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

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)= (1001)_{10}_{2}We can see that in the binary representation of9there 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:

- Calculate
**num**= (1 << (n + m)) – 1. This will produce a number**num**having**(n + m)**number of bits and all are set. - 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 <bits/stdc++.h>` `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

`<?php` `// PHP implementation to find the smallest number` `// with n set and m unset bits` `// function to toggle bits in the given range` `function` `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` `^ ` `$num` `);` `}` `// function to find the smallest number` `// with n set and m unset bits` `function` `smallNumWithNSetAndMUnsetBits(` `$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;` ` ` `echo` `smallNumWithNSetAndMUnsetBits(` `$n` `, ` `$m` `);` `// This Code is Contributed by ajit` `?>` |

## Javascript

`<script>` `// Javascript implementation to find` `// the smallest number with n set and` `// m unset bits` `// Function to toggle bits in the given range` `function` `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` ` ` `let 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` `function` `smallNumWithNSetAndMUnsetBits(n, m)` `{` ` ` ` ` `// Calculating a number 'num' having` ` ` `// '(n+m)' bits and all are set` ` ` `let num = (1 << (n + m)) - 1;` ` ` `// Required smallest number` ` ` `return` `toggleBitsFromLToR(num, n, n + m - 1);` `}` `// Driver code` `let n = 2, m = 2;` `document.write(smallNumWithNSetAndMUnsetBits(n, m));` `// This code is contributed by suresh07` `</script>` |

**Output: **

9

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 contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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