Maximize a given unsigned number number by swapping bits at it’s extreme positions.

Difficulty Level : Hard
Last Updated : 12 Apr, 2021

Given a number maximize it by swapping bits at it’s extreme positions i.e. at first and last position, second and second last position and so on.
Examples:

Input : 4 (0000...0100)
Output : 536870912 (0010...0000)
In the above example swapped 3rd and 3rd last
bit to maximize the given unsigned number.

Input : 12 (00000...1100)
Output : 805306368 (0011000...0000)

In the above example 3rd and 3rd last bit and
4th and 4th last bit are swapped to maximize 
the given unsigned number.

Naive Approach:
1. Convert the number into it’s bit representation and store it’s bit representation in an array.
2. Traverse the array from both ends, if the less significant bit of the bit representation is greater than the more significant bit i.e. if less significant bit is 1 and more significant bit is 0 then swap them else take no action.
3. Convert the obtained binary representation back to the number.
Efficient Approach:
1. Create a copy of the original number because the original number would be modified, iteratively obtain the bits at the extreme positions.
2. If less significant bit is 1 and more significant bit is 0 then swap the bits in the bit from only, continue the process until less significant bit’s position is less than more significant bit’s position.
3. Display the maximized number.

C++

// C++ program to find maximum number by
// swapping extreme bits.
#include <bits/stdc++.h>
using namespace std;
 
#define ull unsigned long long int
 
ull findMax(ull num)
{
    ull num_copy = num;
 
    /* Traverse bits from both extremes */
    int j = sizeof(unsigned long long int) * 8 - 1;
    int i = 0;
    while (i < j) {
 
        // Obtaining i-th and j-th bits
        int m = (num_copy >> i) & 1;
        int n = (num_copy >> j) & 1;
 
        /* Swapping the bits if lesser significant
           is greater than higher significant
           bit and accordingly modifying the number */
        if (m > n) {
            int x = (1 << i | 1 << j);
            num = num ^ x;
        }
 
        i++;
        j--;
    }
    return num;
}
 
// Driver code
int main()
{
    ull num = 4;
    cout << findMax(num);
    return 0;
}

Java

// Java program to find maximum number by
// swapping extreme bits.
 
class GFG {
 
    static int findMax(int num) {
        byte size_of_int = 4;
        int num_copy = num;
 
        /* Traverse bits from both extremes */
        int j = size_of_int * 8 - 1;
        int i = 0;
        while (i < j) {
 
            // Obtaining i-th and j-th bits
            int m = (num_copy >> i) & 1;
            int n = (num_copy >> j) & 1;
 
            /* Swapping the bits if lesser significant
        is greater than higher significant
        bit and accordingly modifying the number */
            if (m > n) {
                int x = (1 << i | 1 << j);
                num = num ^ x;
            }
 
            i++;
            j--;
        }
        return num;
    }
 
    // Driver code
    static public void main(String[] args) {
        int num = 4;
        System.out.println(findMax(num));
    }
}
 
// This code is contributed by 29AjayKumar

Python 3

# Python 3 program to find maximum number
# by swapping extreme bits.
 
def findMax( num):
    num_copy = num
 
    # Traverse bits from both extremes
    j = 4 * 8 - 1;
    i = 0
    while (i < j) :
 
        # Obtaining i-th and j-th bits
        m = (num_copy >> i) & 1
        n = (num_copy >> j) & 1
 
        # Swapping the bits if lesser significant
        # is greater than higher significant
        # bit and accordingly modifying the number
        if (m > n) :
            x = (1 << i | 1 << j)
            num = num ^ x
 
        i += 1
        j -= 1
    return num
 
# Driver code
if __name__ == "__main__":
     
    num = 4
    print(findMax(num))
 
# This code is contributed by ita_c

C#

     
// C# program to find maximum number by
// swapping extreme bits.
using System;
public class GFG {
  
    static int findMax(int num) {
        byte size_of_int = 4;
        int num_copy = num;
  
        /* Traverse bits from both extremes */
        int j = size_of_int * 8 - 1;
        int i = 0;
        while (i < j) {
  
            // Obtaining i-th and j-th bits
            int m = (num_copy >> i) & 1;
            int n = (num_copy >> j) & 1;
  
            /* Swapping the bits if lesser significant
        is greater than higher significant
        bit and accordingly modifying the number */
            if (m > n) {
                int x = (1 << i | 1 << j);
                num = num ^ x;
            }
  
            i++;
            j--;
        }
        return num;
    }
  
// Driver code
    static public void Main() {
        int num = 4;
        Console.Write(findMax(num));
    }
}
  
// This code is contributed by 29AjayKumar

Javascript

<script>
// JavaScript program to find maximum number by
// swapping extreme bits.
 
function findMax(num)
{
    let num_copy = num;
 
    /* Traverse bits from both extremes */
    let j = 4 * 8 - 1;
    let i = 0;
    while (i < j) {
 
        // Obtaining i-th and j-th bits
        let m = (num_copy >> i) & 1;
        let n = (num_copy >> j) & 1;
 
        /* Swapping the bits if lesser significant
        is greater than higher significant
        bit and accordingly modifying the number */
        if (m > n) {
            let x = (1 << i | 1 << j);
            num = num ^ x;
        }
 
        i++;
        j--;
    }
    return num;
}
 
// Driver code
 
    let num = 4;
    document.write(findMax(num));
 
 
// This code is contributed by Manoj.
</script>

Output:

536870912

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