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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