# Count pairs from 1 to N such that their Sum is divisible by their XOR

• Last Updated : 04 Mar, 2021

Given a number , the task is to count pairs (x, y) such that their sum (x+y) is divisible by their xor value (x^y) and the condition 1 ≤ x < y < N holds true.
Examples

```Input: N = 3
Output: 3
Explanation:
(1, 2), (1, 3), (2, 3) are the valid pairs

Input: N = 6
Output: 11```

Approach:

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• After taking the array as input, first we need to find out all the possible pairs in that array.
• So, find out the pairs from the array
• Then for each pair, check whether the sum of the pair is divisible by the xor value of the pair. If it is, then increase the required count by one.
• When all the pairs have been checked, return or print the count of such pair.

Below is the implementation of the above approach:

## C++

 `// C++ program to count pairs from 1 to N``// such that their Sum is divisible by their XOR` `#include ``using` `namespace` `std;` `// Function to count pairs``int` `countPairs(``int` `n)``{``    ``// variable to store count``    ``int` `count = 0;` `    ``// Generate all possible pairs such that``    ``// 1 <= x < y < n``    ``for` `(``int` `x = 1; x < n; x++) {``        ``for` `(``int` `y = x + 1; y <= n; y++) {``            ``if` `((y + x) % (y ^ x) == 0)``                ``count++;``        ``}``    ``}` `    ``return` `count;``}` `// Driver code``int` `main()``{``    ``int` `n = 6;` `    ``cout << countPairs(n);` `    ``return` `0;``}`

## Java

 `// Java program to count pairs from 1 to N``// such that their Sum is divisible by their XOR``class` `GFG``{``    ` `    ``// Function to count pairs``    ``static` `int` `countPairs(``int` `n)``    ``{``        ``// variable to store count``        ``int` `count = ``0``;``    ` `        ``// Generate all possible pairs such that``        ``// 1 <= x < y < n``        ``for` `(``int` `x = ``1``; x < n; x++)``        ``{``            ``for` `(``int` `y = x + ``1``; y <= n; y++)``            ``{``                ``if` `((y + x) % (y ^ x) == ``0``)``                    ``count++;``            ``}``        ``}``        ``return` `count;``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `main (String[] args)``    ``{``        ``int` `n = ``6``;``        ``System.out.println(countPairs(n));``    ``}``}` `// This code is contributed by AnkitRai01`

## Python3

 `# Python3 program to count pairs from 1 to N``# such that their Sum is divisible by their XOR` `# Function to count pairs``def` `countPairs(n) :` `    ``# variable to store count``    ``count ``=` `0``;` `    ``# Generate all possible pairs such that``    ``# 1 <= x < y < n``    ``for` `x ``in` `range``(``1``, n) :``        ``for` `y ``in` `range``(x ``+` `1``, n ``+` `1``) :``            ``if` `((y ``+` `x) ``%` `(y ^ x) ``=``=` `0``) :``                ``count ``+``=` `1``;` `    ``return` `count;` `# Driver code``if` `__name__ ``=``=` `"__main__"` `:` `    ``n ``=` `6``;` `    ``print``(countPairs(n));` `# This code is contributed by AnkitRai01`

## C#

 `// C# program to count pairs from 1 to N``// such that their Sum is divisible by their XOR``using` `System;` `public` `class` `GFG``{``    ` `    ``// Function to count pairs``    ``static` `int` `countPairs(``int` `n)``    ``{``        ``// variable to store count``        ``int` `count = 0;``    ` `        ``// Generate all possible pairs such that``        ``// 1 <= x < y < n``        ``for` `(``int` `x = 1; x < n; x++)``        ``{``            ``for` `(``int` `y = x + 1; y <= n; y++)``            ``{``                ``if` `((y + x) % (y ^ x) == 0)``                    ``count++;``            ``}``        ``}``        ``return` `count;``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ``int` `n = 6;``        ``Console.WriteLine(countPairs(n));``    ``}``}` `// This code is contributed by AnkitRai01`

## Javascript

 ``
Output:
`11`

Time Complexity: O(N2)
Auxiliary Space: O(1)

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