Array containing power of 2 whose XOR and Sum of elements equals X

• Last Updated : 17 Nov, 2021

Given an integer X. The task is to find and return the array containing of powers of 2’s and the xor of the array is X.
Examples:

Input: X = 20
Output: 16 4
Input: X = 15
Output: 1 2 4 8

Approach: The answer lies in the binary representation of the number X.
Since in the power of 2, there is only one set bit. If there are two distinct powers of 2’s present then the xor will be the addition of both the numbers.
Similarly, if xor of the whole array will be taken then it should be equal to X and that will be the binary representation of that number.
Since there is a distinct set bit in every power of 2’s, the xor and the sum of the elements of the array will be the same.
Below is the implementation of the above approach:

C++

 `// C++ implementation of the above approach` `#include ` `using` `namespace` `std;`   `// Function to return the required array` `vector<``long``> getArray(``int` `n)` `{` `    ``vector<``long``> ans;`   `    ``// Store the power of 2` `    ``long` `p2 = 1;`   `    ``// while n is greater than 0` `    ``while` `(n > 0) {` `        `  `        ``// if there is 1 in binary` `        ``// representation` `        ``if` `(n & 1)` `            ``ans.push_back(p2);`   `        ``// Divide n by 2` `        ``// Multiply p2 by 2` `        ``n >>= 1;` `        ``p2 *= 2;` `    ``}`   `    ``return` `ans;` `}`   `// Driver code` `int` `main()` `{` `    ``long` `n = 15;`   `    ``// Get the answer` `    ``vector<``long``> ans = getArray(n);`   `    ``// Printing the array` `    ``for``(``int` `i : ans)` `        ``cout << i << ``" "``;`   `    ``return` `0;` `}`

Java

 `// Java implementation implementation` `// of the above approach` `import` `java.util.*;` `class` `GFG ` `{`   `// Function to return the required array` `static` `Vector getArray(``int` `n)` `{` `    ``Vector ans = ``new` `Vector();`   `    ``// Store the power of 2` `    ``long` `p2 = ``1``;`   `    ``// while n is greater than 0` `    ``while` `(n > ``0``)` `    ``{` `        `  `        ``// if there is 1 in binary` `        ``// representation` `        ``if` `(n % ``2` `== ``1``)` `            ``ans.add(p2);`   `        ``// Divide n by 2` `        ``// Multiply p2 by 2` `        ``n >>= ``1``;` `        ``p2 *= ``2``;` `    ``}` `    ``return` `ans;` `}`   `// Driver code` `public` `static` `void` `main(String[] args) ` `{` `    ``int` `n = ``15``;`   `    ``// Get the answer` `    ``Vector ans = getArray(n);`   `    ``// Printing the array` `    ``for``(Long i : ans)` `        ``System.out.print(i + ``" "``);` `}` `}`   `// This code is contributed by 29AjayKumar`

Python3

 `# Python3 implementation of the above approach `   `# Function to return the required array ` `def` `getArray(n) : `   `    ``ans ``=` `[]; `   `    ``# Store the power of 2 ` `    ``p2 ``=` `1``; `   `    ``# while n is greater than 0 ` `    ``while` `(n > ``0``) :` `        `  `        ``# if there is 1 in binary ` `        ``# representation ` `        ``if` `(n & ``1``) :` `            ``ans.append(p2); `   `        ``# Divide n by 2 ` `        ``# Multiply p2 by 2 ` `        ``n >>``=` `1``; ` `        ``p2 ``*``=` `2``; `   `    ``return` `ans; `   `# Driver code ` `if` `__name__ ``=``=` `"__main__"` `: `   `    ``n ``=` `15``; `   `    ``# Get the answer ` `    ``ans ``=` `getArray(n); `   `    ``# Printing the array ` `    ``for` `i ``in` `ans :` `        ``print``(i, end ``=` `" "``); `   `# This code is contributed by AnkitRai01`

C#

 `// C# implementation of the approach` `using` `System;` `using` `System.Collections.Generic;`   `class` `GFG ` `{`   `// Function to return the required array` `static` `List<``long``> getArray(``int` `n)` `{` `    ``List<``long``> ans = ``new` `List<``long``>();`   `    ``// Store the power of 2` `    ``long` `p2 = 1;`   `    ``// while n is greater than 0` `    ``while` `(n > 0)` `    ``{` `        `  `        ``// if there is 1 in binary` `        ``// representation` `        ``if` `(n % 2 == 1)` `            ``ans.Add(p2);`   `        ``// Divide n by 2` `        ``// Multiply p2 by 2` `        ``n >>= 1;` `        ``p2 *= 2;` `    ``}` `    ``return` `ans;` `}`   `// Driver code` `public` `static` `void` `Main(String[] args) ` `{` `    ``int` `n = 15;`   `    ``// Get the answer` `    ``List<``long``> ans = getArray(n);`   `    ``// Printing the array` `    ``foreach``(``long` `i ``in` `ans)` `        ``Console.Write(i + ``" "``);` `}` `}`   `// This code is contributed by Princi Singh`

Javascript

 ``

Output:

`1 2 4 8 `

Time Complexity: O(n)

Auxiliary Space: O(n)

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