`   `// Driver program to test above` `int` `main()` `{` `    ``unsigned ``int` `n = 2, m = 2;` `    ``cout << smallNumWithNSetAndMUnsetBits(n, m);` `    ``return` `0;` `}`

## Java

 `// Java implementation to find the smallest number` `// with n set and m unset bits`   `class` `GFG ` `{` `    ``// Function to toggle bits in the given range` `    ``static` `int` `toggleBitsFromLToR(``int` `n, ``int` `l, ``int` `r)` `    ``{` `        ``// for invalid range` `        ``if` `(r < l)` `            ``return` `n;` ` `  `        ``// calculating a number 'num' having 'r'` `        ``// number of bits and bits in the range l` `        ``// to r are the only set bits` `        ``int` `num = ((``1` `<< r) - ``1``) ^ ((``1` `<< (l - ``1``)) - ``1``);` ` `  `        ``// toggle bits in the range l to r in 'n'` `        ``// and return the number` `        ``return` `(n ^ num);` `    ``}` `    `  `    ``// Function to find the smallest number` `    ``// with n set and m unset bits` `    ``static` `int` `smallNumWithNSetAndMUnsetBits(``int` `n, ``int` `m)` `    ``{` `        ``// calculating a number 'num' having '(n+m)' bits` `        ``// and all are set` `        ``int` `num = (``1` `<< (n + m)) - ``1``;` ` `  `        ``// required smallest number` `        ``return` `toggleBitsFromLToR(num, n, n + m - ``1``);` `    ``}` `    `  `    ``// driver program` `    ``public` `static` `void` `main (String[] args) ` `    ``{` `        ``int` `n = ``2``, m = ``2``;` `        ``System.out.println(smallNumWithNSetAndMUnsetBits(n, m));` `    ``}` `}`   `// Contributed by Pramod Kumar`

## Python3

 `# Python3 implementation to find` `# the smallest number with n set` `# and m unset bits`   `# function to toggle bits in the` `# given range` `def` `toggleBitsFromLToR(n, l, r):`   `    ``# for invalid range` `    ``if` `(r < l):` `        ``return` `n` ` `  `    ``# calculating a number 'num'` `    ``# having 'r' number of bits` `    ``# and bits in the range l` `    ``# to r are the only set bits` `    ``num ``=` `((``1` `<< r) ``-` `1``) ^ ((``1` `<< (l ``-` `1``)) ``-` `1``)` ` `  `    ``# toggle bits in the range` `    ``# l to r in 'n' and return the number` `    ``return` `(n ^ num)`   `# function to find the smallest number` `# with n set and m unset bits` `def` `smallNumWithNSetAndMUnsetBits(n, m):`   `    ``# calculating a number 'num' having` `    ``# '(n+m)' bits and all are set` `    ``num ``=` `(``1` `<< (n ``+` `m)) ``-` `1` ` `  `    ``# required smallest number` `    ``return` `toggleBitsFromLToR(num, n, n ``+` `m ``-` `1``);`   ` `  `# Driver program to test above` `n ``=` `2` `m ``=` `2`   `ans ``=` `smallNumWithNSetAndMUnsetBits(n, m)` `print` `(ans)`   `# This code is contributed by Saloni Gupta`

## C#

 `// C# implementation to find the smallest number` `// with n set and m unset bits` `using` `System;`   `class` `GFG` `{ ` `    ``// Function to toggle bits in the given range` `    ``static` `int` `toggleBitsFromLToR(``int` `n, ``int` `l, ``int` `r)` `    ``{` `        ``// for invalid range` `        ``if` `(r < l)` `            ``return` `n;`   `        ``// calculating a number 'num' having 'r'` `        ``// number of bits and bits in the range l` `        ``// to r are the only set bits` `        ``int` `num = ((1 << r) - 1) ^ ((1 << (l - 1)) - 1);`   `        ``// toggle bits in the range l to r in 'n'` `        ``// and return the number` `        ``return` `(n ^ num);` `    ``}` `    `  `    ``// Function to find the smallest number` `    ``// with n set and m unset bits` `    ``static` `int` `smallNumWithNSetAndMUnsetBits(``int` `n, ``int` `m)` `    ``{` `        ``// calculating a number 'num' having '(n+m)' bits` `        ``// and all are set` `        ``int` `num = (1 << (n + m)) - 1;`   `        ``// required smallest number` `        ``return` `toggleBitsFromLToR(num, n, n + m - 1);` `    ``}` `    `  `    ``// Driver program` `    ``public` `static` `void` `Main () ` `    ``{` `        ``int` `n = 2, m = 2;` `        ``Console.Write(smallNumWithNSetAndMUnsetBits(n, m));` `    ``}` `}`   `// This code is contributed by Sam007`

## PHP

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## Javascript

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Output:

`9`

Time Complexity : O(1)

Space Complexity : O(1)
For greater values of n and m, you can use long int and long long int datatypes to generate the required number.
This article is contributed by Ayush Jauhari. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.