# Maximize the number by rearranging bits

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

Examples :

```Input : 1 (0000....0001)
Output : 2147483648 (1000....0000)

Input : 7 (0000....0111)
Output : 3758096384 (0111....0000)
```

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

Method 1 (Simple)
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 its ‘n’ most significant bits set to 1.
4. Convert the binary representation back to the number.

## C++

 `// An simple C++ program to find ` `// minimum number formed by bits of a ` `// given number. ` `#include ` `#define ll unsigned int ` `using` `namespace` `std; ` ` `  `// Returns maximum number formed by ` `// bits of a given number. ` `ll maximize(ll a) ` `{ ` `    ``// _popcnt32(a) gives number of 1's ` `    ``// present in binary representation of a. ` `    ``ll n = _popcnt32(a); ` ` `  `    ``// Set most significant n bits of res. ` `    ``ll res = 0; ` `    ``for` `(``int` `i=1; i<=n; i++) ` `       ``res |= (1 << (32 - i)); ` ` `  `    ``return` `res; ` `} ` ` `  `// Driver function. ` `int` `main() ` `{ ` `    ``ll a = 1; ` `    ``cout << maximize(a) << endl; ` `    ``return` `0; ` `} `

## Java

 `// An simple Java program to find ` `// minimum number formed by bits  ` `// of a given number. ` `import` `java.io.*; ` ` `  `class` `GFG ` `{ ` `    ``private` `static` `int` `_popcnt32(``long` `number) ` `    ``{ ` `        ``int` `counter = ``0``; ` `         `  `        ``while``(number > ``0``) ` `        ``{ ` `            ``if``(number % ``2` `== ``1``) ` `            ``{ ` `                ``counter++; ` `            ``} ` `             `  `            ``//or number = number >> 1 ` `            ``number = number / ``2``;  ` `        ``} ` `        ``return` `counter; ` `    ``}  ` `     `  `    ``// Returns maximum number formed  ` `    ``// by bits of a given number. ` `    ``static` `long` `maximize(``long` `a) ` `    ``{ ` `        ``// _popcnt32(a) gives number  ` `        ``// of 1's present in binary  ` `        ``// representation of a. ` `        ``int` `n = _popcnt32(a); ` `                 `  `        ``// Set most significant ` `        ``// n bits of res. ` `        ``long` `res = ``0``; ` `        ``for` `(``int` `i = ``1``; i <= n; i++) ` `        ``res = (``int``)res | (``1` `<< (``32` `- i)); ` `     `  `        ``return` `Math.abs(res); ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``long` `a = ``1``; ` `        ``System.out.print(maximize(a)); ` `    ``} ` `} ` ` `  `// This code is contributed by  ` `// Manish Shaw(manishshaw1) `

## Python3

 `# An simple Python program to  ` `# find minimum number formed  ` `# by bits of a given number. ` `def` `_popcnt32(number) : ` `    ``counter ``=` `0` `     `  `    ``while``(number > ``0``) : ` `        ``if``(number ``%` `2` `=``=` `1``) : ` `            ``counter ``=` `counter ``+` `1` `             `  `        ``# or number = number >> 1 ` `        ``number ``=` `int``(number ``/` `2``)  ` ` `  `    ``return` `counter ` ` `  `# Returns maximum number formed  ` `# by bits of a given number. ` `def` `maximize(a) : ` `     `  `    ``# _popcnt32(a) gives number  ` `    ``# of 1's present in binary  ` `    ``# representation of a. ` `    ``n ``=` `_popcnt32(a) ` `             `  `    ``# Set most significant ` `    ``# n bits of res. ` `    ``res ``=` `0` `    ``for` `i ``in` `range``(``1``, n ``+` `1``) : ` `        ``res ``=` `int``(res |  ` `                 ``(``1` `<< (``32` `-` `i))) ` ` `  `    ``return` `abs``(res) ` ` `  `# Driver Code ` `a ``=` `1` `print` `(maximize(a)) ` ` `  `# This code is contributed by  ` `# Manish Shaw(manishshaw1) `

## C#

 `// An simple C# program to find ` `// minimum number formed by bits  ` `// of a given number. ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `    ``// Returns maximum number formed  ` `    ``// by bits of a given number. ` `    ``static` `long` `maximize(``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; ` `                 `  `        ``// Set most significant n bits of res. ` `        ``long` `res = 0; ` `        ``for` `(``int` `i = 1; i <= n; i++) ` `        ``res = (``int``)res | (1 << (32 - i)); ` `     `  `        ``return` `Math.Abs(res); ` `    ``} ` `     `  `    ``// Driver Code. ` `    ``static` `void` `Main() ` `    ``{ ` `        ``long` `a = 1; ` `        ``Console.WriteLine(maximize(a)); ` `    ``} ` `} ` `// This code is contributed by  ` `// Manish Shaw(manishshaw1) `

## PHP

 ` 0) ` `    ``{ ` `        ``if``(``\$number` `% 2 == 1) ` `        ``{ ` `            ``\$counter``++; ` `        ``} ` `         `  `        ``//or number = number >> 1 ` `        ``\$number` `= ``intval``(``\$number` `/ 2);  ` `    ``} ` `    ``return` `\$counter``; ` `}  ` ` `  `// Returns maximum number formed  ` `// by bits of a given number. ` `function` `maximize(``\$a``) ` `{ ` `    ``// _popcnt32(a) gives number  ` `    ``// of 1's present in binary  ` `    ``// representation of a. ` `    ``\$n` `= _popcnt32(``\$a``); ` `             `  `    ``// Set most significant ` `    ``// n bits of res. ` `    ``\$res` `= 0; ` `    ``for` `(``\$i` `= 1; ``\$i` `<= ``\$n``; ``\$i``++) ` `    ``\$res` `= ``intval``(``\$res` `|  ` `                 ``(1 << (32 - ``\$i``))); ` ` `  `    ``return` `abs``(``\$res``); ` `} ` ` `  `// Driver Code ` `\$a` `= 1; ` `echo` `(maximize(``\$a``)); ` ` `  `// This code is contributed by  ` `// Manish Shaw(manishshaw1) ` `?> `

Output:

```2147483648
```

Method 2 (Efficient)
The idea is to first find a number with n least significant set bits, then shift the number left by 32-n.

## 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 maximum number formed by ` `// bits of a given number. ` `ll maximize(ll a) ` `{ ` `    ``// _popcnt32(a) gives number of 1's ` `    ``// present in binary representation of a. ` `    ``ll n = _popcnt32(a); ` `     `  `    ``// If all 32 bits are set. ` `    ``if` `(n == 32) ` `      ``return` `a; ` ` `  `    ``// find a number witn n least ` `    ``// significant set bits. ` `    ``ll res = (1 << n) - 1; ` `     `  `    ``// Now shift result by 32 - n  ` `    ``return` `(res << (32 - n)) ; ` `} ` ` `  `// Driver function. ` `int` `main() ` `{ ` `    ``ll a = 3; ` `    ``cout << maximize(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 ` `{ ` `    ``static` `long` `_popcnt32(``long` `n)  ` `    ``{ ` `        ``long` `count = ``0``; ` `        ``while` `(n != ``0``) ` `        ``{ ` `            ``n = n & (n - ``1``); ` `            ``count++; ` `        ``} ` `        ``return` `count; ` `    ``} ` `     `  `    ``// Returns maximum number  ` `    ``// formed by bits of a  ` `    ``// given number. ` `    ``static` `long` `maximize(``long` `a) ` `    ``{ ` `        ``// _popcnt32(a) gives number  ` `        ``// of 1's present in binary  ` `        ``// representation of a. ` `        ``long` `n = _popcnt32(a); ` ` `  `        ``// If along 32  ` `        ``// bits are set. ` `        ``if` `(n == ``32``) ` `        ``return` `a; ` `     `  `        ``// find a number witn  ` `        ``// n least significant ` `        ``// set bits. ` `        ``long` `res = (``1` `<< n) - ``1``; ` `         `  `        ``// Now shift result  ` `        ``// by 32 - n  ` `        ``return` `(res << (``32` `- n)) ; ` `    ``}      ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``long` `a = ``3``; ` `        ``System.out.print(maximize(a)); ` `    ``} ` `} ` ` `  `// This code is contributed by  ` `// ManishShaw(manishshaw1) `

## C#

 `// An efficient C# program to  ` `// find minimum number formed  ` `// by bits of a given number. ` `using` `System; ` ` `  `class` `GFG ` `{ ` `    ``static` `long` `_popcnt32(``long` `n)  ` `    ``{ ` `        ``long` `count = 0; ` `        ``while` `(n != 0) ` `        ``{ ` `            ``n = n & (n - 1); ` `            ``count++; ` `        ``} ` `        ``return` `count; ` `    ``} ` `     `  `    ``// Returns maximum number  ` `    ``// formed by bits of a  ` `    ``// given number. ` `    ``static` `long` `maximize(``long` `a) ` `    ``{ ` `        ``// _popcnt32(a) gives number  ` `        ``// of 1's present in binary  ` `        ``// representation of a. ` `        ``long` `n = _popcnt32(a); ` ` `  `        ``// If along 32  ` `        ``// bits are set. ` `        ``if` `(n == 32) ` `        ``return` `a; ` `     `  `        ``// find a number witn n  ` `        ``// least significant set bits. ` `        ``long` `res = (1 << Convert.ToInt32(n)) - 1; ` `         `  `        ``// Now shift result  ` `        ``// by 32 - n  ` `        ``return` `(res << (32 - Convert.ToInt32(n))) ; ` `    ``}      ` `     `  `    ``// Driver Code ` `    ``static` `void` `Main() ` `    ``{ ` `        ``long` `a = 3; ` `        ``Console.WriteLine(maximize(a)); ` `    ``} ` `} ` ` `  `// This code is contributed by  ` `// ManishShaw(manishshaw1) `

## PHP

 ` `

Output:

```3221225472
```

Note: The above codes use 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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