# Maximize a given unsigned 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;` `}` |

## 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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