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# Number of special pairs possible from the given two numbers

• Last Updated : 23 Nov, 2022

Given two numbers A, B. The task is to find the numbers of special pairs of A, B. A special pair of two numbers A, B is a pair of numbers X, Y which satisfies both of the given conditions – A = X | Y, B = X & Y.

Examples:

```Input: A = 3, B = 0
Output: 2
(0, 3), (1, 2) will satisfy the conditions

Input:  A = 5, B = 7
Output: 0```

Approach: The key observation here is that if we want the OR of two numbers, X, Y to be equal to A. Then both X, Y has to be less than or equal to A. If anyone is greater A then there OR won’t be equal to A. This will give us the limits where our loop will terminate, rest we will try and check if two pairs meet the given condition, then we will increment the counter.
Below is the required implementation:

## C++

 `// C++ implementation of above approach``#include ``using` `namespace` `std;` `// Function to count the pairs``int` `countPairs(``int` `A, ``int` `B)``{` `    ``// Variable to store a number of special pairs``    ``int` `cnt = 0;` `    ``for` `(``int` `i = 0; i <= A; ++i) {``        ``for` `(``int` `j = i; j <= A; ++j) {``            ``// Calculating AND of i, j``            ``int` `AND = i & j;` `            ``// Calculating OR of i, j``            ``int` `OR = i | j;` `            ``// If the conditions are met,``            ``// then increment the count of special pairs``            ``if` `(OR == A and AND == B) {``                ``cnt++;``            ``}``        ``}``    ``}``    ``return` `cnt;``}` `// Driver code``int` `main()``{``    ``int` `A = 3, B = 0;``    ``cout << countPairs(A, B);` `    ``return` `0;``}`

## Java

 `// Java implementation of above approach``class` `GFG``{` `// Function to count the pairs``static` `int` `countPairs(``int` `A, ``int` `B)``{` `    ``// Variable to store a number``    ``// of special pairs``    ``int` `cnt = ``0``;` `    ``for` `(``int` `i = ``0``; i <= A; ++i)``    ``{``        ``for` `(``int` `j = i; j <= A; ++j)``        ``{``            ``// Calculating AND of i, j``            ``int` `AND = i & j;` `            ``// Calculating OR of i, j``            ``int` `OR = i | j;` `            ``// If the conditions are met,``            ``// then increment the count``            ``// of special pairs``            ``if` `(OR == A && AND == B)``            ``{``                ``cnt++;``            ``}``        ``}``    ``}``    ``return` `cnt;``}` `// Driver code``public` `static` `void` `main(String [] args)``{``    ``int` `A = ``3``, B = ``0``;``    ``System.out.println(countPairs(A, B));``}``}` `// This code is contributed by ihritik`

## Python3

 `# Python3 implementation of above``# approach` `# Function to count the pairs``def` `countPairs(A,B):` `    ``# Variable to store a number``    ``# of special pairs``    ``cnt``=``0``    ``for` `i ``in` `range``(``0``,A``+``1``):``        ``for` `j ``in` `range``(i,A``+``1``):` `            ``# Calculating AND of i, j``            ``AND ``=` `i&j``            ``OR ``=` `i|j` `            ``# If the conditions are met,``            ``# then increment the count of``            ``# special pairs``            ``if``(OR``=``=``A ``and` `AND``=``=``B):``                ``cnt ``+``=``1``    ``return` `cnt` `if` `__name__``=``=``'__main__'``:``    ``A ``=` `3``    ``B ``=` `0``    ``print``(countPairs(A,B))` `# This code is contributed by``# Shrikant13`

## C#

 `// C# implementation of above approach``using` `System;` `class` `GFG``{``    ` `// Function to count the pairs``static` `int` `countPairs(``int` `A, ``int` `B)``{` `    ``// Variable to store a number``    ``// of special pairs``    ``int` `cnt = 0;` `    ``for` `(``int` `i = 0; i <= A; ++i)``    ``{``        ``for` `(``int` `j = i; j <= A; ++j)``        ``{``            ``// Calculating AND of i, j``            ``int` `AND = i & j;` `            ``// Calculating OR of i, j``            ``int` `OR = i | j;` `            ``// If the conditions are met,``            ``// then increment the count``            ``// of special pairs``            ``if` `(OR == A && AND == B)``            ``{``                ``cnt++;``            ``}``        ``}``    ``}``    ``return` `cnt;``}` `// Driver code``public` `static` `void` `Main()``{``    ``int` `A = 3, B = 0;``    ``Console.WriteLine(countPairs(A, B));``}``}` `// This code is contributed by ihritik`

## PHP

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## Javascript

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Output

`2`

Time Complexity: O(A2)
Auxiliary Space: O(1)

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