# GCD of elements occurring Fibonacci number of times in an Array

• Difficulty Level : Easy
• Last Updated : 16 Aug, 2022

Given an array arr[] containing N elements, the task is to find the GCD of the elements which have frequency count which is a Fibonacci number in the array.
Examples:

Input: arr[] = { 5, 3, 6, 5, 6, 6, 5, 5 }
Output:
Explanation :
Elements 5, 3, 6 appears 4, 1, 3 times respectively.
Hence, 3 and 6 have Fibonacci frequencies.
So, gcd(3, 6) = 1
Input: arr[] = {4, 2, 3, 3, 3, 3}
Output:
Explanation :
Elements 4, 2, 3 appears 1, 1, 4 times respectively.
Hence, 4 and 2 have Fibonacci frequencies.
So, gcd(4, 2) = 2

Approach: The idea is to use hashing to precompute and store the Fibonacci nodes up to the maximum value to make checking easy and efficient (in O(1) time).
After precomputing the hash

1. traverse the array and store the frequencies of all the elements in a map.
2. Using the map and hash, calculate the gcd of elements having fibonacci frequency using the precomputed hash.

Below is the implementation of the above approach:

## C++

 `// C++ program to find the GCD of``// elements which occur Fibonacci``// number of times` `#include ``using` `namespace` `std;` `// Function to create hash table``// to check Fibonacci numbers``void` `createHash(set<``int``>& hash,``                ``int` `maxElement)``{``    ``// Inserting the first two``    ``// numbers into the hash``    ``int` `prev = 0, curr = 1;``    ``hash.insert(prev);``    ``hash.insert(curr);` `    ``// Adding the remaining Fibonacci``    ``// numbers using the previously``    ``// added elements``    ``while` `(curr <= maxElement) {``        ``int` `temp = curr + prev;``        ``hash.insert(temp);``        ``prev = curr;``        ``curr = temp;``    ``}``}` `// Function to return the GCD of elements``// in an array having fibonacci frequency``int` `gcdFibonacciFreq(``int` `arr[], ``int` `n)``{``    ``set<``int``> hash;` `    ``// Creating the hash``    ``createHash(hash,``               ``*max_element(arr,``                            ``arr + n));` `    ``int` `i, j;` `    ``// Map is used to store the``    ``// frequencies of the elements``    ``unordered_map<``int``, ``int``> m;` `    ``// Iterating through the array``    ``for` `(i = 0; i < n; i++)``        ``m[arr[i]]++;` `    ``int` `gcd = 0;` `    ``// Traverse the map using iterators``    ``for` `(``auto` `it = m.begin();``         ``it != m.end(); it++) {` `        ``// Calculate the gcd of elements``        ``// having fibonacci frequencies``        ``if` `(hash.find(it->second)``            ``!= hash.end()) {``            ``gcd = __gcd(gcd,``                        ``it->first);``        ``}``    ``}` `    ``return` `gcd;``}` `// Driver code``int` `main()``{``    ``int` `arr[] = { 5, 3, 6, 5,``                  ``6, 6, 5, 5 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);` `    ``cout << gcdFibonacciFreq(arr, n);` `    ``return` `0;``}`

## Java

 `// Java program to find the GCD of``// elements which occur Fibonacci``// number of times``import` `java.util.*;` `class` `GFG{`` ` `// Function to create hash table``// to check Fibonacci numbers``static` `void` `createHash(HashSet hash,``                ``int` `maxElement)``{``    ``// Inserting the first two``    ``// numbers into the hash``    ``int` `prev = ``0``, curr = ``1``;``    ``hash.add(prev);``    ``hash.add(curr);`` ` `    ``// Adding the remaining Fibonacci``    ``// numbers using the previously``    ``// added elements``    ``while` `(curr <= maxElement) {``        ``int` `temp = curr + prev;``        ``hash.add(temp);``        ``prev = curr;``        ``curr = temp;``    ``}``}`` ` `// Function to return the GCD of elements``// in an array having fibonacci frequency``static` `int` `gcdFibonacciFreq(``int` `arr[], ``int` `n)``{``    ``HashSet hash = ``new` `HashSet();`` ` `    ``// Creating the hash``    ``createHash(hash,Arrays.stream(arr).max().getAsInt());`` ` `    ``int` `i;`` ` `    ``// Map is used to store the``    ``// frequencies of the elements``    ``HashMap m = ``new` `HashMap();`` ` `    ``// Iterating through the array``    ``for` `(i = ``0``; i < n; i++) {``        ``if``(m.containsKey(arr[i])){``            ``m.put(arr[i], m.get(arr[i])+``1``);``        ``}``        ``else``{``            ``m.put(arr[i], ``1``);``        ``}``    ``}`` ` `    ``int` `gcd = ``0``;`` ` `    ``// Traverse the map using iterators``    ``for` `(Map.Entry it : m.entrySet()) {`` ` `        ``// Calculate the gcd of elements``        ``// having fibonacci frequencies``        ``if` `(hash.contains(it.getValue())) {``            ``gcd = __gcd(gcd,``                        ``it.getKey());``        ``}``    ``}`` ` `    ``return` `gcd;``}``static` `int` `__gcd(``int` `a, ``int` `b) ``{ ``    ``return` `b == ``0``? a:__gcd(b, a % b);    ``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``int` `arr[] = { ``5``, ``3``, ``6``, ``5``,``                  ``6``, ``6``, ``5``, ``5` `};``    ``int` `n = arr.length;`` ` `    ``System.out.print(gcdFibonacciFreq(arr, n));``}``}` `// This code is contributed by Princi Singh`

## Python3

 `# Python 3 program to find the GCD of``# elements which occur Fibonacci``# number of times``from` `collections ``import` `defaultdict``import` `math`` ` `# Function to create hash table``# to check Fibonacci numbers``def` `createHash(hash1,maxElement):` `    ``# Inserting the first two``    ``# numbers into the hash``    ``prev , curr ``=` `0``, ``1``    ``hash1.add(prev)``    ``hash1.add(curr)`` ` `    ``# Adding the remaining Fibonacci``    ``# numbers using the previously``    ``# added elements``    ``while` `(curr <``=` `maxElement):``        ``temp ``=` `curr ``+` `prev``        ``if` `temp <``=` `maxElement:``            ``hash1.add(temp)``        ``prev ``=` `curr``        ``curr ``=` `temp`` ` `# Function to return the GCD of elements``# in an array having fibonacci frequency``def` `gcdFibonacciFreq(arr, n):` `    ``hash1 ``=` `set``()`` ` `    ``# Creating the hash``    ``createHash(hash1,``max``(arr))`` ` `    ``# Map is used to store the``    ``# frequencies of the elements``    ``m ``=` `defaultdict(``int``)`` ` `    ``# Iterating through the array``    ``for` `i ``in` `range``(n):``        ``m[arr[i]] ``+``=` `1`` ` `    ``gcd ``=` `0`` ` `    ``# Traverse the map using iterators``    ``for` `it ``in` `m.keys():`` ` `        ``# Calculate the gcd of elements``        ``# having fibonacci frequencies``        ``if` `(m[it] ``in` `hash1):``            ``gcd ``=` `math.gcd(gcd,it)``    ``return` `gcd`` ` `# Driver code``if` `__name__ ``=``=` `"__main__"``:``    ` `    ``arr ``=` `[ ``5``, ``3``, ``6``, ``5``,``                  ``6``, ``6``, ``5``, ``5` `]``    ``n ``=` `len``(arr)`` ` `    ``print``(gcdFibonacciFreq(arr, n))`` ` ` ``# This code is contributed by chitranayal`

## C#

 `// C# program to find the GCD of``// elements which occur Fibonacci``// number of times``using` `System;``using` `System.Linq;``using` `System.Collections.Generic;` `class` `GFG{``  ` `// Function to create hash table``// to check Fibonacci numbers``static` `void` `createHash(HashSet<``int``> hash,``                ``int` `maxElement)``{``    ``// Inserting the first two``    ``// numbers into the hash``    ``int` `prev = 0, curr = 1;``    ``hash.Add(prev);``    ``hash.Add(curr);``  ` `    ``// Adding the remaining Fibonacci``    ``// numbers using the previously``    ``// added elements``    ``while` `(curr <= maxElement) {``        ``int` `temp = curr + prev;``        ``hash.Add(temp);``        ``prev = curr;``        ``curr = temp;``    ``}``}``  ` `// Function to return the GCD of elements``// in an array having fibonacci frequency``static` `int` `gcdFibonacciFreq(``int` `[]arr, ``int` `n)``{``    ``HashSet<``int``> hash = ``new` `HashSet<``int``>();``  ` `    ``// Creating the hash``    ``createHash(hash, hash.Count > 0 ? hash.Max():0);``  ` `    ``int` `i;``  ` `    ``// Map is used to store the``    ``// frequencies of the elements``    ``Dictionary<``int``,``int``> m = ``new` `Dictionary<``int``,``int``>();``  ` `    ``// Iterating through the array``    ``for` `(i = 0; i < n; i++) {``        ``if``(m.ContainsKey(arr[i])){``            ``m[arr[i]] = m[arr[i]] + 1;``        ``}``        ``else``{``            ``m.Add(arr[i], 1);``        ``}``    ``}``  ` `    ``int` `gcd = 0;``  ` `    ``// Traverse the map using iterators``    ``foreach``(KeyValuePair<``int``, ``int``> it ``in` `m) {``  ` `        ``// Calculate the gcd of elements``        ``// having fibonacci frequencies``        ``if` `(hash.Contains(it.Value)) {``            ``gcd = __gcd(gcd,``                        ``it.Key);``        ``}``    ``}``  ` `    ``return` `gcd;``}``static` `int` `__gcd(``int` `a, ``int` `b) ``{ ``    ``return` `b == 0? a:__gcd(b, a % b);    ``}`` ` `// Driver code``public` `static` `void` `Main(String[] args)``{``    ``int` `[]arr = { 5, 3, 6, 5,``                  ``6, 6, 5, 5 };``    ``int` `n = arr.Length;``  ` `    ``Console.Write(gcdFibonacciFreq(arr, n));``}``}` `// This code is contributed by 29AjayKumar`

## Javascript

 ``

Output:

`3`

Time Complexity: O(N)

Auxiliary Space: O(N), since n extra space has been taken.

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