# Distinct pairs from given arrays (a[i], b[j]) such that (a[i] + b[j]) is a Fibonacci number

• Last Updated : 12 May, 2021

Given two arrays a[] and b[], the task is to count the pairs (a[i], b[j]) such that (a[i] + b[j]) is a Fibonacci number.Note that (a, b) is equal to (b, a) and will be counted once.
First few Fibonacci numbers are:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 141, …..

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Examples:

Input: a[] = {99, 1, 33, 2}, b[] = {1, 11, 2}
Output:
Total distinct pairs are (1, 1), (1, 2), (33, 1) and (2, 11)
Input: a[] = {5, 0, 8}, b[] = {0, 9}
Output:

Approach:

• Take an empty set.
• Run two nested loops to generate all possible pairs from the two arrays taking one element from first array(call it a) and one from second array(call it b).
• Apply fibonacci test on (a + b) i.e. in order for a number x to be a Fibonacci number, any one of either 5 * x2 + 4 or 5 * x2 – 4 must be a perfect square.
• If it is Fibonacci number then push (a, b) in the set, if a < b or (b, a) if b < a. This is done to avoid duplicacy.
• The size of the set in the end is the total count of valid pairs.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function that returns true if``// x is a perfect square``bool` `isPerfectSquare(``long` `double` `x)``{``    ``// Find floating point value of``    ``// square root of x``    ``long` `double` `sr = ``sqrt``(x);` `    ``// If square root is an integer``    ``return` `((sr - ``floor``(sr)) == 0);``}` `// Function that returns true if``// n is a Fibonacci Number``bool` `isFibonacci(``int` `n)``{``    ``return` `isPerfectSquare(5 * n * n + 4)``           ``|| isPerfectSquare(5 * n * n - 4);``}` `// Function to return the count of distinct pairs``// from the given array such that the sum of the``// pair elements is a Fibonacci number``int` `totalPairs(``int` `a[], ``int` `b[], ``int` `n, ``int` `m)``{``    ``// Set is used to avoid duplicate pairs``    ``set > s;` `    ``for` `(``int` `i = 0; i < n; i++) {``        ``for` `(``int` `j = 0; j < m; j++) {` `            ``// If sum is a Fibonacci number``            ``if` `(isFibonacci(a[i] + b[j]) == ``true``) {``                ``if` `(a[i] < b[j])``                    ``s.insert(make_pair(a[i], b[j]));``                ``else``                    ``s.insert(make_pair(b[j], a[i]));``            ``}``        ``}``    ``}` `    ``// Return the size of the set``    ``return` `s.size();``}` `// Driver code``int` `main()``{``    ``int` `a[] = { 99, 1, 33, 2 };``    ``int` `b[] = { 1, 11, 2 };``    ``int` `n = ``sizeof``(a) / ``sizeof``(a[0]);``    ``int` `m = ``sizeof``(b) / ``sizeof``(b[0]);` `    ``cout << totalPairs(a, b, n, m);``    ``return` `0;``}`

## Java

 `// Java implementation of the approach``import` `java.util.*;` `class` `GFG``{``    ` `static` `class` `pair``{``    ``int` `first, second;``    ``public` `pair(``int` `first, ``int` `second)``    ``{``        ``this``.first = first;``        ``this``.second = second;``    ``}``}` `// Function that returns true if``// x is a perfect square``static` `boolean` `isPerfectSquare(``double` `x)``{``    ``// Find floating point value of``    ``// square root of x``    ``double` `sr = Math.sqrt(x);` `    ``// If square root is an integer``    ``return` `((sr - Math.floor(sr)) == ``0``);``}` `// Function that returns true if``// n is a Fibonacci Number``static` `boolean` `isFibonacci(``int` `n)``{``    ``return` `isPerfectSquare(``5` `* n * n + ``4``) ||``           ``isPerfectSquare(``5` `* n * n - ``4``);``}` `// Function to return the count of distinct pairs``// from the given array such that the sum of the``// pair elements is a Fibonacci number``static` `int` `totalPairs(``int` `a[], ``int` `b[],``                      ``int` `n, ``int` `m)``{``    ``// Set is used to avoid duplicate pairs``    ``List s = ``new` `LinkedList<>();` `    ``for` `(``int` `i = ``0``; i < n; i++)``    ``{``        ``for` `(``int` `j = ``0``; j < m; j++)``        ``{` `            ``// If sum is a Fibonacci number``            ``if` `(isFibonacci(a[i] + b[j]) == ``true``)``            ``{``                ` `                ``if` `(a[i] < b[j])``                ``{``                    ``if``(checkDuplicate(s, ``new` `pair(a[i], b[j])))``                        ``s.add(``new` `pair(a[i], b[j]));``                ``}``                ``else``                ``{``                    ``if``(checkDuplicate(s, ``new` `pair(b[j], a[i])))``                        ``s.add(``new` `pair(b[j], a[i]));``                ``}``            ``}``        ``}``    ``}` `    ``// Return the size of the set``    ``return` `s.size();``}` `static` `boolean` `checkDuplicate(List pairList,``                                    ``pair newPair)``{``    ``for``(pair p: pairList)``    ``{``        ``if``(p.first == newPair.first &&``           ``p.second == newPair.second)``            ``return` `false``;``    ``}``    ``return` `true``;``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``int` `a[] = { ``99``, ``1``, ``33``, ``2` `};``    ``int` `b[] = { ``1``, ``11``, ``2` `};``    ``int` `n = a.length;``    ``int` `m = b.length;` `    ``System.out.println(totalPairs(a, b, n, m));``}``}` `// This code is contributed by Rajput-Ji`

## Python3

 `# Python3 implementation of the approach``from` `math ``import` `sqrt,floor` `# Function that returns true if``# x is a perfect square``def` `isPerfectSquare(x) :` `    ``# Find floating point value of``    ``# square root of x``    ``sr ``=` `sqrt(x)` `    ``# If square root is an integer``    ``return` `((sr ``-` `floor(sr)) ``=``=` `0``)` `# Function that returns true if``# n is a Fibonacci Number``def` `isFibonacci(n ) :` `    ``return` `(isPerfectSquare(``5` `*` `n ``*` `n ``+` `4``) ``or``            ``isPerfectSquare(``5` `*` `n ``*` `n ``-` `4``))` `# Function to return the count of distinct pairs``# from the given array such that the sum of the``# pair elements is a Fibonacci number``def` `totalPairs(a, b, n, m) :` `    ``# Set is used to avoid duplicate pairs``    ``s ``=` `set``();` `    ``for` `i ``in` `range``(n) :``        ``for` `j ``in` `range``(m) :` `            ``# If sum is a Fibonacci number``            ``if` `(isFibonacci(a[i] ``+` `b[j]) ``=``=` `True``) :``                ``if` `(a[i] < b[j]) :``                    ``s.add((a[i], b[j]));``                ``else` `:``                    ``s.add((b[j], a[i]));` `    ``# Return the size of the set``    ``return` `len``(s);` `# Driver code``if` `__name__ ``=``=` `"__main__"` `:``    ` `    ``a ``=` `[ ``99``, ``1``, ``33``, ``2` `];``    ``b ``=` `[ ``1``, ``11``, ``2` `];``    ``n ``=` `len``(a);``    ``m ``=` `len``(b);` `    ``print``(totalPairs(a, b, n, m));` `# This code is contributed by Ryuga`

## C#

 `// C# implementation of the approach``using` `System;``using` `System.Collections.Generic;            ` `class` `GFG``{``public` `class` `pair``{``    ``public` `int` `first, second;``    ``public` `pair(``int` `first, ``int` `second)``    ``{``        ``this``.first = first;``        ``this``.second = second;``    ``}``}` `// Function that returns true if``// x is a perfect square``static` `bool` `isPerfectSquare(``double` `x)``{``    ``// Find floating point value of``    ``// square root of x``    ``double` `sr = Math.Sqrt(x);` `    ``// If square root is an integer``    ``return` `((sr - Math.Floor(sr)) == 0);``}` `// Function that returns true if``// n is a Fibonacci Number``static` `bool` `isFibonacci(``int` `n)``{``    ``return` `isPerfectSquare(5 * n * n + 4) ||``           ``isPerfectSquare(5 * n * n - 4);``}` `// Function to return the count of distinct pairs``// from the given array such that the sum of the``// pair elements is a Fibonacci number``static` `int` `totalPairs(``int` `[]a, ``int` `[]b,``                      ``int` `n, ``int` `m)``{``    ``// Set is used to avoid duplicate pairs``    ``List s = ``new` `List();` `    ``for` `(``int` `i = 0; i < n; i++)``    ``{``        ``for` `(``int` `j = 0; j < m; j++)``        ``{` `            ``// If sum is a Fibonacci number``            ``if` `(isFibonacci(a[i] + b[j]) == ``true``)``            ``{``                ` `                ``if` `(a[i] < b[j])``                ``{``                    ``if``(checkDuplicate(s, ``new` `pair(a[i], b[j])))``                                   ``s.Add(``new` `pair(a[i], b[j]));``                ``}``                ``else``                ``{``                    ``if``(checkDuplicate(s, ``new` `pair(b[j], a[i])))``                                   ``s.Add(``new` `pair(b[j], a[i]));``                ``}``            ``}``        ``}``    ``}` `    ``// Return the size of the set``    ``return` `s.Count;``}` `static` `bool` `checkDuplicate(List pairList,``                                      ``pair newPair)``{``    ``foreach``(pair p ``in` `pairList)``    ``{``        ``if``(p.first == newPair.first &&``           ``p.second == newPair.second)``            ``return` `false``;``    ``}``    ``return` `true``;``}` `// Driver code``public` `static` `void` `Main(String[] args)``{``    ``int` `[]a = { 99, 1, 33, 2 };``    ``int` `[]b = { 1, 11, 2 };``    ``int` `n = a.Length;``    ``int` `m = b.Length;` `    ``Console.WriteLine(totalPairs(a, b, n, m));``}``}` `// This code is contributed by Rajput-Ji`

## Javascript

 ``
Output:
`4`

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