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

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.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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++ 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) {
x = (1 << i | 1 << j);
num = num ^ x;
}

i++;
j--;
}
return num;
}

// Driver code
int main()
{
ull num = 4;
cout << findMax(num);
return 0;
}

Output:

536870912

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