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Maximize the number by rearranging bits
  • Difficulty Level : Easy
  • Last Updated : 09 Aug, 2018

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)

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 <bits/stdc++.h>
#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




<?php
// An simple PHP program to find
// minimum number formed by bits 
// of a given number.
function _popcnt32($number)
{
    $counter = 0;
      
    while($number > 0)
    {
        if($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 <bits/stdc++.h>
#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




<?php
// An efficient Java program to 
// find minimum number formed 
// by bits of a given number.
  
function _popcnt32($n
{
    $count = 0;
    while ($n != 0)
    {
        $n = $n & ($n - 1);
        $count++;
    }
    return $count;
}
  
// 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);
  
    // If a$32 
    // bits are set.
    if ($n == 32)
    return $a;
  
    // find a number witn 
    // n least significant
    // set bits.
    $res = (1 << $n) - 1;
      
    // Now shift result 
    // by 32 - n 
    return ($res << (32 - $n)) ;
}     
  
// Driver Code
$a = 3;
echo (maximize($a));
  
// This code is contributed by 
// ManishShaw(manishshaw1)
?>


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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