Maximize the number by rearranging bits - GeeksforGeeks

15 Feb, 2022
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++
Java
Python3
C#
PHP
Javascript
// An simple C++ program to find// minimum number formed by bits of a// given number.#include <bits/stdc++.h>#define ll unsigned intusing 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;}
// 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)
# 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 Codea = 1print (maximize(a)) # This code is contributed by# Manish Shaw(manishshaw1)
// 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// 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)?>
<script>  // An simple JavaScript program to find// minimum number formed by bits of a// given number.  function _popcnt32(number){    var counter = 0;         while(number > 0)    {        if(number % 2 == 1)        {            counter++;        }                 //or number = number >> 1        number = parseInt(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.    var n = _popcnt32(a);     // Set most significant n bits of res.    var res = 0;    for (var i=1; i<=n; i++)       res |= (1 << (32 - i));     return Math.abs(res);} // Driver function.var a = 1;document.write(maximize(a)); </script>
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++
Java
Python3
C#
PHP
// An efficient C++ program to find// minimum number formed by bits of a// given number.#include <bits/stdc++.h>#define ll unsigned intusing 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 with 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;}
// 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 with        // 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)
# An efficient python3 program to find# minimum number formed by bits of a# given number.def _popcnt32(n):         count = 0         while (n != 0):        n = n & (n - 1)        count = count + 1             return count # 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)     # If all 32 bits are set.    if (n == 32):        return a     # Find a number with n least    # significant set bits.    res = (1 << n) - 1     # Now shift result by 32 - n    return (res << (32 - n)) # Driver codeif __name__ == '__main__':         a = 3    print(maximize(a)) # This code is contributed by nirajgusain5
// 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 with 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// 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 with    // 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)?>
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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Bit Magic
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Bit Magic
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