# Minimum number using set bits of a given number

Given an unsigned number, find the minimum number that could be formed by using the bits of the given unsigned number.

Examples :

Input : 6
Output : 3
Binary representation of 6 is 0000….0110. Smallest number with same number of set bits 0000….0011.

Input : 11
Output : 7

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Simple Approach:
1. Find binary representation of the number using simple decimal to binary representation technique.
2. Count number of set bits in the binary representation equal to ‘n’.
3. Create a binary representation with it’s ‘n’ least significant bits set to 1.
4. Convert the binary representation back to the number.

Efficient Approach:
1. Just measure the number of 1’s present in the bit representation of the number.
2. (Number of set bits raised to the power of 2) – 1 represents the minimized number.

## C++

 `// An efficient C++ program to find ` `// minimum number formed by bits of a given number. ` `#include ` `#define ll unsigned int ` `using` `namespace` `std; ` ` `  `// Returns minimum number formed by ` `// bits of a given number. ` `ll minimize(ll a) ` `{ ` `    ``// _popcnt32(a) gives number of 1's  ` `    ``// present in binary representation  ` `    ``// of a. ` `    ``ll n = _popcnt32(a); ` ` `  `    ``return` `(``pow``(2, n) - 1); ` `} ` ` `  `// Driver function. ` `int` `main() ` `{ ` `    ``ll a = 11; ` `    ``cout << minimize(a) << endl; ` `    ``return` `0; ` `} `

## Java

 `// An efficient Java program to  ` `// find minimum number formed ` `// by bits of a given number. ` `import` `java.io.*; ` ` `  `class` `GFG ` `{ ` `    ``public` `static` `int` `_popcnt32(``long` `number)  ` `    ``{ ` `        ``int` `count = ``0``; ` `        ``while` `(number > ``0``) ` `        ``{ ` `            ``count += number & 1L; ` `            ``number >>= 1L; ` `        ``} ` `        ``return` `count; ` `    ``} ` `     `  `    ``// Returns minimum number formed  ` `    ``// by bits of a given number. ` `    ``static` `long` `minimize(``long` `a) ` `    ``{ ` `        ``// _popcnt32(a) gives number  ` `        ``// of 1's present in binary  ` `        ``// representation of a. ` `        ``int` `n = _popcnt32(a); ` ` `  `        ``return` `((``long``)Math.pow(``2``, n) - ``1``); ` `    ``} ` `     `  `    ``// Driver Code. ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``long` `a = ``11``; ` `        ``System.out.print(minimize(a)); ` `    ``} ` `} ` ` `  `// This code is contributed by  ` `// Manish Shaw(manishshaw1) `

## Python3

 `# An efficient Python3 program  ` `# to find minimum number formed ` `# by bits of a given number. ` ` `  `# Returns minimum number formed by ` `# bits of a given number. ` `def` `minimize(a): ` `     `  `    ``# _popcnt32(a) gives number of 1's ` `    ``# present in binary representation ` `    ``# of a. ` `    ``n ``=` `bin``(a).count(``"1"``) ` ` `  `    ``return` `(``pow``(``2``, n) ``-` `1``) ` ` `  `# Driver Code ` `a ``=` `11` `print``(minimize(a)) ` ` `  `# This code is contributed by Mohit Kumar `

## C#

 `// An efficient C# program to  ` `// find minimum number formed ` `// by bits of a given number. ` `using` `System; ` `using` `System.Linq; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG ` `{ ` `    ``// Returns minimum number formed  ` `    ``// by bits of a given number. ` `    ``static` `long` `minimize(``long` `a) ` `    ``{ ` `        ``// _popcnt32(a) gives number  ` `        ``// of 1's present in binary   ` `        ``// representation of a. ` `        ``string` `binaryString = Convert.ToString(a, 2); ` `        ``int` `n = binaryString.Split(``new` `[] {``'0'``},  ` `                ``StringSplitOptions.RemoveEmptyEntries).Length + 1; ` ` `  `        ``return` `((``long``)Math.Pow(2, n) - 1); ` `    ``} ` `     `  `    ``// Driver Code. ` `    ``static` `void` `Main() ` `    ``{ ` `        ``long` `a = 11; ` `        ``Console.Write(minimize(a)); ` `    ``} ` `} ` ` `  `// This code is contributed by  ` `// Manish Shaw(manishshaw1) `

Output :

`7`

Note : The above code uses GCC specific functions. If we wish to write code for other compilers, we may use Count set bits in an integer.

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