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

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

Input : n = 2, m = 2 Output : 12(12)= (1100)_{10}_{2}We can see that in the binary representation of12there are 2 set and 2 unsets bits and it is the largest number. Input : n = 4, m = 1 Output : 30

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 the last
**m**bits of**num**and then return the toggled number. Refer this post.

## C++

`// C++ implementation to find the largest number` `// with n set and m unset bits` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// function to toggle the last m bits` `unsigned ` `int` `toggleLastMBits(unsigned ` `int` `n,` ` ` `unsigned ` `int` `m)` `{` ` ` `// if no bits are required to be toggled` ` ` `if` `(m == 0)` ` ` `return` `n;` ` ` `// calculating a number 'num' having 'm' bits` ` ` `// and all are set` ` ` `unsigned ` `int` `num = (1 << m) - 1;` ` ` `// toggle the last m bits and return the number` ` ` `return` `(n ^ num);` `}` `// function to find the largest number` `// with n set and m unset bits` `unsigned ` `int` `largeNumWithNSetAndMUnsetBits(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 largest number` ` ` `return` `toggleLastMBits(num, m);` `}` `// Driver program to test above` `int` `main()` `{` ` ` `unsigned ` `int` `n = 2, m = 2;` ` ` `cout << largeNumWithNSetAndMUnsetBits(n, m);` ` ` `return` `0;` `}` |

## Java

`// Java implementation to find the largest number` `// with n set and m unset bits` `import` `java.io.*;` `class` `GFG ` `{` ` ` `// Function to toggle the last m bits` ` ` `static` `int` `toggleLastMBits(` `int` `n, ` `int` `m)` ` ` `{` ` ` `// if no bits are required to be toggled` ` ` `if` `(m == ` `0` `)` ` ` `return` `n;` ` ` ` ` `// calculating a number 'num' having 'm' bits` ` ` `// and all are set` ` ` `int` `num = (` `1` `<< m) - ` `1` `;` ` ` ` ` `// toggle the last m bits and return the number` ` ` `return` `(n ^ num);` ` ` `}` ` ` ` ` `// Function to find the largest number` ` ` `// with n set and m unset bits` ` ` `static` `int` `largeNumWithNSetAndMUnsetBits(` `int` `n, ` `int` `m)` ` ` `{` ` ` `// calculating a number 'num' having '(n+m)' bits` ` ` `// and all are set` ` ` `int` `num = (` `1` `<< (n + m)) - ` `1` `;` ` ` ` ` `// required largest number` ` ` `return` `toggleLastMBits(num, m);` ` ` `}` ` ` ` ` `// driver program` ` ` `public` `static` `void` `main (String[] args) ` ` ` `{` ` ` `int` `n = ` `2` `, m = ` `2` `;` ` ` `System.out.println(largeNumWithNSetAndMUnsetBits(n, m));` ` ` `}` `}` `// Contributed by Pramod Kumar` |

## Python3

`# Python implementation to` `# find the largest number` `# with n set and m unset bits` `# function to toggle` `# the last m bits` `def` `toggleLastMBits(n,m):` ` ` `# if no bits are required` ` ` `# to be toggled` ` ` `if` `(m ` `=` `=` `0` `):` ` ` `return` `n` ` ` `# calculating a number` ` ` `# 'num' having 'm' bits` ` ` `# and all are set` ` ` `num ` `=` `(` `1` `<< m) ` `-` `1` ` ` `# toggle the last m bits` ` ` `# and return the number` ` ` `return` `(n ^ num)` `# function to find` `# the largest number` `# with n set and m unset bits` `def` `largeNumWithNSetAndMUnsetBits(n,m):` ` ` `# calculating a number` ` ` `# 'num' having '(n+m)' bits` ` ` `# and all are set` ` ` `num ` `=` `(` `1` `<< (n ` `+` `m)) ` `-` `1` ` ` `# required largest number` ` ` `return` `toggleLastMBits(num, m)` `# Driver code` `n ` `=` `2` `m ` `=` `2` `print` `(largeNumWithNSetAndMUnsetBits(n, m))` `# This code is contributed` `# by Anant Agarwal.` |

## C#

`// C# implementation to find the largest number` `// with n set and m unset bits` `using` `System;` `class` `GFG` `{ ` ` ` `// Function to toggle the last m bits` ` ` `static` `int` `toggleLastMBits(` `int` `n, ` `int` `m)` ` ` `{` ` ` `// if no bits are required to be toggled` ` ` `if` `(m == 0)` ` ` `return` `n;` ` ` `// calculating a number 'num' having 'm' bits` ` ` `// and all are set` ` ` `int` `num = (1 << m) - 1;` ` ` `// toggle the last m bits and return the number` ` ` `return` `(n ^ num);` ` ` `}` ` ` `// Function to find the largest number` ` ` `// with n set and m unset bits` ` ` `static` `int` `largeNumWithNSetAndMUnsetBits(` `int` `n, ` `int` `m)` ` ` `{` ` ` `// calculating a number 'num' having '(n+m)' bits` ` ` `// and all are set` ` ` `int` `num = (1 << (n + m)) - 1;` ` ` `// required largest number` ` ` `return` `toggleLastMBits(num, m);` ` ` `}` ` ` ` ` `// Driver program` ` ` `public` `static` `void` `Main () ` ` ` `{` ` ` `int` `n = 2, m = 2;` ` ` `Console.Write(largeNumWithNSetAndMUnsetBits(n, m));` ` ` `}` `}` `// This code is contributed by Sam007` |

## PHP

`<?php` `// PHP implementation to find ` `// the largest number with n ` `// set and m unset bits` `// function to toggle ` `// the last m bits` `function` `toggleLastMBits(` `$n` `, ` `$m` `)` `{` ` ` `// if no bits are required ` ` ` `// to be toggled` ` ` `if` `(` `$m` `== 0)` ` ` `return` `$n` `;` ` ` `// calculating a number 'num'` ` ` `// having 'm' bits and all are set` ` ` `$num` `= (1 << ` `$m` `) - 1;` ` ` `// toggle the last m bits ` ` ` `// and return the number` ` ` `return` `(` `$n` `^ ` `$num` `);` `}` `// function to find the largest number` `// with n set and m unset bits` `function` `largeNumWithNSetAndMUnsetBits(` `$n` `,` ` ` `$m` `)` `{` ` ` `// calculating a number 'num' ` ` ` `// having '(n+m)' bits and all are set` ` ` `$num` `= (1 << (` `$n` `+ ` `$m` `)) - 1;` ` ` `// required largest number` ` ` `return` `toggleLastMBits(` `$num` `, ` `$m` `);` `}` `// Driver Code` `$n` `= 2; ` `$m` `= 2;` `echo` `largeNumWithNSetAndMUnsetBits(` `$n` `, ` `$m` `);` `// This code is contributed by vt_m.` `?>` |

## Javascript

`<script>` `// Javascript implementation to find the largest number` `// with n set and m unset bits` `// function to toggle the last m bits` `function` `toggleLastMBits(n, m)` `{` ` ` `// if no bits are required to be toggled` ` ` `if` `(m == 0)` ` ` `return` `n;` ` ` `// calculating a number 'num' having 'm' bits` ` ` `// and all are set` ` ` `var` `num = (1 << m) - 1;` ` ` `// toggle the last m bits and return the number` ` ` `return` `(n ^ num);` `}` `// function to find the largest number` `// with n set and m unset bits` `function` `largeNumWithNSetAndMUnsetBits(n, m)` `{` ` ` `// calculating a number 'num' having '(n+m)' bits` ` ` `// and all are set` ` ` `num = (1 << (n + m)) - 1;` ` ` `// required largest number` ` ` `return` `toggleLastMBits(num, m);` `}` `// Driver program to test above` `var` `n = 2, m = 2;` `document.write( largeNumWithNSetAndMUnsetBits(n, m));` `</script>` |

**Output :**

12

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.

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