Minimum number using set bits of a given number

Last Updated : 25 Nov, 2022

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

Examples :

Input : 6
Output : 3
Binary representation of 6 is 0000....0110. Smallest number with same number of set bits 0000....0011.

Input : 11
Output : 7

Simple Approach:
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 it's 'n' least significant bits set to 1.
4. Convert the binary representation back to the number.
Efficient Approach:
1. Just measure the number of 1’s present in the bit representation of the number.
2. (Number of set bits raised to the power of 2) - 1 represents the minimized number.

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 minimum number formed by
// bits of a given number.
ll minimize(ll a)
{
    // _popcnt32(a) gives number of 1's 
    // present in binary representation 
    // of a.
    ll n = _popcnt32(a);

    return (pow(2, n) - 1);
}

// Driver function.
int main()
{
    ll a = 11;
    cout << minimize(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
{
    public static int _popcnt32(long number) 
    {
        int count = 0;
        while (number > 0)
        {
            count += number & 1L;
            number >>= 1L;
        }
        return count;
    }
    
    // Returns minimum number formed 
    // by bits of a given number.
    static long minimize(long a)
    {
        // _popcnt32(a) gives number 
        // of 1's present in binary 
        // representation of a.
        int n = _popcnt32(a);

        return ((long)Math.pow(2, n) - 1);
    }
    
    // Driver Code.
    public static void main(String args[])
    {
        long a = 11;
        System.out.print(minimize(a));
    }
}

// This code is contributed by 
// Manish Shaw(manishshaw1)

Python3

# An efficient Python3 program 
# to find minimum number formed
# by bits of a given number.

# Returns minimum number formed by
# bits of a given number.
def minimize(a):
    
    # _popcnt32(a) gives number of 1's
    # present in binary representation
    # of a.
    n = bin(a).count("1")

    return (pow(2, n) - 1)

# Driver Code
a = 11
print(minimize(a))

# This code is contributed by Mohit Kumar

// An efficient C# program to 
// find minimum number formed
// by bits of a given number.
using System;
using System.Linq;
using System.Collections.Generic;

class GFG
{
    // Returns minimum number formed 
    // by bits of a given number.
    static long minimize(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 + 1;

        return ((long)Math.Pow(2, n) - 1);
    }
    
    // Driver Code.
    static void Main()
    {
        long a = 11;
        Console.Write(minimize(a));
    }
}

// This code is contributed by 
// Manish Shaw(manishshaw1)

JavaScript

<script>
// An efficient Javascript program to 
// find minimum number formed
// by bits of a given number.
    
    function _popcnt32(number)
    {
        let count = 0;
        while (number > 0)
        {
            count += number & 1;
            number >>= 1;
        }
        return count;
    }
    
    // Returns minimum number formed 
    // by bits of a given number.
    function minimize(a)
    {
    
        // _popcnt32(a) gives number 
        // of 1's present in binary 
        // representation of a.
        let n = _popcnt32(a);
  
        return (Math.pow(2, n) - 1);
    }
    
    // Driver Code.
    let a = 11;
    document.write(minimize(a));
    
// This code is contributed by unknown2108
</script>

Time Complexity: O(log N), as the _popcnt32 has a time complexity O(logN), however, _popcnt32 has a maximum value of O(log32), so it can be interpreted as O(1) as well.
Auxiliary Space: O(1)
Note : The above code uses GCC specific functions. If we wish to write code for other compilers, we may use Count set bits in an integer.

Minimum number using set bits of a given number

aditya gupta 4

Improve

Article Tags :

Practice Tags :

Bit Magic

Minimum number using set bits of a given number

Similar Reads