Maximize the number by rearranging bits
Last Updated :
13 Jun, 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++
// 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;
}
// 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 Code
a = 1
print (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>
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 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 code
if __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)
?>
// An efficient JS program to find
// minimum number formed by bits of a
// given number.
function _popcnt32(n)
{
var count = 0n;
while (n != 0n)
{
n = n & (n - 1n);
count = count + 1n;
}
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.
var n = _popcnt32(a);
// If all 32 bits are set.
if (n == 32n)
return a;
// Find a number with n least
// significant set bits.
var res = (1n << n) - 1n;
// Now shift result by 32 - n
return (res << (32n - n));
}
var a = 3n;
console.log(Number(maximize(a)));
// This code is contributed by phasing17
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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