# Count numbers whose sum with x is equal to XOR with x

Given a integer ‘x’, find the number of values of ‘a’ satisfying the following conditions:

- 0 <= a <= x
- a XOR x = a + x

**Examples :**

Input :5Output :2Explanation:For x = 5, following 2 values of 'a' satisfy the conditions: 5 XOR 0 = 5+0 5 XOR 2 = 5+2Input :10Output :4Explanation:For x = 10, following 4 values of 'a' satisfy the conditions: 10 XOR 0 = 10+0 10 XOR 1 = 10+1 10 XOR 4 = 10+4 10 XOR 5 = 10+5

**Naive Approach:**

A Simple approach is to check for all values of ‘a’ between 0 and ‘x’ (both inclusive) and calculate its XOR with x and check if the condition 2 satisfies.

Below is the implementation of the above idea:

## C++

`// C++ program to find count of values whose XOR` `// with x is equal to the sum of value and x` `// and values are smaller than equal to x` `#include <bits/stdc++.h>` `using` `namespace` `std;` `int` `FindValues(` `int` `x)` `{` ` ` `// Initialize result` ` ` `int` `count = 0;` ` ` `// Traversing through all values between` ` ` `// 0 and x both inclusive and counting` ` ` `// numbers that satisfy given property` ` ` `for` `(` `int` `i = 0; i <= x; i++)` ` ` `if` `((x + i) == (x ^ i))` ` ` `count++;` ` ` `return` `count;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `x = 10;` ` ` ` ` `// Function call` ` ` `cout << FindValues(x);` ` ` `return` `0;` `}` |

## Java

`// Java program to find count of values whose XOR` `// with x is equal to the sum of value and x` `// and values are smaller than equal to x` `class` `Fib` `{` ` ` `static` `int` `FindValues(` `int` `x)` ` ` `{` ` ` `// Initialize result` ` ` `int` `count = ` `0` `;` ` ` `// Traversing through all values between` ` ` `// 0 and x both inclusive and counting` ` ` `// numbers that satisfy given property` ` ` `for` `(` `int` `i = ` `0` `; i <= x; i++)` ` ` `if` `((x + i) == (x ^ i))` ` ` `count++;` ` ` `return` `count;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `int` `x = ` `10` `;` ` ` ` ` `// Function call` ` ` `System.out.println(FindValues(x));` ` ` `}` `}` |

## Python3

`# Python3 program to find count of` `# values whose XOR with x is equal` `# to the sum of value and x and` `# values are smaller than equal to x` `def` `FindValues(x):` ` ` `# Initialize result` ` ` `count ` `=` `0` ` ` `# Traversing through all values` ` ` `# between 0 and x both inclusive` ` ` `# and counting numbers that` ` ` `# satisfy given property` ` ` `for` `i ` `in` `range` `(` `0` `, x):` ` ` `if` `((x ` `+` `i) ` `=` `=` `(x ^ i)):` ` ` `count ` `=` `count ` `+` `1` ` ` `return` `count` `# Driver code` `x ` `=` `10` `# Function call` `print` `(FindValues(x))` `# This code is contributed` `# by Shivi_Aggarwal` |

## C#

`// C# program to find count of values whose XOR` `// with x is equal to the sum of value and x` `// and values are smaller than equal to x` `using` `System;` `class` `Fib` `{` ` ` `static` `int` `FindValues(` `int` `x)` ` ` `{` ` ` `// Initialize result` ` ` `int` `count = 0;` ` ` `// Traversing through all values between` ` ` `// 0 and x both inclusive and counting` ` ` `// numbers that satisfy given property` ` ` `for` `(` `int` `i = 0; i <= x; i++)` ` ` `if` `((x + i) == (x ^ i))` ` ` `count++;` ` ` `return` `count;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `x = 10;` ` ` ` ` `// Function call` ` ` `Console.Write(FindValues(x));` ` ` `}` `}` `// This code is contributed by Nitin Mittal.` |

## PHP

`<?php` `// PHP program to find count` `// of values whose XOR with x` `// is equal to the sum of value` `// and x and values are smaller` `// than equal to x` `// function return the` `// value of count` `function` `FindValues(` `$x` `)` `{` ` ` ` ` `// Initialize result` ` ` `$count` `= 0;` ` ` `// Traversing through all values between` ` ` `// 0 and x both inclusive and counting` ` ` `// numbers that satisfy given property` ` ` `for` `(` `$i` `= 0; ` `$i` `<= ` `$x` `; ` `$i` `++)` ` ` `if` `((` `$x` `+ ` `$i` `) == (` `$x` `^ ` `$i` `))` ` ` `$count` `++;` ` ` `return` `$count` `;` `}` ` ` `// Driver code` ` ` `$x` `= 10;` ` ` `// Function call` ` ` `echo` `FindValues(` `$x` `);` ` ` `// This code is contributed by anuj_67.` `?>` |

## Javascript

`<script>` ` ` `// Javascript program to find count of values whose XOR` ` ` `// with x is equal to the sum of value and x` ` ` `// and values are smaller than equal to x` ` ` ` ` `function` `FindValues(x)` ` ` `{` ` ` `// Initialize result` ` ` `let count = 0;` ` ` ` ` `// Traversing through all values between` ` ` `// 0 and x both inclusive and counting` ` ` `// numbers that satisfy given property` ` ` `for` `(let i = 0; i <= x; i++)` ` ` `if` `((x + i) == (x ^ i))` ` ` `count++;` ` ` ` ` `return` `count;` ` ` `}` ` ` ` ` `let x = 10;` ` ` ` ` `// Function call` ` ` `document.write(FindValues(x));` ` ` `</script>` |

**Output**

4

**Time complexity:** O(x).

**Efficient Approach:**

XOR simulates binary addition without the carry over to the next digit. For the zero digits of ‘a’ we can either add a 1 or 0 without getting a carry which implies xor = + whereas if a digit in ‘a’ is 1 then the matching digit in x is forced to be 0 in order to avoid carry. For each 0 in ‘a’ in the matching digit in x can either being a 1 or 0 with a total combination count of 2^(num of zero). Hence, we just need to count the number of 0’s in binary representation of the number and answer will by 2^(number of zeroes).

Below is the implementation of the above idea:

## C++

`// C++ program to count numbers whose bitwise` `// XOR and sum with x are equal` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find total 0 bit in a number` `long` `CountZeroBit(` `long` `x)` `{` ` ` `unsigned ` `int` `count = 0;` ` ` `while` `(x)` ` ` `{` ` ` `if` `(!(x & 1LL))` ` ` `count++;` ` ` `x >>= 1LL;` ` ` `}` ` ` `return` `count;` `}` `// Function to find Count of non-negative numbers` `// less than or equal to x, whose bitwise XOR and` `// SUM with x are equal.` `long` `CountXORandSumEqual(` `long` `x)` `{` ` ` `// count number of zero bit in x` ` ` `long` `count = CountZeroBit(x);` ` ` `// power of 2 to count` ` ` `return` `(1LL << count);` `}` `// Driver code` `int` `main()` `{` ` ` `long` `x = 10;` ` ` ` ` `// Function call` ` ` `cout << CountXORandSumEqual(x);` ` ` `return` `0;` `}` |

## Java

`// Java program to count` `// numbers whose bitwise` `// XOR and sum with x` `// are equal` `import` `java.io.*;` `class` `GFG {` ` ` `// Function to find total` ` ` `// 0 bit in a number` ` ` `static` `long` `CountZeroBit(` `long` `x)` ` ` `{` ` ` `long` `count = ` `0` `;` ` ` `while` `(x > ` `0` `) {` ` ` `if` `((x & 1L) == ` `0` `)` ` ` `count++;` ` ` `x >>= 1L;` ` ` `}` ` ` `return` `count;` ` ` `}` ` ` `// Function to find Count` ` ` `// of non-negative numbers` ` ` `// less than or equal to x,` ` ` `// whose bitwise XOR and` ` ` `// SUM with x are equal.` ` ` `static` `long` `CountXORandSumEqual(` `long` `x)` ` ` `{` ` ` `// count number of` ` ` `// zero bit in x` ` ` `long` `count = CountZeroBit(x);` ` ` `// power of 2 to count` ` ` `return` `(1L << count);` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `long` `x = ` `10` `;` ` ` `// Function call` ` ` `System.out.println(CountXORandSumEqual(x));` ` ` `}` `}` `// The code is contributed by ajit` |

## Python3

`# Python3 program to count numbers whose bitwise` `# XOR and sum with x are equal` `# Function to find total 0 bit in a number` `def` `CountZeroBit(x):` ` ` `count ` `=` `0` ` ` `while` `(x):` ` ` `if` `((x & ` `1` `) ` `=` `=` `0` `):` ` ` `count ` `+` `=` `1` ` ` `x >>` `=` `1` ` ` `return` `count` `# Function to find Count of non-negative numbers` `# less than or equal to x, whose bitwise XOR and` `# SUM with x are equal.` `def` `CountXORandSumEqual(x):` ` ` `# count number of zero bit in x` ` ` `count ` `=` `CountZeroBit(x)` ` ` `# power of 2 to count` ` ` `return` `(` `1` `<< count)` `# Driver code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` `x ` `=` `10` ` ` ` ` `# Function call` ` ` `print` `(CountXORandSumEqual(x))` `# This code is contributed by 29AjayKumar` |

## C#

`// C# program to count` `// numbers whose bitwise` `// XOR and sum with x` `// are equal` `using` `System;` `class` `GFG {` ` ` `// Function to find total` ` ` `// 0 bit in a number` ` ` `static` `int` `CountZeroBit(` `int` `x)` ` ` `{` ` ` `int` `count = 0;` ` ` `while` `(x > 0) {` ` ` `if` `((x & 1) == 0)` ` ` `count++;` ` ` `x >>= 1;` ` ` `}` ` ` `return` `count;` ` ` `}` ` ` `// Function to find Count` ` ` `// of non-negative numbers` ` ` `// less than or equal to x,` ` ` `// whose bitwise XOR and` ` ` `// SUM with x are equal.` ` ` `static` `int` `CountXORandSumEqual(` `int` `x)` ` ` `{` ` ` `// count number of` ` ` `// zero bit in x` ` ` `int` `count = CountZeroBit(x);` ` ` `// power of 2 to count` ` ` `return` `(1 << count);` ` ` `}` ` ` `// Driver code` ` ` `static` `public` `void` `Main()` ` ` `{` ` ` `int` `x = 10;` ` ` ` ` `// Function call` ` ` `Console.WriteLine(CountXORandSumEqual(x));` ` ` `}` `}` `// The code is contributed by ajit` |

## PHP

`<?php` `// PHP program to count numbers whose bitwise` `// XOR and sum with x are equal` `// Function to find total 0 bit in a number` `function` `CountZeroBit(` `$x` `)` `{` ` ` `$count` `= 0;` ` ` `while` `(` `$x` `)` ` ` `{` ` ` `if` `(!(` `$x` `& 1))` ` ` `$count` `++;` ` ` `$x` `>>= 1;` ` ` `}` ` ` `return` `$count` `;` `}` `// Function to find Count of` `// non-negative numbers less` `// than or equal to x, whose` `// bitwise XOR and SUM with` `// x are equal.` `function` `CountXORandSumEqual(` `$x` `)` `{` ` ` `// count number of zero bit in x` ` ` `$count` `= CountZeroBit(` `$x` `);` ` ` `// power of 2 to count` ` ` `return` `(1 << ` `$count` `);` `}` ` ` `// Driver code` ` ` `$x` `= 10;` ` ` `// Function call` ` ` `echo` `CountXORandSumEqual(` `$x` `);` `// This code is contributed by m_kit` `?>` |

## Javascript

`<script>` `// Javascript program to count` `// numbers whose bitwise` `// XOR and sum with x` `// are equal` `// Function to find total` `// 0 bit in a number` `function` `CountZeroBit(x)` `{` ` ` `let count = 0;` ` ` ` ` `while` `(x > 0)` ` ` `{` ` ` `if` `((x & 1) == 0)` ` ` `count++;` ` ` `x >>= 1;` ` ` `}` ` ` `return` `count;` `}` `// Function to find Count` `// of non-negative numbers` `// less than or equal to x,` `// whose bitwise XOR and` `// SUM with x are equal.` `function` `CountXORandSumEqual(x)` `{` ` ` ` ` `// count number of` ` ` `// zero bit in x` ` ` `let count = CountZeroBit(x);` ` ` `// power of 2 to count` ` ` `return` `(1 << count);` `}` `// Driver code` `let x = 10;` ` ` `// Function call` `document.write(CountXORandSumEqual(x));` `// This code is contributed by suresh07` `</script>` |

**Output**

4

**Time complexity: **O(Log x)

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