# Count numbers whose difference with N is equal to XOR with N

Given a number N. The task is to count the all possible values of x such that nx is equal to (N-x), where denotes bitwise XOR operation.

**Examples:**

Input: N = 3 Output: 4 The all possible values of x are respectively 0, 1, 2, 3. Input: N = 6 Output: 4 The all possible values of x are respectively 0, 2, 4, 6.

**Approach:** The XOR value of two bits will be 1 if both bits have opposite sign, and 0 when both bits are same. So on the basis of the property of XOR, we can say that n x is always greater than or equal to n-x. The only condition when its value is equal with n-x is bits of x form a subset of bits of n. Because if in the i’th position both **x** and **n** has set bits then after xor the value will decrease, and the decreased value will be , where **i** is 0-based position.

So the answer is the total count of subsets of bits of number n is , where k is the count of set bits in n.

Below is the implementation of above approach:

## C++

`#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// function to Count all values of x ` `void` `count_values(` `int` `n) ` `{ ` ` ` `// Count set bits in n ` ` ` `// by using stl function ` ` ` `int` `set_bits = __builtin_popcount(n); ` ` ` ` ` `// count all subset of set bits ` ` ` `cout << ` `pow` `(2, set_bits) << ` `"\n"` `; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` ` ` `int` `n = 27; ` ` ` `count_values(n); ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`import` `java.util.*; ` ` ` `class` `Solution ` `{ ` `//count number of set bits ` `static` `int` `__builtin_popcount(` `int` `n) ` `{ ` ` ` `//count variable ` ` ` `int` `count=` `0` `; ` ` ` ` ` `while` `(n>` `0` `) ` ` ` `{ ` ` ` `//if the bit is 1 ` ` ` `if` `(n%` `2` `==` `1` `) ` ` ` `count++; ` ` ` ` ` `n=n/` `2` `; ` ` ` `} ` ` ` `return` `count; ` `} ` ` ` `// function to Count all values of x ` `static` `void` `count_values(` `int` `n) ` `{ ` ` ` `// Count set bits in n ` ` ` `// by using stl function ` ` ` `int` `set_bits = __builtin_popcount(n); ` ` ` ` ` `// count all subset of set bits ` ` ` `System.out.println((` `int` `)Math.pow(` `2` `, set_bits)); ` `} ` ` ` `// Driver code ` `public` `static` `void` `main(String args[]) ` `{ ` ` ` ` ` `int` `n = ` `27` `; ` ` ` `count_values(n); ` ` ` ` ` `} ` `} ` ` ` `// This code is contributed ` `// by Arnab Kundu ` |

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## Python 3

`# Python3 program to implement ` `# above approach ` ` ` `# from math import pow method ` `from` `math ` `import` `pow` ` ` `# count number of set bits ` `def` `__builtin_popcount(n) : ` ` ` ` ` `# count variable ` ` ` `count ` `=` `0` ` ` ` ` `while` `n > ` `0` `: ` ` ` ` ` `# if the bit is 1 ` ` ` `if` `n ` `%` `2` `=` `=` `1` `: ` ` ` `count ` `+` `=` `1` ` ` ` ` `n ` `=` `n` `/` `/` `2` ` ` ` ` `return` `count ` ` ` ` ` `# function to Count all values of x ` `def` `count_values(n) : ` ` ` ` ` `set_bits ` `=` `__builtin_popcount(n) ` ` ` ` ` `# count all subset of set bits ` ` ` `print` `(` `int` `(` `pow` `(` `2` `, set_bits))) ` ` ` ` ` `# Driver code ` `if` `__name__ ` `=` `=` `"__main__"` `: ` ` ` ` ` `n ` `=` `27` ` ` `count_values(n) ` ` ` `# This code is contributed by ` `# ANKITRAI1 ` |

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## C#

`using` `System; ` `class` `GFG ` `{ ` `// count number of set bits ` `static` `int` `__builtin_popcount(` `int` `n) ` `{ ` ` ` `// count variable ` ` ` `int` `count = 0; ` ` ` ` ` `while` `(n > 0) ` ` ` `{ ` ` ` `//if the bit is 1 ` ` ` `if` `(n % 2 == 1) ` ` ` `count++; ` ` ` ` ` `n = n / 2; ` ` ` `} ` ` ` `return` `count; ` `} ` ` ` `// function to Count all values of x ` `static` `void` `count_values(` `int` `n) ` `{ ` ` ` `// Count set bits in n ` ` ` `// by using stl function ` ` ` `int` `set_bits = __builtin_popcount(n); ` ` ` ` ` `// count all subset of set bits ` ` ` `Console.Write((` `int` `)Math.Pow(2, set_bits)); ` `} ` ` ` `// Driver code ` `public` `static` `void` `Main() ` `{ ` ` ` `int` `n = 27; ` ` ` `count_values(n); ` `} ` `} ` ` ` `// This code is contributed by Smitha ` |

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## PHP

`<?php ` `// count number of set bits ` `function` `__builtin_popcount(` `$n` `) ` `{ ` ` ` `// count variable ` ` ` `$count` `= 0; ` ` ` ` ` `while` `(` `$n` `> 0) ` ` ` `{ ` ` ` `//if the bit is 1 ` ` ` `if` `(` `$n` `% 2 == 1) ` ` ` `$count` `++; ` ` ` ` ` `$n` `= ` `$n` `/ 2; ` ` ` `} ` ` ` `return` `$count` `; ` `} ` ` ` `// function to Count all values of x ` `function` `count_values(` `$n` `) ` `{ ` ` ` `// Count set bits in n ` ` ` `// by using stl function ` ` ` `$set_bits` `= __builtin_popcount(` `$n` `); ` ` ` ` ` `// count all subset of set bits ` ` ` `echo` `(int)pow(2, ` `$set_bits` `); ` `} ` ` ` `// Driver code ` `$n` `= 27; ` `count_values(` `$n` `); ` ` ` `// This code is contributed ` `// by Akanksha Rai(Abby_akku) ` `?> ` |

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**Output:**

16

**Time Complexity:** O(k), where k is number of set bits in N.

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