# 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.

**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; ` `} ` |

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## 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 ` |

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## 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
[tabby title="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 ` |

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**Output:**

536870912

This article is contributed by **Aditya Gupta**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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